Theme 3 – Nature of Waves · PDF fileFrequency and Periodic Time are related by a simple formula: f = 1 T ... Since the sounds are travelling at about the same ... Unit 1 – Theme
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Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
1
Theme 3 ndash Nature of Waves
All Waves transfer energy from one place to another They do
this by vibrating something up and down or back and forth
Two different types of waves
There are two types of wave motion transverse and
longitudinal
Transverse Waves
In this kind of wave the direction of wave motion is at 90deg to
the direction of travel Most waves are transverse Here is a
list of transverse waves
all electromagnetic waves
ie radio micro infra red light ultra violet X-rays and
gamma waves
water waves - ripples on the surface of a sea or lake
waves along a rope
Describing waves
An oscillation is a complete to-and-fro movement One
complete cycle
Amplitude Amplitude is the maximum displacement of a
wave from the rest position
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
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Periodic Time This is the time taken to perform one
oscillation
Wavelength wavelength is the distance between two crests
(or troughs) or the distance of one cycle Wavelength is given
the symbol (Greek lambda pronounced lam-der)
and is measured in metres because it is a distance
Frequency This is the number of oscillations in one second
Measured in hertz (Hz)
1 kilohertz = 1 kHz = 1000 Hz 1 megahertz = 1 MHz = 1000000 Hz
1 gigahertz = 1 GHz = 1000000000 Hz
-distance
Longitudinal Waves
In this kind of wave the direction of wave motion is at 180deg
parallel to the direction of travel The oscillations are in the
same direction as the wave All longitudinal waves are
mechanical waves They need a material to travel in they
cannot travel in a vacuum
Examples of longitudinal waves are
Sound ultrasound and earthquake P-waves
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3
The features of a longitudinal wave are
Compression - area of high pressure
Rarefaction - area of low pressure
Wavelength - distance between two compressions or two
rarefactions
Frequency and Periodic Time are related by a simple formula
f = 1
T
The Wave Equation
All waves whether longitudinal or transverse obey the wave
equation
Wave speed (ms) = frequency (Hz) times wavelength (m)
In Physics code
Here are a few wave speeds
Electromagnetic waves in a vacuum - 3 times 108 ms
Electromagnetic waves in glass - 2 times 108 ms
Sound in steel - 6000 ms
Sound in water - 1500 ms Sound in air - 340 ms
Speed Frequency amp Wavelength
The frequency of waves is set at the source itself For instance if John pokes a pond with a stick twice each second
the frequency will be 2 Hz
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4
As the waves travel over the ponds surface this frequency
will not change What may change is the distance between
waves - the wavelength - and their speed
Water waves
Progressive Waves - Waves that travel or propagate from a
source are called progressive waves An obvious example is
the ripples on a pond when you throw a stone into the water
Both longitudinal and transverse waves can travel through
water
Longitudinal waves travel through water underneath the surface This is under water sound and can be used by
sea creatures to communicate (whales dolphins etc)
and by boats for echo location
Transverse waves travel on the water
surface and these are the waves which
we see as they make the surface go up
and down Transverse water waves are
shown as a series of parallel lines
These lines represent the peaks of the
wave as you are looking down on it
from above
Reflection Refraction and Diffraction
The wavelength is the distance between two peaks or the
distance between two troughs
Water waves are reflected from hard flat surfaces as shown
below
After reflection a wave has
the same speed frequency and wavelength it is only
the direction of the wave
that has changed
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
5
Water waves travel faster on the surface of deep water than
they do on shallow water The change in speed of the wave will
cause refraction
The slower wave in the shallow water has a smaller
wavelength The amount of refraction increases as the change
in speed increases
Waves Diffraction
Diffraction occurs when the wavelength of a wave
is of a similar size to an obstacle or a gap in a barrier
After diffraction a wave will have the same speed frequency
and wavelength
Electromagnetic waves have a huge range of wavelengths
Radio waves can diffract around hills mountains or even the
whole planet Light waves can diffract through tiny slits
X-rays can diffract around atoms
Water waves can diffract when passing through a gap in a
harbour wall
The wavelength of water waves
may be several metres
If the wavelength is of a similar
size to a gap in a harbour wall
then the wave will diffract as
shown below
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
6
If the wavelength does not match
the size of the gap
then only a little diffraction will
occur at the edge of the wave The part of the wave which hits the wall
in the above two pictures is
reflected straight back on itself
Sound
Sound is always produced by
something vibrating The
vibrations will make matter -
either solid liquid or gas - near it vibrate In this way energy is
taken away from the source of the
vibrations The amplitude of the
wave determines the volume of a
sound
We call these vibrations sound Our ears pick them up and tell
our brain what we can hear The vibrations are longitudinal
Bell Jar Experiment
With the bell ringing continuously inside it can be easily heard outside of the jar Once a
vacuum pump is turned on the air is slowly
removed As this happens the sound gets
quieter until eventually it cannot be heard at
all
Inside the bell jar the bell can still be seen to
ring If the rubber bands hanging it are good
enough few vibrations will pass up them to the glass (to be
heard) Letting the air back in allows the sound to be heard
again
Sounds cannot travel through a vacuum
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
7
Speed Of Sound
Sound waves are vibrations which cannot travel through
a vacuum - the total absence of matter The more matter
there is and the closer atoms are together the easier it is for
sound can travel
In air which is a mixture of gases the speed of sound is
around 340 ms depending on air temperature For water the
molecules are much closer together so vibrations pass much
more quickly between them As a result sound can travel at
around 1500 ms In solids where atoms are really close
together and very tightly attached to each other the speed of
sound is even higher - typically 5000 ms
Ultasound
This consist of sound that is above the range of human
hearing It even travels at exactly the same speed as sound in
any medium Humans can hear sound within the frequency
range of about 20 to 20000 Hz so any sound above 20 kHz is
ultrasound Uses ndash
1 Unborn babies can be photographed to check its size - and
even if there is more than one Its use in scanning goes far
beyond pregnancies Many other parts of the body are
analysed using it (bladder gallstones the heart etc) but it
doesnt even stop there Aeroplane wings can be checked for cracks that would be invisible on the surface
2 Ultrasound Treatments to clean things In fact really dirty
teeth can be cleaned superbly in this way Really delicate
mechanisms - such as in antique clocks and watches - can
also be safely cleaned
3 Ships use in Ultrasound and SONAR to detect fish sea
bottom
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
8
A ship sends a pulse of ultrasound
and receives an echo 0middot3 seconds
later If the speed of sound in water
is 1500 ms calculate its depth
speed = distance time
distance = speed times time
distance = 1500 times 0middot3 = 450 m
BUT this is the total distance travelled by the sound - so the
depth is half of this
Depth = 450 2 = 225 m
4 Used by animals to communicate ndash BatsDolphins
Any sound that you hear as a tone is made of regular evenly spaced waves of air molecules The most noticeable difference
between various tonal sounds is that some sound higher or
lower than others These differences in the pitch of the sound
are caused by different spacing in the waves that is different
frequency
Since the sounds are travelling at about the same speed the
one with the shorter wavelength will go by more frequently it
has a higher frequency or pitch In other words it sounds
higher
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9
The amplitude of the wave determines the loudness of the
sound
The amplitude of sound waves is
measured in decibels Leaves
rustling in the wind are about 10
decibels a jet engine is about 120
decibels
Amplitude is Loudness
THEME 3 - OPTICS
The only special thing about light is that our eyes can detect it
However it is just a tiny part of a collection of electromagnetic
waves that make up the electromagnetic spectrum
The objects which we see can be placed into one of two
categories luminous objects and non luminous objects
Luminous objects are objects which generate their own light
Eg sun electric bulb
Non Luminous objects are objects which are capable of
reflecting light to our eyes Eg moon grass sky
Without light there would be no sight
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
10
Light is a transverse wave It is one part (region) of the
electromagnetic spectrum Light is the visible region it is
the part used by our eyes to see Like any electromagnetic
wave light can travel through a vacuum Light travels through
the vacuum of space from the Sun to the Earth
Light travels very quickly There is nothing which can travel
faster The speed of light is 300000000 ms
(that is 300 million metres per second - not easy to imagine)
Reflection - ( Bouncing of light)
Any type of wave can be reflected Reflection best occurs from
flat hard surfaces After reflection a wave has the same
speed frequency and wavelength it is only the direction of the
wave that has changed
For light (and other electromagnetic radiation) a flat shiny
surface like a plane mirror is a good reflector
A plane mirror is one
which is straight and not
curved
The light ray which hits
the mirror is called the
incident ray The light ray which
bounces off the mirror is
called the reflected ray The angle of incidence equals the
angle of reflection i = r This means that whatever angle the light ray hits the mirror it will be reflected off at the same
angle
If the surface of the mirror is not smooth but rough or bumpy
then light will be reflected at many different angles The image
in the mirror will be blurred and unclear This is called diffuse
reflection When you look into a mirror you see a reflection
which is an image of the real object
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11
The image appears to be the
same distance behind the
mirror as the real object is in front of it
This is because the brain
thinks that light travels in
straight lines without changing
direction
The image is called virtual
because it does not really
exist behind the mirror The
virtual image is the same size as the object but with left and
right reversed ( laterally inverted)
Refraction ( bending of light)
Any type of wave can be refracted which means a change of
direction Refraction can occur when the speed of a wave
changes as it moves from one medium to another
After refraction the wave has the same frequency
but a different speed wavelength and direction
When a wave enters a new medium its change in speed will
also change its wavelength If the wave enters the new
medium at any angle other than normal to the boundary then
the change in the waves speed will also change its direction
A material is transparent if you can see through it If you can
see through it it means that light can travel through it
Transparent materials include air glass Perspex and water
Light travels at different speeds in different materials because
they have different densities The higher the density the
slower light travels Light travels fastest in space (a vacuum)
and a little slower in air Light moves noticeably more slowly in
glass than in air because glass is obviously more dense
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
12
A line drawn at right
angles to the
boundary between the
two media (air and
glass) is called a
normal
Light which enters a glass block along a normal (at 90 degrees) does not change direction but it does travel more slowly
through the glass When a ray of light enters a glass block at
an angle other than the normal it changes speed wavelength
and direction as shown below
Conditions of Refraction
The angle i is called the angle of incidence while
angle r is called angle of
refraction The light must
change speed when
crossing the boundary
In going from a less dense medium (air) to a more dense
medium (glass) light bends towards the normalThis means
that i gt r (the angle i is greater than the angle r)
In going from a more dense to a less dense medium (glass to
air) light bends away from the normal How much the light
bends depends on its colour
The change in angle of the light ray is the same when it enters
and leaves the glass If the incident ray had continued without
changing direction then the emergent ray would be parallel to
it Like any wave the speed of a light wave is dependent
upon the properties of the medium
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
13
Refractive Index - n
Index of refraction values (represented by the symbol n) are
numerical index values which are expressed relative to the
speed of light in a vacuum The index of refraction value of a
material is a number which indicates the number of times
slower that a light wave would be in that material than it is in a
vacuum
ή = Speed of light in air
Speed of light in medium
Material Index of Refraction
Vacuum 100
Water 133
Glass 150
Diamond 240
The index of refraction values thus provide a measure of the
relative speed of a light wave in a particular medium
Real and Apparent Depth
To an observer standing at
the side of a swimming pool
objects under the water
appear to be nearer the
surface than they really are
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
14
A fish appears to be nearer to
the surface than it really is
A straight stick appears to be
bent when part in and part
out of water
Both these effects are caused by
refraction of light at the surface of the water Therefore this
effect is related to the refractive
index of the media involved
The real depth of the fish is R and its apparent depth is A It is
clear that n represents the refractive index of light going from
air to water we have
Refractive index n = Real Depth Apparent depth
When light emerges from glass or water into air it speeds up
again As it meets the glass-air boundary at any angle greater than 0o it will refract away from the normal If you look at a
stick that is poking into some water at an angle the stick looks
bent because of refraction The bottom of the stick seems to be
nearer the surface of the water than it really is It also explains
why flat-based swimming pools appear to get shallower as you
look towards the end furthest from you
Total Internal Reflection - Critical Angle
When a light ray emerges from glass into air it is refracted and bends away from the normal so i lt r As i is made bigger the
refracted ray gets closer and closer to the surface of the glass
When the refracted ray is just touching the glass surface that is angle r = 90 degrees than angle i is called the critical
angle
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
15
The critical angle is different for different materials for glass it is about 42 degrees Total internal reflection happens when i is
bigger than the critical angleWhen a light ray tries to move
from glass to air at an angle greater than the critical angle the
refracted ray cannot escape from the glass and total internal
reflection occurs
Refraction cannot happen and all
of the light is reflected
at the glass air boundary as if it
had hit a mirror i = r
It is called internal reflection
because it occurs inside the glass
and total because all the light must
be reflected
Total Internal Reflection (TIR) can occur in prisms and optical
fibres
Total Internal Reflection - Prisms
A right angle prism can be used to
change the direction of a light ray by
90 degrees or 180 degrees
The light ray enters along a normal
and continues straight on until it hits
the back face of the prism Total
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
16
internal reflection occurs here because light strikes the surface
at 45 degrees which is greater than the critical angle
The light ray then emerges from the
prism along a normal and so continues
straight through This type of prism
can be used in a periscope Two right
angle prisms can be used to form a periscope as shown below Total
internal reflection occurs at the back
face of the prisms
A periscope may be used by people
(i) in a submarine to see above the
sea surface
(ii) to see over the heads of people in a crowd
A right angle prism can be used to change
the direction of light by 180
degrees as shown below
The same effect can result from two prisms arranged as shown
belowEither of these arrangements may be used in
binoculars or reflectors on the rear of cars and bicycles
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
2
Periodic Time This is the time taken to perform one
oscillation
Wavelength wavelength is the distance between two crests
(or troughs) or the distance of one cycle Wavelength is given
the symbol (Greek lambda pronounced lam-der)
and is measured in metres because it is a distance
Frequency This is the number of oscillations in one second
Measured in hertz (Hz)
1 kilohertz = 1 kHz = 1000 Hz 1 megahertz = 1 MHz = 1000000 Hz
1 gigahertz = 1 GHz = 1000000000 Hz
-distance
Longitudinal Waves
In this kind of wave the direction of wave motion is at 180deg
parallel to the direction of travel The oscillations are in the
same direction as the wave All longitudinal waves are
mechanical waves They need a material to travel in they
cannot travel in a vacuum
Examples of longitudinal waves are
Sound ultrasound and earthquake P-waves
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
3
The features of a longitudinal wave are
Compression - area of high pressure
Rarefaction - area of low pressure
Wavelength - distance between two compressions or two
rarefactions
Frequency and Periodic Time are related by a simple formula
f = 1
T
The Wave Equation
All waves whether longitudinal or transverse obey the wave
equation
Wave speed (ms) = frequency (Hz) times wavelength (m)
In Physics code
Here are a few wave speeds
Electromagnetic waves in a vacuum - 3 times 108 ms
Electromagnetic waves in glass - 2 times 108 ms
Sound in steel - 6000 ms
Sound in water - 1500 ms Sound in air - 340 ms
Speed Frequency amp Wavelength
The frequency of waves is set at the source itself For instance if John pokes a pond with a stick twice each second
the frequency will be 2 Hz
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
4
As the waves travel over the ponds surface this frequency
will not change What may change is the distance between
waves - the wavelength - and their speed
Water waves
Progressive Waves - Waves that travel or propagate from a
source are called progressive waves An obvious example is
the ripples on a pond when you throw a stone into the water
Both longitudinal and transverse waves can travel through
water
Longitudinal waves travel through water underneath the surface This is under water sound and can be used by
sea creatures to communicate (whales dolphins etc)
and by boats for echo location
Transverse waves travel on the water
surface and these are the waves which
we see as they make the surface go up
and down Transverse water waves are
shown as a series of parallel lines
These lines represent the peaks of the
wave as you are looking down on it
from above
Reflection Refraction and Diffraction
The wavelength is the distance between two peaks or the
distance between two troughs
Water waves are reflected from hard flat surfaces as shown
below
After reflection a wave has
the same speed frequency and wavelength it is only
the direction of the wave
that has changed
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
5
Water waves travel faster on the surface of deep water than
they do on shallow water The change in speed of the wave will
cause refraction
The slower wave in the shallow water has a smaller
wavelength The amount of refraction increases as the change
in speed increases
Waves Diffraction
Diffraction occurs when the wavelength of a wave
is of a similar size to an obstacle or a gap in a barrier
After diffraction a wave will have the same speed frequency
and wavelength
Electromagnetic waves have a huge range of wavelengths
Radio waves can diffract around hills mountains or even the
whole planet Light waves can diffract through tiny slits
X-rays can diffract around atoms
Water waves can diffract when passing through a gap in a
harbour wall
The wavelength of water waves
may be several metres
If the wavelength is of a similar
size to a gap in a harbour wall
then the wave will diffract as
shown below
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
6
If the wavelength does not match
the size of the gap
then only a little diffraction will
occur at the edge of the wave The part of the wave which hits the wall
in the above two pictures is
reflected straight back on itself
Sound
Sound is always produced by
something vibrating The
vibrations will make matter -
either solid liquid or gas - near it vibrate In this way energy is
taken away from the source of the
vibrations The amplitude of the
wave determines the volume of a
sound
We call these vibrations sound Our ears pick them up and tell
our brain what we can hear The vibrations are longitudinal
Bell Jar Experiment
With the bell ringing continuously inside it can be easily heard outside of the jar Once a
vacuum pump is turned on the air is slowly
removed As this happens the sound gets
quieter until eventually it cannot be heard at
all
Inside the bell jar the bell can still be seen to
ring If the rubber bands hanging it are good
enough few vibrations will pass up them to the glass (to be
heard) Letting the air back in allows the sound to be heard
again
Sounds cannot travel through a vacuum
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
7
Speed Of Sound
Sound waves are vibrations which cannot travel through
a vacuum - the total absence of matter The more matter
there is and the closer atoms are together the easier it is for
sound can travel
In air which is a mixture of gases the speed of sound is
around 340 ms depending on air temperature For water the
molecules are much closer together so vibrations pass much
more quickly between them As a result sound can travel at
around 1500 ms In solids where atoms are really close
together and very tightly attached to each other the speed of
sound is even higher - typically 5000 ms
Ultasound
This consist of sound that is above the range of human
hearing It even travels at exactly the same speed as sound in
any medium Humans can hear sound within the frequency
range of about 20 to 20000 Hz so any sound above 20 kHz is
ultrasound Uses ndash
1 Unborn babies can be photographed to check its size - and
even if there is more than one Its use in scanning goes far
beyond pregnancies Many other parts of the body are
analysed using it (bladder gallstones the heart etc) but it
doesnt even stop there Aeroplane wings can be checked for cracks that would be invisible on the surface
2 Ultrasound Treatments to clean things In fact really dirty
teeth can be cleaned superbly in this way Really delicate
mechanisms - such as in antique clocks and watches - can
also be safely cleaned
3 Ships use in Ultrasound and SONAR to detect fish sea
bottom
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
8
A ship sends a pulse of ultrasound
and receives an echo 0middot3 seconds
later If the speed of sound in water
is 1500 ms calculate its depth
speed = distance time
distance = speed times time
distance = 1500 times 0middot3 = 450 m
BUT this is the total distance travelled by the sound - so the
depth is half of this
Depth = 450 2 = 225 m
4 Used by animals to communicate ndash BatsDolphins
Any sound that you hear as a tone is made of regular evenly spaced waves of air molecules The most noticeable difference
between various tonal sounds is that some sound higher or
lower than others These differences in the pitch of the sound
are caused by different spacing in the waves that is different
frequency
Since the sounds are travelling at about the same speed the
one with the shorter wavelength will go by more frequently it
has a higher frequency or pitch In other words it sounds
higher
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
9
The amplitude of the wave determines the loudness of the
sound
The amplitude of sound waves is
measured in decibels Leaves
rustling in the wind are about 10
decibels a jet engine is about 120
decibels
Amplitude is Loudness
THEME 3 - OPTICS
The only special thing about light is that our eyes can detect it
However it is just a tiny part of a collection of electromagnetic
waves that make up the electromagnetic spectrum
The objects which we see can be placed into one of two
categories luminous objects and non luminous objects
Luminous objects are objects which generate their own light
Eg sun electric bulb
Non Luminous objects are objects which are capable of
reflecting light to our eyes Eg moon grass sky
Without light there would be no sight
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
10
Light is a transverse wave It is one part (region) of the
electromagnetic spectrum Light is the visible region it is
the part used by our eyes to see Like any electromagnetic
wave light can travel through a vacuum Light travels through
the vacuum of space from the Sun to the Earth
Light travels very quickly There is nothing which can travel
faster The speed of light is 300000000 ms
(that is 300 million metres per second - not easy to imagine)
Reflection - ( Bouncing of light)
Any type of wave can be reflected Reflection best occurs from
flat hard surfaces After reflection a wave has the same
speed frequency and wavelength it is only the direction of the
wave that has changed
For light (and other electromagnetic radiation) a flat shiny
surface like a plane mirror is a good reflector
A plane mirror is one
which is straight and not
curved
The light ray which hits
the mirror is called the
incident ray The light ray which
bounces off the mirror is
called the reflected ray The angle of incidence equals the
angle of reflection i = r This means that whatever angle the light ray hits the mirror it will be reflected off at the same
angle
If the surface of the mirror is not smooth but rough or bumpy
then light will be reflected at many different angles The image
in the mirror will be blurred and unclear This is called diffuse
reflection When you look into a mirror you see a reflection
which is an image of the real object
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
11
The image appears to be the
same distance behind the
mirror as the real object is in front of it
This is because the brain
thinks that light travels in
straight lines without changing
direction
The image is called virtual
because it does not really
exist behind the mirror The
virtual image is the same size as the object but with left and
right reversed ( laterally inverted)
Refraction ( bending of light)
Any type of wave can be refracted which means a change of
direction Refraction can occur when the speed of a wave
changes as it moves from one medium to another
After refraction the wave has the same frequency
but a different speed wavelength and direction
When a wave enters a new medium its change in speed will
also change its wavelength If the wave enters the new
medium at any angle other than normal to the boundary then
the change in the waves speed will also change its direction
A material is transparent if you can see through it If you can
see through it it means that light can travel through it
Transparent materials include air glass Perspex and water
Light travels at different speeds in different materials because
they have different densities The higher the density the
slower light travels Light travels fastest in space (a vacuum)
and a little slower in air Light moves noticeably more slowly in
glass than in air because glass is obviously more dense
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
12
A line drawn at right
angles to the
boundary between the
two media (air and
glass) is called a
normal
Light which enters a glass block along a normal (at 90 degrees) does not change direction but it does travel more slowly
through the glass When a ray of light enters a glass block at
an angle other than the normal it changes speed wavelength
and direction as shown below
Conditions of Refraction
The angle i is called the angle of incidence while
angle r is called angle of
refraction The light must
change speed when
crossing the boundary
In going from a less dense medium (air) to a more dense
medium (glass) light bends towards the normalThis means
that i gt r (the angle i is greater than the angle r)
In going from a more dense to a less dense medium (glass to
air) light bends away from the normal How much the light
bends depends on its colour
The change in angle of the light ray is the same when it enters
and leaves the glass If the incident ray had continued without
changing direction then the emergent ray would be parallel to
it Like any wave the speed of a light wave is dependent
upon the properties of the medium
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
13
Refractive Index - n
Index of refraction values (represented by the symbol n) are
numerical index values which are expressed relative to the
speed of light in a vacuum The index of refraction value of a
material is a number which indicates the number of times
slower that a light wave would be in that material than it is in a
vacuum
ή = Speed of light in air
Speed of light in medium
Material Index of Refraction
Vacuum 100
Water 133
Glass 150
Diamond 240
The index of refraction values thus provide a measure of the
relative speed of a light wave in a particular medium
Real and Apparent Depth
To an observer standing at
the side of a swimming pool
objects under the water
appear to be nearer the
surface than they really are
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
14
A fish appears to be nearer to
the surface than it really is
A straight stick appears to be
bent when part in and part
out of water
Both these effects are caused by
refraction of light at the surface of the water Therefore this
effect is related to the refractive
index of the media involved
The real depth of the fish is R and its apparent depth is A It is
clear that n represents the refractive index of light going from
air to water we have
Refractive index n = Real Depth Apparent depth
When light emerges from glass or water into air it speeds up
again As it meets the glass-air boundary at any angle greater than 0o it will refract away from the normal If you look at a
stick that is poking into some water at an angle the stick looks
bent because of refraction The bottom of the stick seems to be
nearer the surface of the water than it really is It also explains
why flat-based swimming pools appear to get shallower as you
look towards the end furthest from you
Total Internal Reflection - Critical Angle
When a light ray emerges from glass into air it is refracted and bends away from the normal so i lt r As i is made bigger the
refracted ray gets closer and closer to the surface of the glass
When the refracted ray is just touching the glass surface that is angle r = 90 degrees than angle i is called the critical
angle
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
15
The critical angle is different for different materials for glass it is about 42 degrees Total internal reflection happens when i is
bigger than the critical angleWhen a light ray tries to move
from glass to air at an angle greater than the critical angle the
refracted ray cannot escape from the glass and total internal
reflection occurs
Refraction cannot happen and all
of the light is reflected
at the glass air boundary as if it
had hit a mirror i = r
It is called internal reflection
because it occurs inside the glass
and total because all the light must
be reflected
Total Internal Reflection (TIR) can occur in prisms and optical
fibres
Total Internal Reflection - Prisms
A right angle prism can be used to
change the direction of a light ray by
90 degrees or 180 degrees
The light ray enters along a normal
and continues straight on until it hits
the back face of the prism Total
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
16
internal reflection occurs here because light strikes the surface
at 45 degrees which is greater than the critical angle
The light ray then emerges from the
prism along a normal and so continues
straight through This type of prism
can be used in a periscope Two right
angle prisms can be used to form a periscope as shown below Total
internal reflection occurs at the back
face of the prisms
A periscope may be used by people
(i) in a submarine to see above the
sea surface
(ii) to see over the heads of people in a crowd
A right angle prism can be used to change
the direction of light by 180
degrees as shown below
The same effect can result from two prisms arranged as shown
belowEither of these arrangements may be used in
binoculars or reflectors on the rear of cars and bicycles
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
3
The features of a longitudinal wave are
Compression - area of high pressure
Rarefaction - area of low pressure
Wavelength - distance between two compressions or two
rarefactions
Frequency and Periodic Time are related by a simple formula
f = 1
T
The Wave Equation
All waves whether longitudinal or transverse obey the wave
equation
Wave speed (ms) = frequency (Hz) times wavelength (m)
In Physics code
Here are a few wave speeds
Electromagnetic waves in a vacuum - 3 times 108 ms
Electromagnetic waves in glass - 2 times 108 ms
Sound in steel - 6000 ms
Sound in water - 1500 ms Sound in air - 340 ms
Speed Frequency amp Wavelength
The frequency of waves is set at the source itself For instance if John pokes a pond with a stick twice each second
the frequency will be 2 Hz
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
4
As the waves travel over the ponds surface this frequency
will not change What may change is the distance between
waves - the wavelength - and their speed
Water waves
Progressive Waves - Waves that travel or propagate from a
source are called progressive waves An obvious example is
the ripples on a pond when you throw a stone into the water
Both longitudinal and transverse waves can travel through
water
Longitudinal waves travel through water underneath the surface This is under water sound and can be used by
sea creatures to communicate (whales dolphins etc)
and by boats for echo location
Transverse waves travel on the water
surface and these are the waves which
we see as they make the surface go up
and down Transverse water waves are
shown as a series of parallel lines
These lines represent the peaks of the
wave as you are looking down on it
from above
Reflection Refraction and Diffraction
The wavelength is the distance between two peaks or the
distance between two troughs
Water waves are reflected from hard flat surfaces as shown
below
After reflection a wave has
the same speed frequency and wavelength it is only
the direction of the wave
that has changed
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
5
Water waves travel faster on the surface of deep water than
they do on shallow water The change in speed of the wave will
cause refraction
The slower wave in the shallow water has a smaller
wavelength The amount of refraction increases as the change
in speed increases
Waves Diffraction
Diffraction occurs when the wavelength of a wave
is of a similar size to an obstacle or a gap in a barrier
After diffraction a wave will have the same speed frequency
and wavelength
Electromagnetic waves have a huge range of wavelengths
Radio waves can diffract around hills mountains or even the
whole planet Light waves can diffract through tiny slits
X-rays can diffract around atoms
Water waves can diffract when passing through a gap in a
harbour wall
The wavelength of water waves
may be several metres
If the wavelength is of a similar
size to a gap in a harbour wall
then the wave will diffract as
shown below
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
6
If the wavelength does not match
the size of the gap
then only a little diffraction will
occur at the edge of the wave The part of the wave which hits the wall
in the above two pictures is
reflected straight back on itself
Sound
Sound is always produced by
something vibrating The
vibrations will make matter -
either solid liquid or gas - near it vibrate In this way energy is
taken away from the source of the
vibrations The amplitude of the
wave determines the volume of a
sound
We call these vibrations sound Our ears pick them up and tell
our brain what we can hear The vibrations are longitudinal
Bell Jar Experiment
With the bell ringing continuously inside it can be easily heard outside of the jar Once a
vacuum pump is turned on the air is slowly
removed As this happens the sound gets
quieter until eventually it cannot be heard at
all
Inside the bell jar the bell can still be seen to
ring If the rubber bands hanging it are good
enough few vibrations will pass up them to the glass (to be
heard) Letting the air back in allows the sound to be heard
again
Sounds cannot travel through a vacuum
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
7
Speed Of Sound
Sound waves are vibrations which cannot travel through
a vacuum - the total absence of matter The more matter
there is and the closer atoms are together the easier it is for
sound can travel
In air which is a mixture of gases the speed of sound is
around 340 ms depending on air temperature For water the
molecules are much closer together so vibrations pass much
more quickly between them As a result sound can travel at
around 1500 ms In solids where atoms are really close
together and very tightly attached to each other the speed of
sound is even higher - typically 5000 ms
Ultasound
This consist of sound that is above the range of human
hearing It even travels at exactly the same speed as sound in
any medium Humans can hear sound within the frequency
range of about 20 to 20000 Hz so any sound above 20 kHz is
ultrasound Uses ndash
1 Unborn babies can be photographed to check its size - and
even if there is more than one Its use in scanning goes far
beyond pregnancies Many other parts of the body are
analysed using it (bladder gallstones the heart etc) but it
doesnt even stop there Aeroplane wings can be checked for cracks that would be invisible on the surface
2 Ultrasound Treatments to clean things In fact really dirty
teeth can be cleaned superbly in this way Really delicate
mechanisms - such as in antique clocks and watches - can
also be safely cleaned
3 Ships use in Ultrasound and SONAR to detect fish sea
bottom
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
8
A ship sends a pulse of ultrasound
and receives an echo 0middot3 seconds
later If the speed of sound in water
is 1500 ms calculate its depth
speed = distance time
distance = speed times time
distance = 1500 times 0middot3 = 450 m
BUT this is the total distance travelled by the sound - so the
depth is half of this
Depth = 450 2 = 225 m
4 Used by animals to communicate ndash BatsDolphins
Any sound that you hear as a tone is made of regular evenly spaced waves of air molecules The most noticeable difference
between various tonal sounds is that some sound higher or
lower than others These differences in the pitch of the sound
are caused by different spacing in the waves that is different
frequency
Since the sounds are travelling at about the same speed the
one with the shorter wavelength will go by more frequently it
has a higher frequency or pitch In other words it sounds
higher
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
9
The amplitude of the wave determines the loudness of the
sound
The amplitude of sound waves is
measured in decibels Leaves
rustling in the wind are about 10
decibels a jet engine is about 120
decibels
Amplitude is Loudness
THEME 3 - OPTICS
The only special thing about light is that our eyes can detect it
However it is just a tiny part of a collection of electromagnetic
waves that make up the electromagnetic spectrum
The objects which we see can be placed into one of two
categories luminous objects and non luminous objects
Luminous objects are objects which generate their own light
Eg sun electric bulb
Non Luminous objects are objects which are capable of
reflecting light to our eyes Eg moon grass sky
Without light there would be no sight
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
10
Light is a transverse wave It is one part (region) of the
electromagnetic spectrum Light is the visible region it is
the part used by our eyes to see Like any electromagnetic
wave light can travel through a vacuum Light travels through
the vacuum of space from the Sun to the Earth
Light travels very quickly There is nothing which can travel
faster The speed of light is 300000000 ms
(that is 300 million metres per second - not easy to imagine)
Reflection - ( Bouncing of light)
Any type of wave can be reflected Reflection best occurs from
flat hard surfaces After reflection a wave has the same
speed frequency and wavelength it is only the direction of the
wave that has changed
For light (and other electromagnetic radiation) a flat shiny
surface like a plane mirror is a good reflector
A plane mirror is one
which is straight and not
curved
The light ray which hits
the mirror is called the
incident ray The light ray which
bounces off the mirror is
called the reflected ray The angle of incidence equals the
angle of reflection i = r This means that whatever angle the light ray hits the mirror it will be reflected off at the same
angle
If the surface of the mirror is not smooth but rough or bumpy
then light will be reflected at many different angles The image
in the mirror will be blurred and unclear This is called diffuse
reflection When you look into a mirror you see a reflection
which is an image of the real object
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
11
The image appears to be the
same distance behind the
mirror as the real object is in front of it
This is because the brain
thinks that light travels in
straight lines without changing
direction
The image is called virtual
because it does not really
exist behind the mirror The
virtual image is the same size as the object but with left and
right reversed ( laterally inverted)
Refraction ( bending of light)
Any type of wave can be refracted which means a change of
direction Refraction can occur when the speed of a wave
changes as it moves from one medium to another
After refraction the wave has the same frequency
but a different speed wavelength and direction
When a wave enters a new medium its change in speed will
also change its wavelength If the wave enters the new
medium at any angle other than normal to the boundary then
the change in the waves speed will also change its direction
A material is transparent if you can see through it If you can
see through it it means that light can travel through it
Transparent materials include air glass Perspex and water
Light travels at different speeds in different materials because
they have different densities The higher the density the
slower light travels Light travels fastest in space (a vacuum)
and a little slower in air Light moves noticeably more slowly in
glass than in air because glass is obviously more dense
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
12
A line drawn at right
angles to the
boundary between the
two media (air and
glass) is called a
normal
Light which enters a glass block along a normal (at 90 degrees) does not change direction but it does travel more slowly
through the glass When a ray of light enters a glass block at
an angle other than the normal it changes speed wavelength
and direction as shown below
Conditions of Refraction
The angle i is called the angle of incidence while
angle r is called angle of
refraction The light must
change speed when
crossing the boundary
In going from a less dense medium (air) to a more dense
medium (glass) light bends towards the normalThis means
that i gt r (the angle i is greater than the angle r)
In going from a more dense to a less dense medium (glass to
air) light bends away from the normal How much the light
bends depends on its colour
The change in angle of the light ray is the same when it enters
and leaves the glass If the incident ray had continued without
changing direction then the emergent ray would be parallel to
it Like any wave the speed of a light wave is dependent
upon the properties of the medium
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
13
Refractive Index - n
Index of refraction values (represented by the symbol n) are
numerical index values which are expressed relative to the
speed of light in a vacuum The index of refraction value of a
material is a number which indicates the number of times
slower that a light wave would be in that material than it is in a
vacuum
ή = Speed of light in air
Speed of light in medium
Material Index of Refraction
Vacuum 100
Water 133
Glass 150
Diamond 240
The index of refraction values thus provide a measure of the
relative speed of a light wave in a particular medium
Real and Apparent Depth
To an observer standing at
the side of a swimming pool
objects under the water
appear to be nearer the
surface than they really are
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
14
A fish appears to be nearer to
the surface than it really is
A straight stick appears to be
bent when part in and part
out of water
Both these effects are caused by
refraction of light at the surface of the water Therefore this
effect is related to the refractive
index of the media involved
The real depth of the fish is R and its apparent depth is A It is
clear that n represents the refractive index of light going from
air to water we have
Refractive index n = Real Depth Apparent depth
When light emerges from glass or water into air it speeds up
again As it meets the glass-air boundary at any angle greater than 0o it will refract away from the normal If you look at a
stick that is poking into some water at an angle the stick looks
bent because of refraction The bottom of the stick seems to be
nearer the surface of the water than it really is It also explains
why flat-based swimming pools appear to get shallower as you
look towards the end furthest from you
Total Internal Reflection - Critical Angle
When a light ray emerges from glass into air it is refracted and bends away from the normal so i lt r As i is made bigger the
refracted ray gets closer and closer to the surface of the glass
When the refracted ray is just touching the glass surface that is angle r = 90 degrees than angle i is called the critical
angle
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
15
The critical angle is different for different materials for glass it is about 42 degrees Total internal reflection happens when i is
bigger than the critical angleWhen a light ray tries to move
from glass to air at an angle greater than the critical angle the
refracted ray cannot escape from the glass and total internal
reflection occurs
Refraction cannot happen and all
of the light is reflected
at the glass air boundary as if it
had hit a mirror i = r
It is called internal reflection
because it occurs inside the glass
and total because all the light must
be reflected
Total Internal Reflection (TIR) can occur in prisms and optical
fibres
Total Internal Reflection - Prisms
A right angle prism can be used to
change the direction of a light ray by
90 degrees or 180 degrees
The light ray enters along a normal
and continues straight on until it hits
the back face of the prism Total
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
16
internal reflection occurs here because light strikes the surface
at 45 degrees which is greater than the critical angle
The light ray then emerges from the
prism along a normal and so continues
straight through This type of prism
can be used in a periscope Two right
angle prisms can be used to form a periscope as shown below Total
internal reflection occurs at the back
face of the prisms
A periscope may be used by people
(i) in a submarine to see above the
sea surface
(ii) to see over the heads of people in a crowd
A right angle prism can be used to change
the direction of light by 180
degrees as shown below
The same effect can result from two prisms arranged as shown
belowEither of these arrangements may be used in
binoculars or reflectors on the rear of cars and bicycles
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
4
As the waves travel over the ponds surface this frequency
will not change What may change is the distance between
waves - the wavelength - and their speed
Water waves
Progressive Waves - Waves that travel or propagate from a
source are called progressive waves An obvious example is
the ripples on a pond when you throw a stone into the water
Both longitudinal and transverse waves can travel through
water
Longitudinal waves travel through water underneath the surface This is under water sound and can be used by
sea creatures to communicate (whales dolphins etc)
and by boats for echo location
Transverse waves travel on the water
surface and these are the waves which
we see as they make the surface go up
and down Transverse water waves are
shown as a series of parallel lines
These lines represent the peaks of the
wave as you are looking down on it
from above
Reflection Refraction and Diffraction
The wavelength is the distance between two peaks or the
distance between two troughs
Water waves are reflected from hard flat surfaces as shown
below
After reflection a wave has
the same speed frequency and wavelength it is only
the direction of the wave
that has changed
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
5
Water waves travel faster on the surface of deep water than
they do on shallow water The change in speed of the wave will
cause refraction
The slower wave in the shallow water has a smaller
wavelength The amount of refraction increases as the change
in speed increases
Waves Diffraction
Diffraction occurs when the wavelength of a wave
is of a similar size to an obstacle or a gap in a barrier
After diffraction a wave will have the same speed frequency
and wavelength
Electromagnetic waves have a huge range of wavelengths
Radio waves can diffract around hills mountains or even the
whole planet Light waves can diffract through tiny slits
X-rays can diffract around atoms
Water waves can diffract when passing through a gap in a
harbour wall
The wavelength of water waves
may be several metres
If the wavelength is of a similar
size to a gap in a harbour wall
then the wave will diffract as
shown below
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
6
If the wavelength does not match
the size of the gap
then only a little diffraction will
occur at the edge of the wave The part of the wave which hits the wall
in the above two pictures is
reflected straight back on itself
Sound
Sound is always produced by
something vibrating The
vibrations will make matter -
either solid liquid or gas - near it vibrate In this way energy is
taken away from the source of the
vibrations The amplitude of the
wave determines the volume of a
sound
We call these vibrations sound Our ears pick them up and tell
our brain what we can hear The vibrations are longitudinal
Bell Jar Experiment
With the bell ringing continuously inside it can be easily heard outside of the jar Once a
vacuum pump is turned on the air is slowly
removed As this happens the sound gets
quieter until eventually it cannot be heard at
all
Inside the bell jar the bell can still be seen to
ring If the rubber bands hanging it are good
enough few vibrations will pass up them to the glass (to be
heard) Letting the air back in allows the sound to be heard
again
Sounds cannot travel through a vacuum
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
7
Speed Of Sound
Sound waves are vibrations which cannot travel through
a vacuum - the total absence of matter The more matter
there is and the closer atoms are together the easier it is for
sound can travel
In air which is a mixture of gases the speed of sound is
around 340 ms depending on air temperature For water the
molecules are much closer together so vibrations pass much
more quickly between them As a result sound can travel at
around 1500 ms In solids where atoms are really close
together and very tightly attached to each other the speed of
sound is even higher - typically 5000 ms
Ultasound
This consist of sound that is above the range of human
hearing It even travels at exactly the same speed as sound in
any medium Humans can hear sound within the frequency
range of about 20 to 20000 Hz so any sound above 20 kHz is
ultrasound Uses ndash
1 Unborn babies can be photographed to check its size - and
even if there is more than one Its use in scanning goes far
beyond pregnancies Many other parts of the body are
analysed using it (bladder gallstones the heart etc) but it
doesnt even stop there Aeroplane wings can be checked for cracks that would be invisible on the surface
2 Ultrasound Treatments to clean things In fact really dirty
teeth can be cleaned superbly in this way Really delicate
mechanisms - such as in antique clocks and watches - can
also be safely cleaned
3 Ships use in Ultrasound and SONAR to detect fish sea
bottom
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
8
A ship sends a pulse of ultrasound
and receives an echo 0middot3 seconds
later If the speed of sound in water
is 1500 ms calculate its depth
speed = distance time
distance = speed times time
distance = 1500 times 0middot3 = 450 m
BUT this is the total distance travelled by the sound - so the
depth is half of this
Depth = 450 2 = 225 m
4 Used by animals to communicate ndash BatsDolphins
Any sound that you hear as a tone is made of regular evenly spaced waves of air molecules The most noticeable difference
between various tonal sounds is that some sound higher or
lower than others These differences in the pitch of the sound
are caused by different spacing in the waves that is different
frequency
Since the sounds are travelling at about the same speed the
one with the shorter wavelength will go by more frequently it
has a higher frequency or pitch In other words it sounds
higher
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
9
The amplitude of the wave determines the loudness of the
sound
The amplitude of sound waves is
measured in decibels Leaves
rustling in the wind are about 10
decibels a jet engine is about 120
decibels
Amplitude is Loudness
THEME 3 - OPTICS
The only special thing about light is that our eyes can detect it
However it is just a tiny part of a collection of electromagnetic
waves that make up the electromagnetic spectrum
The objects which we see can be placed into one of two
categories luminous objects and non luminous objects
Luminous objects are objects which generate their own light
Eg sun electric bulb
Non Luminous objects are objects which are capable of
reflecting light to our eyes Eg moon grass sky
Without light there would be no sight
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
10
Light is a transverse wave It is one part (region) of the
electromagnetic spectrum Light is the visible region it is
the part used by our eyes to see Like any electromagnetic
wave light can travel through a vacuum Light travels through
the vacuum of space from the Sun to the Earth
Light travels very quickly There is nothing which can travel
faster The speed of light is 300000000 ms
(that is 300 million metres per second - not easy to imagine)
Reflection - ( Bouncing of light)
Any type of wave can be reflected Reflection best occurs from
flat hard surfaces After reflection a wave has the same
speed frequency and wavelength it is only the direction of the
wave that has changed
For light (and other electromagnetic radiation) a flat shiny
surface like a plane mirror is a good reflector
A plane mirror is one
which is straight and not
curved
The light ray which hits
the mirror is called the
incident ray The light ray which
bounces off the mirror is
called the reflected ray The angle of incidence equals the
angle of reflection i = r This means that whatever angle the light ray hits the mirror it will be reflected off at the same
angle
If the surface of the mirror is not smooth but rough or bumpy
then light will be reflected at many different angles The image
in the mirror will be blurred and unclear This is called diffuse
reflection When you look into a mirror you see a reflection
which is an image of the real object
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
11
The image appears to be the
same distance behind the
mirror as the real object is in front of it
This is because the brain
thinks that light travels in
straight lines without changing
direction
The image is called virtual
because it does not really
exist behind the mirror The
virtual image is the same size as the object but with left and
right reversed ( laterally inverted)
Refraction ( bending of light)
Any type of wave can be refracted which means a change of
direction Refraction can occur when the speed of a wave
changes as it moves from one medium to another
After refraction the wave has the same frequency
but a different speed wavelength and direction
When a wave enters a new medium its change in speed will
also change its wavelength If the wave enters the new
medium at any angle other than normal to the boundary then
the change in the waves speed will also change its direction
A material is transparent if you can see through it If you can
see through it it means that light can travel through it
Transparent materials include air glass Perspex and water
Light travels at different speeds in different materials because
they have different densities The higher the density the
slower light travels Light travels fastest in space (a vacuum)
and a little slower in air Light moves noticeably more slowly in
glass than in air because glass is obviously more dense
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
12
A line drawn at right
angles to the
boundary between the
two media (air and
glass) is called a
normal
Light which enters a glass block along a normal (at 90 degrees) does not change direction but it does travel more slowly
through the glass When a ray of light enters a glass block at
an angle other than the normal it changes speed wavelength
and direction as shown below
Conditions of Refraction
The angle i is called the angle of incidence while
angle r is called angle of
refraction The light must
change speed when
crossing the boundary
In going from a less dense medium (air) to a more dense
medium (glass) light bends towards the normalThis means
that i gt r (the angle i is greater than the angle r)
In going from a more dense to a less dense medium (glass to
air) light bends away from the normal How much the light
bends depends on its colour
The change in angle of the light ray is the same when it enters
and leaves the glass If the incident ray had continued without
changing direction then the emergent ray would be parallel to
it Like any wave the speed of a light wave is dependent
upon the properties of the medium
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
13
Refractive Index - n
Index of refraction values (represented by the symbol n) are
numerical index values which are expressed relative to the
speed of light in a vacuum The index of refraction value of a
material is a number which indicates the number of times
slower that a light wave would be in that material than it is in a
vacuum
ή = Speed of light in air
Speed of light in medium
Material Index of Refraction
Vacuum 100
Water 133
Glass 150
Diamond 240
The index of refraction values thus provide a measure of the
relative speed of a light wave in a particular medium
Real and Apparent Depth
To an observer standing at
the side of a swimming pool
objects under the water
appear to be nearer the
surface than they really are
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
14
A fish appears to be nearer to
the surface than it really is
A straight stick appears to be
bent when part in and part
out of water
Both these effects are caused by
refraction of light at the surface of the water Therefore this
effect is related to the refractive
index of the media involved
The real depth of the fish is R and its apparent depth is A It is
clear that n represents the refractive index of light going from
air to water we have
Refractive index n = Real Depth Apparent depth
When light emerges from glass or water into air it speeds up
again As it meets the glass-air boundary at any angle greater than 0o it will refract away from the normal If you look at a
stick that is poking into some water at an angle the stick looks
bent because of refraction The bottom of the stick seems to be
nearer the surface of the water than it really is It also explains
why flat-based swimming pools appear to get shallower as you
look towards the end furthest from you
Total Internal Reflection - Critical Angle
When a light ray emerges from glass into air it is refracted and bends away from the normal so i lt r As i is made bigger the
refracted ray gets closer and closer to the surface of the glass
When the refracted ray is just touching the glass surface that is angle r = 90 degrees than angle i is called the critical
angle
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
15
The critical angle is different for different materials for glass it is about 42 degrees Total internal reflection happens when i is
bigger than the critical angleWhen a light ray tries to move
from glass to air at an angle greater than the critical angle the
refracted ray cannot escape from the glass and total internal
reflection occurs
Refraction cannot happen and all
of the light is reflected
at the glass air boundary as if it
had hit a mirror i = r
It is called internal reflection
because it occurs inside the glass
and total because all the light must
be reflected
Total Internal Reflection (TIR) can occur in prisms and optical
fibres
Total Internal Reflection - Prisms
A right angle prism can be used to
change the direction of a light ray by
90 degrees or 180 degrees
The light ray enters along a normal
and continues straight on until it hits
the back face of the prism Total
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
16
internal reflection occurs here because light strikes the surface
at 45 degrees which is greater than the critical angle
The light ray then emerges from the
prism along a normal and so continues
straight through This type of prism
can be used in a periscope Two right
angle prisms can be used to form a periscope as shown below Total
internal reflection occurs at the back
face of the prisms
A periscope may be used by people
(i) in a submarine to see above the
sea surface
(ii) to see over the heads of people in a crowd
A right angle prism can be used to change
the direction of light by 180
degrees as shown below
The same effect can result from two prisms arranged as shown
belowEither of these arrangements may be used in
binoculars or reflectors on the rear of cars and bicycles
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
5
Water waves travel faster on the surface of deep water than
they do on shallow water The change in speed of the wave will
cause refraction
The slower wave in the shallow water has a smaller
wavelength The amount of refraction increases as the change
in speed increases
Waves Diffraction
Diffraction occurs when the wavelength of a wave
is of a similar size to an obstacle or a gap in a barrier
After diffraction a wave will have the same speed frequency
and wavelength
Electromagnetic waves have a huge range of wavelengths
Radio waves can diffract around hills mountains or even the
whole planet Light waves can diffract through tiny slits
X-rays can diffract around atoms
Water waves can diffract when passing through a gap in a
harbour wall
The wavelength of water waves
may be several metres
If the wavelength is of a similar
size to a gap in a harbour wall
then the wave will diffract as
shown below
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
6
If the wavelength does not match
the size of the gap
then only a little diffraction will
occur at the edge of the wave The part of the wave which hits the wall
in the above two pictures is
reflected straight back on itself
Sound
Sound is always produced by
something vibrating The
vibrations will make matter -
either solid liquid or gas - near it vibrate In this way energy is
taken away from the source of the
vibrations The amplitude of the
wave determines the volume of a
sound
We call these vibrations sound Our ears pick them up and tell
our brain what we can hear The vibrations are longitudinal
Bell Jar Experiment
With the bell ringing continuously inside it can be easily heard outside of the jar Once a
vacuum pump is turned on the air is slowly
removed As this happens the sound gets
quieter until eventually it cannot be heard at
all
Inside the bell jar the bell can still be seen to
ring If the rubber bands hanging it are good
enough few vibrations will pass up them to the glass (to be
heard) Letting the air back in allows the sound to be heard
again
Sounds cannot travel through a vacuum
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
7
Speed Of Sound
Sound waves are vibrations which cannot travel through
a vacuum - the total absence of matter The more matter
there is and the closer atoms are together the easier it is for
sound can travel
In air which is a mixture of gases the speed of sound is
around 340 ms depending on air temperature For water the
molecules are much closer together so vibrations pass much
more quickly between them As a result sound can travel at
around 1500 ms In solids where atoms are really close
together and very tightly attached to each other the speed of
sound is even higher - typically 5000 ms
Ultasound
This consist of sound that is above the range of human
hearing It even travels at exactly the same speed as sound in
any medium Humans can hear sound within the frequency
range of about 20 to 20000 Hz so any sound above 20 kHz is
ultrasound Uses ndash
1 Unborn babies can be photographed to check its size - and
even if there is more than one Its use in scanning goes far
beyond pregnancies Many other parts of the body are
analysed using it (bladder gallstones the heart etc) but it
doesnt even stop there Aeroplane wings can be checked for cracks that would be invisible on the surface
2 Ultrasound Treatments to clean things In fact really dirty
teeth can be cleaned superbly in this way Really delicate
mechanisms - such as in antique clocks and watches - can
also be safely cleaned
3 Ships use in Ultrasound and SONAR to detect fish sea
bottom
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
8
A ship sends a pulse of ultrasound
and receives an echo 0middot3 seconds
later If the speed of sound in water
is 1500 ms calculate its depth
speed = distance time
distance = speed times time
distance = 1500 times 0middot3 = 450 m
BUT this is the total distance travelled by the sound - so the
depth is half of this
Depth = 450 2 = 225 m
4 Used by animals to communicate ndash BatsDolphins
Any sound that you hear as a tone is made of regular evenly spaced waves of air molecules The most noticeable difference
between various tonal sounds is that some sound higher or
lower than others These differences in the pitch of the sound
are caused by different spacing in the waves that is different
frequency
Since the sounds are travelling at about the same speed the
one with the shorter wavelength will go by more frequently it
has a higher frequency or pitch In other words it sounds
higher
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
9
The amplitude of the wave determines the loudness of the
sound
The amplitude of sound waves is
measured in decibels Leaves
rustling in the wind are about 10
decibels a jet engine is about 120
decibels
Amplitude is Loudness
THEME 3 - OPTICS
The only special thing about light is that our eyes can detect it
However it is just a tiny part of a collection of electromagnetic
waves that make up the electromagnetic spectrum
The objects which we see can be placed into one of two
categories luminous objects and non luminous objects
Luminous objects are objects which generate their own light
Eg sun electric bulb
Non Luminous objects are objects which are capable of
reflecting light to our eyes Eg moon grass sky
Without light there would be no sight
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
10
Light is a transverse wave It is one part (region) of the
electromagnetic spectrum Light is the visible region it is
the part used by our eyes to see Like any electromagnetic
wave light can travel through a vacuum Light travels through
the vacuum of space from the Sun to the Earth
Light travels very quickly There is nothing which can travel
faster The speed of light is 300000000 ms
(that is 300 million metres per second - not easy to imagine)
Reflection - ( Bouncing of light)
Any type of wave can be reflected Reflection best occurs from
flat hard surfaces After reflection a wave has the same
speed frequency and wavelength it is only the direction of the
wave that has changed
For light (and other electromagnetic radiation) a flat shiny
surface like a plane mirror is a good reflector
A plane mirror is one
which is straight and not
curved
The light ray which hits
the mirror is called the
incident ray The light ray which
bounces off the mirror is
called the reflected ray The angle of incidence equals the
angle of reflection i = r This means that whatever angle the light ray hits the mirror it will be reflected off at the same
angle
If the surface of the mirror is not smooth but rough or bumpy
then light will be reflected at many different angles The image
in the mirror will be blurred and unclear This is called diffuse
reflection When you look into a mirror you see a reflection
which is an image of the real object
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
11
The image appears to be the
same distance behind the
mirror as the real object is in front of it
This is because the brain
thinks that light travels in
straight lines without changing
direction
The image is called virtual
because it does not really
exist behind the mirror The
virtual image is the same size as the object but with left and
right reversed ( laterally inverted)
Refraction ( bending of light)
Any type of wave can be refracted which means a change of
direction Refraction can occur when the speed of a wave
changes as it moves from one medium to another
After refraction the wave has the same frequency
but a different speed wavelength and direction
When a wave enters a new medium its change in speed will
also change its wavelength If the wave enters the new
medium at any angle other than normal to the boundary then
the change in the waves speed will also change its direction
A material is transparent if you can see through it If you can
see through it it means that light can travel through it
Transparent materials include air glass Perspex and water
Light travels at different speeds in different materials because
they have different densities The higher the density the
slower light travels Light travels fastest in space (a vacuum)
and a little slower in air Light moves noticeably more slowly in
glass than in air because glass is obviously more dense
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
12
A line drawn at right
angles to the
boundary between the
two media (air and
glass) is called a
normal
Light which enters a glass block along a normal (at 90 degrees) does not change direction but it does travel more slowly
through the glass When a ray of light enters a glass block at
an angle other than the normal it changes speed wavelength
and direction as shown below
Conditions of Refraction
The angle i is called the angle of incidence while
angle r is called angle of
refraction The light must
change speed when
crossing the boundary
In going from a less dense medium (air) to a more dense
medium (glass) light bends towards the normalThis means
that i gt r (the angle i is greater than the angle r)
In going from a more dense to a less dense medium (glass to
air) light bends away from the normal How much the light
bends depends on its colour
The change in angle of the light ray is the same when it enters
and leaves the glass If the incident ray had continued without
changing direction then the emergent ray would be parallel to
it Like any wave the speed of a light wave is dependent
upon the properties of the medium
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
13
Refractive Index - n
Index of refraction values (represented by the symbol n) are
numerical index values which are expressed relative to the
speed of light in a vacuum The index of refraction value of a
material is a number which indicates the number of times
slower that a light wave would be in that material than it is in a
vacuum
ή = Speed of light in air
Speed of light in medium
Material Index of Refraction
Vacuum 100
Water 133
Glass 150
Diamond 240
The index of refraction values thus provide a measure of the
relative speed of a light wave in a particular medium
Real and Apparent Depth
To an observer standing at
the side of a swimming pool
objects under the water
appear to be nearer the
surface than they really are
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
14
A fish appears to be nearer to
the surface than it really is
A straight stick appears to be
bent when part in and part
out of water
Both these effects are caused by
refraction of light at the surface of the water Therefore this
effect is related to the refractive
index of the media involved
The real depth of the fish is R and its apparent depth is A It is
clear that n represents the refractive index of light going from
air to water we have
Refractive index n = Real Depth Apparent depth
When light emerges from glass or water into air it speeds up
again As it meets the glass-air boundary at any angle greater than 0o it will refract away from the normal If you look at a
stick that is poking into some water at an angle the stick looks
bent because of refraction The bottom of the stick seems to be
nearer the surface of the water than it really is It also explains
why flat-based swimming pools appear to get shallower as you
look towards the end furthest from you
Total Internal Reflection - Critical Angle
When a light ray emerges from glass into air it is refracted and bends away from the normal so i lt r As i is made bigger the
refracted ray gets closer and closer to the surface of the glass
When the refracted ray is just touching the glass surface that is angle r = 90 degrees than angle i is called the critical
angle
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
15
The critical angle is different for different materials for glass it is about 42 degrees Total internal reflection happens when i is
bigger than the critical angleWhen a light ray tries to move
from glass to air at an angle greater than the critical angle the
refracted ray cannot escape from the glass and total internal
reflection occurs
Refraction cannot happen and all
of the light is reflected
at the glass air boundary as if it
had hit a mirror i = r
It is called internal reflection
because it occurs inside the glass
and total because all the light must
be reflected
Total Internal Reflection (TIR) can occur in prisms and optical
fibres
Total Internal Reflection - Prisms
A right angle prism can be used to
change the direction of a light ray by
90 degrees or 180 degrees
The light ray enters along a normal
and continues straight on until it hits
the back face of the prism Total
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
16
internal reflection occurs here because light strikes the surface
at 45 degrees which is greater than the critical angle
The light ray then emerges from the
prism along a normal and so continues
straight through This type of prism
can be used in a periscope Two right
angle prisms can be used to form a periscope as shown below Total
internal reflection occurs at the back
face of the prisms
A periscope may be used by people
(i) in a submarine to see above the
sea surface
(ii) to see over the heads of people in a crowd
A right angle prism can be used to change
the direction of light by 180
degrees as shown below
The same effect can result from two prisms arranged as shown
belowEither of these arrangements may be used in
binoculars or reflectors on the rear of cars and bicycles
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
6
If the wavelength does not match
the size of the gap
then only a little diffraction will
occur at the edge of the wave The part of the wave which hits the wall
in the above two pictures is
reflected straight back on itself
Sound
Sound is always produced by
something vibrating The
vibrations will make matter -
either solid liquid or gas - near it vibrate In this way energy is
taken away from the source of the
vibrations The amplitude of the
wave determines the volume of a
sound
We call these vibrations sound Our ears pick them up and tell
our brain what we can hear The vibrations are longitudinal
Bell Jar Experiment
With the bell ringing continuously inside it can be easily heard outside of the jar Once a
vacuum pump is turned on the air is slowly
removed As this happens the sound gets
quieter until eventually it cannot be heard at
all
Inside the bell jar the bell can still be seen to
ring If the rubber bands hanging it are good
enough few vibrations will pass up them to the glass (to be
heard) Letting the air back in allows the sound to be heard
again
Sounds cannot travel through a vacuum
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
7
Speed Of Sound
Sound waves are vibrations which cannot travel through
a vacuum - the total absence of matter The more matter
there is and the closer atoms are together the easier it is for
sound can travel
In air which is a mixture of gases the speed of sound is
around 340 ms depending on air temperature For water the
molecules are much closer together so vibrations pass much
more quickly between them As a result sound can travel at
around 1500 ms In solids where atoms are really close
together and very tightly attached to each other the speed of
sound is even higher - typically 5000 ms
Ultasound
This consist of sound that is above the range of human
hearing It even travels at exactly the same speed as sound in
any medium Humans can hear sound within the frequency
range of about 20 to 20000 Hz so any sound above 20 kHz is
ultrasound Uses ndash
1 Unborn babies can be photographed to check its size - and
even if there is more than one Its use in scanning goes far
beyond pregnancies Many other parts of the body are
analysed using it (bladder gallstones the heart etc) but it
doesnt even stop there Aeroplane wings can be checked for cracks that would be invisible on the surface
2 Ultrasound Treatments to clean things In fact really dirty
teeth can be cleaned superbly in this way Really delicate
mechanisms - such as in antique clocks and watches - can
also be safely cleaned
3 Ships use in Ultrasound and SONAR to detect fish sea
bottom
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
8
A ship sends a pulse of ultrasound
and receives an echo 0middot3 seconds
later If the speed of sound in water
is 1500 ms calculate its depth
speed = distance time
distance = speed times time
distance = 1500 times 0middot3 = 450 m
BUT this is the total distance travelled by the sound - so the
depth is half of this
Depth = 450 2 = 225 m
4 Used by animals to communicate ndash BatsDolphins
Any sound that you hear as a tone is made of regular evenly spaced waves of air molecules The most noticeable difference
between various tonal sounds is that some sound higher or
lower than others These differences in the pitch of the sound
are caused by different spacing in the waves that is different
frequency
Since the sounds are travelling at about the same speed the
one with the shorter wavelength will go by more frequently it
has a higher frequency or pitch In other words it sounds
higher
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
9
The amplitude of the wave determines the loudness of the
sound
The amplitude of sound waves is
measured in decibels Leaves
rustling in the wind are about 10
decibels a jet engine is about 120
decibels
Amplitude is Loudness
THEME 3 - OPTICS
The only special thing about light is that our eyes can detect it
However it is just a tiny part of a collection of electromagnetic
waves that make up the electromagnetic spectrum
The objects which we see can be placed into one of two
categories luminous objects and non luminous objects
Luminous objects are objects which generate their own light
Eg sun electric bulb
Non Luminous objects are objects which are capable of
reflecting light to our eyes Eg moon grass sky
Without light there would be no sight
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
10
Light is a transverse wave It is one part (region) of the
electromagnetic spectrum Light is the visible region it is
the part used by our eyes to see Like any electromagnetic
wave light can travel through a vacuum Light travels through
the vacuum of space from the Sun to the Earth
Light travels very quickly There is nothing which can travel
faster The speed of light is 300000000 ms
(that is 300 million metres per second - not easy to imagine)
Reflection - ( Bouncing of light)
Any type of wave can be reflected Reflection best occurs from
flat hard surfaces After reflection a wave has the same
speed frequency and wavelength it is only the direction of the
wave that has changed
For light (and other electromagnetic radiation) a flat shiny
surface like a plane mirror is a good reflector
A plane mirror is one
which is straight and not
curved
The light ray which hits
the mirror is called the
incident ray The light ray which
bounces off the mirror is
called the reflected ray The angle of incidence equals the
angle of reflection i = r This means that whatever angle the light ray hits the mirror it will be reflected off at the same
angle
If the surface of the mirror is not smooth but rough or bumpy
then light will be reflected at many different angles The image
in the mirror will be blurred and unclear This is called diffuse
reflection When you look into a mirror you see a reflection
which is an image of the real object
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
11
The image appears to be the
same distance behind the
mirror as the real object is in front of it
This is because the brain
thinks that light travels in
straight lines without changing
direction
The image is called virtual
because it does not really
exist behind the mirror The
virtual image is the same size as the object but with left and
right reversed ( laterally inverted)
Refraction ( bending of light)
Any type of wave can be refracted which means a change of
direction Refraction can occur when the speed of a wave
changes as it moves from one medium to another
After refraction the wave has the same frequency
but a different speed wavelength and direction
When a wave enters a new medium its change in speed will
also change its wavelength If the wave enters the new
medium at any angle other than normal to the boundary then
the change in the waves speed will also change its direction
A material is transparent if you can see through it If you can
see through it it means that light can travel through it
Transparent materials include air glass Perspex and water
Light travels at different speeds in different materials because
they have different densities The higher the density the
slower light travels Light travels fastest in space (a vacuum)
and a little slower in air Light moves noticeably more slowly in
glass than in air because glass is obviously more dense
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
12
A line drawn at right
angles to the
boundary between the
two media (air and
glass) is called a
normal
Light which enters a glass block along a normal (at 90 degrees) does not change direction but it does travel more slowly
through the glass When a ray of light enters a glass block at
an angle other than the normal it changes speed wavelength
and direction as shown below
Conditions of Refraction
The angle i is called the angle of incidence while
angle r is called angle of
refraction The light must
change speed when
crossing the boundary
In going from a less dense medium (air) to a more dense
medium (glass) light bends towards the normalThis means
that i gt r (the angle i is greater than the angle r)
In going from a more dense to a less dense medium (glass to
air) light bends away from the normal How much the light
bends depends on its colour
The change in angle of the light ray is the same when it enters
and leaves the glass If the incident ray had continued without
changing direction then the emergent ray would be parallel to
it Like any wave the speed of a light wave is dependent
upon the properties of the medium
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
13
Refractive Index - n
Index of refraction values (represented by the symbol n) are
numerical index values which are expressed relative to the
speed of light in a vacuum The index of refraction value of a
material is a number which indicates the number of times
slower that a light wave would be in that material than it is in a
vacuum
ή = Speed of light in air
Speed of light in medium
Material Index of Refraction
Vacuum 100
Water 133
Glass 150
Diamond 240
The index of refraction values thus provide a measure of the
relative speed of a light wave in a particular medium
Real and Apparent Depth
To an observer standing at
the side of a swimming pool
objects under the water
appear to be nearer the
surface than they really are
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
14
A fish appears to be nearer to
the surface than it really is
A straight stick appears to be
bent when part in and part
out of water
Both these effects are caused by
refraction of light at the surface of the water Therefore this
effect is related to the refractive
index of the media involved
The real depth of the fish is R and its apparent depth is A It is
clear that n represents the refractive index of light going from
air to water we have
Refractive index n = Real Depth Apparent depth
When light emerges from glass or water into air it speeds up
again As it meets the glass-air boundary at any angle greater than 0o it will refract away from the normal If you look at a
stick that is poking into some water at an angle the stick looks
bent because of refraction The bottom of the stick seems to be
nearer the surface of the water than it really is It also explains
why flat-based swimming pools appear to get shallower as you
look towards the end furthest from you
Total Internal Reflection - Critical Angle
When a light ray emerges from glass into air it is refracted and bends away from the normal so i lt r As i is made bigger the
refracted ray gets closer and closer to the surface of the glass
When the refracted ray is just touching the glass surface that is angle r = 90 degrees than angle i is called the critical
angle
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
15
The critical angle is different for different materials for glass it is about 42 degrees Total internal reflection happens when i is
bigger than the critical angleWhen a light ray tries to move
from glass to air at an angle greater than the critical angle the
refracted ray cannot escape from the glass and total internal
reflection occurs
Refraction cannot happen and all
of the light is reflected
at the glass air boundary as if it
had hit a mirror i = r
It is called internal reflection
because it occurs inside the glass
and total because all the light must
be reflected
Total Internal Reflection (TIR) can occur in prisms and optical
fibres
Total Internal Reflection - Prisms
A right angle prism can be used to
change the direction of a light ray by
90 degrees or 180 degrees
The light ray enters along a normal
and continues straight on until it hits
the back face of the prism Total
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
16
internal reflection occurs here because light strikes the surface
at 45 degrees which is greater than the critical angle
The light ray then emerges from the
prism along a normal and so continues
straight through This type of prism
can be used in a periscope Two right
angle prisms can be used to form a periscope as shown below Total
internal reflection occurs at the back
face of the prisms
A periscope may be used by people
(i) in a submarine to see above the
sea surface
(ii) to see over the heads of people in a crowd
A right angle prism can be used to change
the direction of light by 180
degrees as shown below
The same effect can result from two prisms arranged as shown
belowEither of these arrangements may be used in
binoculars or reflectors on the rear of cars and bicycles
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
7
Speed Of Sound
Sound waves are vibrations which cannot travel through
a vacuum - the total absence of matter The more matter
there is and the closer atoms are together the easier it is for
sound can travel
In air which is a mixture of gases the speed of sound is
around 340 ms depending on air temperature For water the
molecules are much closer together so vibrations pass much
more quickly between them As a result sound can travel at
around 1500 ms In solids where atoms are really close
together and very tightly attached to each other the speed of
sound is even higher - typically 5000 ms
Ultasound
This consist of sound that is above the range of human
hearing It even travels at exactly the same speed as sound in
any medium Humans can hear sound within the frequency
range of about 20 to 20000 Hz so any sound above 20 kHz is
ultrasound Uses ndash
1 Unborn babies can be photographed to check its size - and
even if there is more than one Its use in scanning goes far
beyond pregnancies Many other parts of the body are
analysed using it (bladder gallstones the heart etc) but it
doesnt even stop there Aeroplane wings can be checked for cracks that would be invisible on the surface
2 Ultrasound Treatments to clean things In fact really dirty
teeth can be cleaned superbly in this way Really delicate
mechanisms - such as in antique clocks and watches - can
also be safely cleaned
3 Ships use in Ultrasound and SONAR to detect fish sea
bottom
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
8
A ship sends a pulse of ultrasound
and receives an echo 0middot3 seconds
later If the speed of sound in water
is 1500 ms calculate its depth
speed = distance time
distance = speed times time
distance = 1500 times 0middot3 = 450 m
BUT this is the total distance travelled by the sound - so the
depth is half of this
Depth = 450 2 = 225 m
4 Used by animals to communicate ndash BatsDolphins
Any sound that you hear as a tone is made of regular evenly spaced waves of air molecules The most noticeable difference
between various tonal sounds is that some sound higher or
lower than others These differences in the pitch of the sound
are caused by different spacing in the waves that is different
frequency
Since the sounds are travelling at about the same speed the
one with the shorter wavelength will go by more frequently it
has a higher frequency or pitch In other words it sounds
higher
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
9
The amplitude of the wave determines the loudness of the
sound
The amplitude of sound waves is
measured in decibels Leaves
rustling in the wind are about 10
decibels a jet engine is about 120
decibels
Amplitude is Loudness
THEME 3 - OPTICS
The only special thing about light is that our eyes can detect it
However it is just a tiny part of a collection of electromagnetic
waves that make up the electromagnetic spectrum
The objects which we see can be placed into one of two
categories luminous objects and non luminous objects
Luminous objects are objects which generate their own light
Eg sun electric bulb
Non Luminous objects are objects which are capable of
reflecting light to our eyes Eg moon grass sky
Without light there would be no sight
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
10
Light is a transverse wave It is one part (region) of the
electromagnetic spectrum Light is the visible region it is
the part used by our eyes to see Like any electromagnetic
wave light can travel through a vacuum Light travels through
the vacuum of space from the Sun to the Earth
Light travels very quickly There is nothing which can travel
faster The speed of light is 300000000 ms
(that is 300 million metres per second - not easy to imagine)
Reflection - ( Bouncing of light)
Any type of wave can be reflected Reflection best occurs from
flat hard surfaces After reflection a wave has the same
speed frequency and wavelength it is only the direction of the
wave that has changed
For light (and other electromagnetic radiation) a flat shiny
surface like a plane mirror is a good reflector
A plane mirror is one
which is straight and not
curved
The light ray which hits
the mirror is called the
incident ray The light ray which
bounces off the mirror is
called the reflected ray The angle of incidence equals the
angle of reflection i = r This means that whatever angle the light ray hits the mirror it will be reflected off at the same
angle
If the surface of the mirror is not smooth but rough or bumpy
then light will be reflected at many different angles The image
in the mirror will be blurred and unclear This is called diffuse
reflection When you look into a mirror you see a reflection
which is an image of the real object
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
11
The image appears to be the
same distance behind the
mirror as the real object is in front of it
This is because the brain
thinks that light travels in
straight lines without changing
direction
The image is called virtual
because it does not really
exist behind the mirror The
virtual image is the same size as the object but with left and
right reversed ( laterally inverted)
Refraction ( bending of light)
Any type of wave can be refracted which means a change of
direction Refraction can occur when the speed of a wave
changes as it moves from one medium to another
After refraction the wave has the same frequency
but a different speed wavelength and direction
When a wave enters a new medium its change in speed will
also change its wavelength If the wave enters the new
medium at any angle other than normal to the boundary then
the change in the waves speed will also change its direction
A material is transparent if you can see through it If you can
see through it it means that light can travel through it
Transparent materials include air glass Perspex and water
Light travels at different speeds in different materials because
they have different densities The higher the density the
slower light travels Light travels fastest in space (a vacuum)
and a little slower in air Light moves noticeably more slowly in
glass than in air because glass is obviously more dense
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
12
A line drawn at right
angles to the
boundary between the
two media (air and
glass) is called a
normal
Light which enters a glass block along a normal (at 90 degrees) does not change direction but it does travel more slowly
through the glass When a ray of light enters a glass block at
an angle other than the normal it changes speed wavelength
and direction as shown below
Conditions of Refraction
The angle i is called the angle of incidence while
angle r is called angle of
refraction The light must
change speed when
crossing the boundary
In going from a less dense medium (air) to a more dense
medium (glass) light bends towards the normalThis means
that i gt r (the angle i is greater than the angle r)
In going from a more dense to a less dense medium (glass to
air) light bends away from the normal How much the light
bends depends on its colour
The change in angle of the light ray is the same when it enters
and leaves the glass If the incident ray had continued without
changing direction then the emergent ray would be parallel to
it Like any wave the speed of a light wave is dependent
upon the properties of the medium
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
13
Refractive Index - n
Index of refraction values (represented by the symbol n) are
numerical index values which are expressed relative to the
speed of light in a vacuum The index of refraction value of a
material is a number which indicates the number of times
slower that a light wave would be in that material than it is in a
vacuum
ή = Speed of light in air
Speed of light in medium
Material Index of Refraction
Vacuum 100
Water 133
Glass 150
Diamond 240
The index of refraction values thus provide a measure of the
relative speed of a light wave in a particular medium
Real and Apparent Depth
To an observer standing at
the side of a swimming pool
objects under the water
appear to be nearer the
surface than they really are
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
14
A fish appears to be nearer to
the surface than it really is
A straight stick appears to be
bent when part in and part
out of water
Both these effects are caused by
refraction of light at the surface of the water Therefore this
effect is related to the refractive
index of the media involved
The real depth of the fish is R and its apparent depth is A It is
clear that n represents the refractive index of light going from
air to water we have
Refractive index n = Real Depth Apparent depth
When light emerges from glass or water into air it speeds up
again As it meets the glass-air boundary at any angle greater than 0o it will refract away from the normal If you look at a
stick that is poking into some water at an angle the stick looks
bent because of refraction The bottom of the stick seems to be
nearer the surface of the water than it really is It also explains
why flat-based swimming pools appear to get shallower as you
look towards the end furthest from you
Total Internal Reflection - Critical Angle
When a light ray emerges from glass into air it is refracted and bends away from the normal so i lt r As i is made bigger the
refracted ray gets closer and closer to the surface of the glass
When the refracted ray is just touching the glass surface that is angle r = 90 degrees than angle i is called the critical
angle
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
15
The critical angle is different for different materials for glass it is about 42 degrees Total internal reflection happens when i is
bigger than the critical angleWhen a light ray tries to move
from glass to air at an angle greater than the critical angle the
refracted ray cannot escape from the glass and total internal
reflection occurs
Refraction cannot happen and all
of the light is reflected
at the glass air boundary as if it
had hit a mirror i = r
It is called internal reflection
because it occurs inside the glass
and total because all the light must
be reflected
Total Internal Reflection (TIR) can occur in prisms and optical
fibres
Total Internal Reflection - Prisms
A right angle prism can be used to
change the direction of a light ray by
90 degrees or 180 degrees
The light ray enters along a normal
and continues straight on until it hits
the back face of the prism Total
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
16
internal reflection occurs here because light strikes the surface
at 45 degrees which is greater than the critical angle
The light ray then emerges from the
prism along a normal and so continues
straight through This type of prism
can be used in a periscope Two right
angle prisms can be used to form a periscope as shown below Total
internal reflection occurs at the back
face of the prisms
A periscope may be used by people
(i) in a submarine to see above the
sea surface
(ii) to see over the heads of people in a crowd
A right angle prism can be used to change
the direction of light by 180
degrees as shown below
The same effect can result from two prisms arranged as shown
belowEither of these arrangements may be used in
binoculars or reflectors on the rear of cars and bicycles
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
8
A ship sends a pulse of ultrasound
and receives an echo 0middot3 seconds
later If the speed of sound in water
is 1500 ms calculate its depth
speed = distance time
distance = speed times time
distance = 1500 times 0middot3 = 450 m
BUT this is the total distance travelled by the sound - so the
depth is half of this
Depth = 450 2 = 225 m
4 Used by animals to communicate ndash BatsDolphins
Any sound that you hear as a tone is made of regular evenly spaced waves of air molecules The most noticeable difference
between various tonal sounds is that some sound higher or
lower than others These differences in the pitch of the sound
are caused by different spacing in the waves that is different
frequency
Since the sounds are travelling at about the same speed the
one with the shorter wavelength will go by more frequently it
has a higher frequency or pitch In other words it sounds
higher
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
9
The amplitude of the wave determines the loudness of the
sound
The amplitude of sound waves is
measured in decibels Leaves
rustling in the wind are about 10
decibels a jet engine is about 120
decibels
Amplitude is Loudness
THEME 3 - OPTICS
The only special thing about light is that our eyes can detect it
However it is just a tiny part of a collection of electromagnetic
waves that make up the electromagnetic spectrum
The objects which we see can be placed into one of two
categories luminous objects and non luminous objects
Luminous objects are objects which generate their own light
Eg sun electric bulb
Non Luminous objects are objects which are capable of
reflecting light to our eyes Eg moon grass sky
Without light there would be no sight
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
10
Light is a transverse wave It is one part (region) of the
electromagnetic spectrum Light is the visible region it is
the part used by our eyes to see Like any electromagnetic
wave light can travel through a vacuum Light travels through
the vacuum of space from the Sun to the Earth
Light travels very quickly There is nothing which can travel
faster The speed of light is 300000000 ms
(that is 300 million metres per second - not easy to imagine)
Reflection - ( Bouncing of light)
Any type of wave can be reflected Reflection best occurs from
flat hard surfaces After reflection a wave has the same
speed frequency and wavelength it is only the direction of the
wave that has changed
For light (and other electromagnetic radiation) a flat shiny
surface like a plane mirror is a good reflector
A plane mirror is one
which is straight and not
curved
The light ray which hits
the mirror is called the
incident ray The light ray which
bounces off the mirror is
called the reflected ray The angle of incidence equals the
angle of reflection i = r This means that whatever angle the light ray hits the mirror it will be reflected off at the same
angle
If the surface of the mirror is not smooth but rough or bumpy
then light will be reflected at many different angles The image
in the mirror will be blurred and unclear This is called diffuse
reflection When you look into a mirror you see a reflection
which is an image of the real object
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
11
The image appears to be the
same distance behind the
mirror as the real object is in front of it
This is because the brain
thinks that light travels in
straight lines without changing
direction
The image is called virtual
because it does not really
exist behind the mirror The
virtual image is the same size as the object but with left and
right reversed ( laterally inverted)
Refraction ( bending of light)
Any type of wave can be refracted which means a change of
direction Refraction can occur when the speed of a wave
changes as it moves from one medium to another
After refraction the wave has the same frequency
but a different speed wavelength and direction
When a wave enters a new medium its change in speed will
also change its wavelength If the wave enters the new
medium at any angle other than normal to the boundary then
the change in the waves speed will also change its direction
A material is transparent if you can see through it If you can
see through it it means that light can travel through it
Transparent materials include air glass Perspex and water
Light travels at different speeds in different materials because
they have different densities The higher the density the
slower light travels Light travels fastest in space (a vacuum)
and a little slower in air Light moves noticeably more slowly in
glass than in air because glass is obviously more dense
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
12
A line drawn at right
angles to the
boundary between the
two media (air and
glass) is called a
normal
Light which enters a glass block along a normal (at 90 degrees) does not change direction but it does travel more slowly
through the glass When a ray of light enters a glass block at
an angle other than the normal it changes speed wavelength
and direction as shown below
Conditions of Refraction
The angle i is called the angle of incidence while
angle r is called angle of
refraction The light must
change speed when
crossing the boundary
In going from a less dense medium (air) to a more dense
medium (glass) light bends towards the normalThis means
that i gt r (the angle i is greater than the angle r)
In going from a more dense to a less dense medium (glass to
air) light bends away from the normal How much the light
bends depends on its colour
The change in angle of the light ray is the same when it enters
and leaves the glass If the incident ray had continued without
changing direction then the emergent ray would be parallel to
it Like any wave the speed of a light wave is dependent
upon the properties of the medium
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
13
Refractive Index - n
Index of refraction values (represented by the symbol n) are
numerical index values which are expressed relative to the
speed of light in a vacuum The index of refraction value of a
material is a number which indicates the number of times
slower that a light wave would be in that material than it is in a
vacuum
ή = Speed of light in air
Speed of light in medium
Material Index of Refraction
Vacuum 100
Water 133
Glass 150
Diamond 240
The index of refraction values thus provide a measure of the
relative speed of a light wave in a particular medium
Real and Apparent Depth
To an observer standing at
the side of a swimming pool
objects under the water
appear to be nearer the
surface than they really are
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
14
A fish appears to be nearer to
the surface than it really is
A straight stick appears to be
bent when part in and part
out of water
Both these effects are caused by
refraction of light at the surface of the water Therefore this
effect is related to the refractive
index of the media involved
The real depth of the fish is R and its apparent depth is A It is
clear that n represents the refractive index of light going from
air to water we have
Refractive index n = Real Depth Apparent depth
When light emerges from glass or water into air it speeds up
again As it meets the glass-air boundary at any angle greater than 0o it will refract away from the normal If you look at a
stick that is poking into some water at an angle the stick looks
bent because of refraction The bottom of the stick seems to be
nearer the surface of the water than it really is It also explains
why flat-based swimming pools appear to get shallower as you
look towards the end furthest from you
Total Internal Reflection - Critical Angle
When a light ray emerges from glass into air it is refracted and bends away from the normal so i lt r As i is made bigger the
refracted ray gets closer and closer to the surface of the glass
When the refracted ray is just touching the glass surface that is angle r = 90 degrees than angle i is called the critical
angle
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
15
The critical angle is different for different materials for glass it is about 42 degrees Total internal reflection happens when i is
bigger than the critical angleWhen a light ray tries to move
from glass to air at an angle greater than the critical angle the
refracted ray cannot escape from the glass and total internal
reflection occurs
Refraction cannot happen and all
of the light is reflected
at the glass air boundary as if it
had hit a mirror i = r
It is called internal reflection
because it occurs inside the glass
and total because all the light must
be reflected
Total Internal Reflection (TIR) can occur in prisms and optical
fibres
Total Internal Reflection - Prisms
A right angle prism can be used to
change the direction of a light ray by
90 degrees or 180 degrees
The light ray enters along a normal
and continues straight on until it hits
the back face of the prism Total
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
16
internal reflection occurs here because light strikes the surface
at 45 degrees which is greater than the critical angle
The light ray then emerges from the
prism along a normal and so continues
straight through This type of prism
can be used in a periscope Two right
angle prisms can be used to form a periscope as shown below Total
internal reflection occurs at the back
face of the prisms
A periscope may be used by people
(i) in a submarine to see above the
sea surface
(ii) to see over the heads of people in a crowd
A right angle prism can be used to change
the direction of light by 180
degrees as shown below
The same effect can result from two prisms arranged as shown
belowEither of these arrangements may be used in
binoculars or reflectors on the rear of cars and bicycles
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
9
The amplitude of the wave determines the loudness of the
sound
The amplitude of sound waves is
measured in decibels Leaves
rustling in the wind are about 10
decibels a jet engine is about 120
decibels
Amplitude is Loudness
THEME 3 - OPTICS
The only special thing about light is that our eyes can detect it
However it is just a tiny part of a collection of electromagnetic
waves that make up the electromagnetic spectrum
The objects which we see can be placed into one of two
categories luminous objects and non luminous objects
Luminous objects are objects which generate their own light
Eg sun electric bulb
Non Luminous objects are objects which are capable of
reflecting light to our eyes Eg moon grass sky
Without light there would be no sight
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
10
Light is a transverse wave It is one part (region) of the
electromagnetic spectrum Light is the visible region it is
the part used by our eyes to see Like any electromagnetic
wave light can travel through a vacuum Light travels through
the vacuum of space from the Sun to the Earth
Light travels very quickly There is nothing which can travel
faster The speed of light is 300000000 ms
(that is 300 million metres per second - not easy to imagine)
Reflection - ( Bouncing of light)
Any type of wave can be reflected Reflection best occurs from
flat hard surfaces After reflection a wave has the same
speed frequency and wavelength it is only the direction of the
wave that has changed
For light (and other electromagnetic radiation) a flat shiny
surface like a plane mirror is a good reflector
A plane mirror is one
which is straight and not
curved
The light ray which hits
the mirror is called the
incident ray The light ray which
bounces off the mirror is
called the reflected ray The angle of incidence equals the
angle of reflection i = r This means that whatever angle the light ray hits the mirror it will be reflected off at the same
angle
If the surface of the mirror is not smooth but rough or bumpy
then light will be reflected at many different angles The image
in the mirror will be blurred and unclear This is called diffuse
reflection When you look into a mirror you see a reflection
which is an image of the real object
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
11
The image appears to be the
same distance behind the
mirror as the real object is in front of it
This is because the brain
thinks that light travels in
straight lines without changing
direction
The image is called virtual
because it does not really
exist behind the mirror The
virtual image is the same size as the object but with left and
right reversed ( laterally inverted)
Refraction ( bending of light)
Any type of wave can be refracted which means a change of
direction Refraction can occur when the speed of a wave
changes as it moves from one medium to another
After refraction the wave has the same frequency
but a different speed wavelength and direction
When a wave enters a new medium its change in speed will
also change its wavelength If the wave enters the new
medium at any angle other than normal to the boundary then
the change in the waves speed will also change its direction
A material is transparent if you can see through it If you can
see through it it means that light can travel through it
Transparent materials include air glass Perspex and water
Light travels at different speeds in different materials because
they have different densities The higher the density the
slower light travels Light travels fastest in space (a vacuum)
and a little slower in air Light moves noticeably more slowly in
glass than in air because glass is obviously more dense
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
12
A line drawn at right
angles to the
boundary between the
two media (air and
glass) is called a
normal
Light which enters a glass block along a normal (at 90 degrees) does not change direction but it does travel more slowly
through the glass When a ray of light enters a glass block at
an angle other than the normal it changes speed wavelength
and direction as shown below
Conditions of Refraction
The angle i is called the angle of incidence while
angle r is called angle of
refraction The light must
change speed when
crossing the boundary
In going from a less dense medium (air) to a more dense
medium (glass) light bends towards the normalThis means
that i gt r (the angle i is greater than the angle r)
In going from a more dense to a less dense medium (glass to
air) light bends away from the normal How much the light
bends depends on its colour
The change in angle of the light ray is the same when it enters
and leaves the glass If the incident ray had continued without
changing direction then the emergent ray would be parallel to
it Like any wave the speed of a light wave is dependent
upon the properties of the medium
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
13
Refractive Index - n
Index of refraction values (represented by the symbol n) are
numerical index values which are expressed relative to the
speed of light in a vacuum The index of refraction value of a
material is a number which indicates the number of times
slower that a light wave would be in that material than it is in a
vacuum
ή = Speed of light in air
Speed of light in medium
Material Index of Refraction
Vacuum 100
Water 133
Glass 150
Diamond 240
The index of refraction values thus provide a measure of the
relative speed of a light wave in a particular medium
Real and Apparent Depth
To an observer standing at
the side of a swimming pool
objects under the water
appear to be nearer the
surface than they really are
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
14
A fish appears to be nearer to
the surface than it really is
A straight stick appears to be
bent when part in and part
out of water
Both these effects are caused by
refraction of light at the surface of the water Therefore this
effect is related to the refractive
index of the media involved
The real depth of the fish is R and its apparent depth is A It is
clear that n represents the refractive index of light going from
air to water we have
Refractive index n = Real Depth Apparent depth
When light emerges from glass or water into air it speeds up
again As it meets the glass-air boundary at any angle greater than 0o it will refract away from the normal If you look at a
stick that is poking into some water at an angle the stick looks
bent because of refraction The bottom of the stick seems to be
nearer the surface of the water than it really is It also explains
why flat-based swimming pools appear to get shallower as you
look towards the end furthest from you
Total Internal Reflection - Critical Angle
When a light ray emerges from glass into air it is refracted and bends away from the normal so i lt r As i is made bigger the
refracted ray gets closer and closer to the surface of the glass
When the refracted ray is just touching the glass surface that is angle r = 90 degrees than angle i is called the critical
angle
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
15
The critical angle is different for different materials for glass it is about 42 degrees Total internal reflection happens when i is
bigger than the critical angleWhen a light ray tries to move
from glass to air at an angle greater than the critical angle the
refracted ray cannot escape from the glass and total internal
reflection occurs
Refraction cannot happen and all
of the light is reflected
at the glass air boundary as if it
had hit a mirror i = r
It is called internal reflection
because it occurs inside the glass
and total because all the light must
be reflected
Total Internal Reflection (TIR) can occur in prisms and optical
fibres
Total Internal Reflection - Prisms
A right angle prism can be used to
change the direction of a light ray by
90 degrees or 180 degrees
The light ray enters along a normal
and continues straight on until it hits
the back face of the prism Total
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
16
internal reflection occurs here because light strikes the surface
at 45 degrees which is greater than the critical angle
The light ray then emerges from the
prism along a normal and so continues
straight through This type of prism
can be used in a periscope Two right
angle prisms can be used to form a periscope as shown below Total
internal reflection occurs at the back
face of the prisms
A periscope may be used by people
(i) in a submarine to see above the
sea surface
(ii) to see over the heads of people in a crowd
A right angle prism can be used to change
the direction of light by 180
degrees as shown below
The same effect can result from two prisms arranged as shown
belowEither of these arrangements may be used in
binoculars or reflectors on the rear of cars and bicycles
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
10
Light is a transverse wave It is one part (region) of the
electromagnetic spectrum Light is the visible region it is
the part used by our eyes to see Like any electromagnetic
wave light can travel through a vacuum Light travels through
the vacuum of space from the Sun to the Earth
Light travels very quickly There is nothing which can travel
faster The speed of light is 300000000 ms
(that is 300 million metres per second - not easy to imagine)
Reflection - ( Bouncing of light)
Any type of wave can be reflected Reflection best occurs from
flat hard surfaces After reflection a wave has the same
speed frequency and wavelength it is only the direction of the
wave that has changed
For light (and other electromagnetic radiation) a flat shiny
surface like a plane mirror is a good reflector
A plane mirror is one
which is straight and not
curved
The light ray which hits
the mirror is called the
incident ray The light ray which
bounces off the mirror is
called the reflected ray The angle of incidence equals the
angle of reflection i = r This means that whatever angle the light ray hits the mirror it will be reflected off at the same
angle
If the surface of the mirror is not smooth but rough or bumpy
then light will be reflected at many different angles The image
in the mirror will be blurred and unclear This is called diffuse
reflection When you look into a mirror you see a reflection
which is an image of the real object
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
11
The image appears to be the
same distance behind the
mirror as the real object is in front of it
This is because the brain
thinks that light travels in
straight lines without changing
direction
The image is called virtual
because it does not really
exist behind the mirror The
virtual image is the same size as the object but with left and
right reversed ( laterally inverted)
Refraction ( bending of light)
Any type of wave can be refracted which means a change of
direction Refraction can occur when the speed of a wave
changes as it moves from one medium to another
After refraction the wave has the same frequency
but a different speed wavelength and direction
When a wave enters a new medium its change in speed will
also change its wavelength If the wave enters the new
medium at any angle other than normal to the boundary then
the change in the waves speed will also change its direction
A material is transparent if you can see through it If you can
see through it it means that light can travel through it
Transparent materials include air glass Perspex and water
Light travels at different speeds in different materials because
they have different densities The higher the density the
slower light travels Light travels fastest in space (a vacuum)
and a little slower in air Light moves noticeably more slowly in
glass than in air because glass is obviously more dense
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
12
A line drawn at right
angles to the
boundary between the
two media (air and
glass) is called a
normal
Light which enters a glass block along a normal (at 90 degrees) does not change direction but it does travel more slowly
through the glass When a ray of light enters a glass block at
an angle other than the normal it changes speed wavelength
and direction as shown below
Conditions of Refraction
The angle i is called the angle of incidence while
angle r is called angle of
refraction The light must
change speed when
crossing the boundary
In going from a less dense medium (air) to a more dense
medium (glass) light bends towards the normalThis means
that i gt r (the angle i is greater than the angle r)
In going from a more dense to a less dense medium (glass to
air) light bends away from the normal How much the light
bends depends on its colour
The change in angle of the light ray is the same when it enters
and leaves the glass If the incident ray had continued without
changing direction then the emergent ray would be parallel to
it Like any wave the speed of a light wave is dependent
upon the properties of the medium
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
13
Refractive Index - n
Index of refraction values (represented by the symbol n) are
numerical index values which are expressed relative to the
speed of light in a vacuum The index of refraction value of a
material is a number which indicates the number of times
slower that a light wave would be in that material than it is in a
vacuum
ή = Speed of light in air
Speed of light in medium
Material Index of Refraction
Vacuum 100
Water 133
Glass 150
Diamond 240
The index of refraction values thus provide a measure of the
relative speed of a light wave in a particular medium
Real and Apparent Depth
To an observer standing at
the side of a swimming pool
objects under the water
appear to be nearer the
surface than they really are
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
14
A fish appears to be nearer to
the surface than it really is
A straight stick appears to be
bent when part in and part
out of water
Both these effects are caused by
refraction of light at the surface of the water Therefore this
effect is related to the refractive
index of the media involved
The real depth of the fish is R and its apparent depth is A It is
clear that n represents the refractive index of light going from
air to water we have
Refractive index n = Real Depth Apparent depth
When light emerges from glass or water into air it speeds up
again As it meets the glass-air boundary at any angle greater than 0o it will refract away from the normal If you look at a
stick that is poking into some water at an angle the stick looks
bent because of refraction The bottom of the stick seems to be
nearer the surface of the water than it really is It also explains
why flat-based swimming pools appear to get shallower as you
look towards the end furthest from you
Total Internal Reflection - Critical Angle
When a light ray emerges from glass into air it is refracted and bends away from the normal so i lt r As i is made bigger the
refracted ray gets closer and closer to the surface of the glass
When the refracted ray is just touching the glass surface that is angle r = 90 degrees than angle i is called the critical
angle
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
15
The critical angle is different for different materials for glass it is about 42 degrees Total internal reflection happens when i is
bigger than the critical angleWhen a light ray tries to move
from glass to air at an angle greater than the critical angle the
refracted ray cannot escape from the glass and total internal
reflection occurs
Refraction cannot happen and all
of the light is reflected
at the glass air boundary as if it
had hit a mirror i = r
It is called internal reflection
because it occurs inside the glass
and total because all the light must
be reflected
Total Internal Reflection (TIR) can occur in prisms and optical
fibres
Total Internal Reflection - Prisms
A right angle prism can be used to
change the direction of a light ray by
90 degrees or 180 degrees
The light ray enters along a normal
and continues straight on until it hits
the back face of the prism Total
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
16
internal reflection occurs here because light strikes the surface
at 45 degrees which is greater than the critical angle
The light ray then emerges from the
prism along a normal and so continues
straight through This type of prism
can be used in a periscope Two right
angle prisms can be used to form a periscope as shown below Total
internal reflection occurs at the back
face of the prisms
A periscope may be used by people
(i) in a submarine to see above the
sea surface
(ii) to see over the heads of people in a crowd
A right angle prism can be used to change
the direction of light by 180
degrees as shown below
The same effect can result from two prisms arranged as shown
belowEither of these arrangements may be used in
binoculars or reflectors on the rear of cars and bicycles
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
11
The image appears to be the
same distance behind the
mirror as the real object is in front of it
This is because the brain
thinks that light travels in
straight lines without changing
direction
The image is called virtual
because it does not really
exist behind the mirror The
virtual image is the same size as the object but with left and
right reversed ( laterally inverted)
Refraction ( bending of light)
Any type of wave can be refracted which means a change of
direction Refraction can occur when the speed of a wave
changes as it moves from one medium to another
After refraction the wave has the same frequency
but a different speed wavelength and direction
When a wave enters a new medium its change in speed will
also change its wavelength If the wave enters the new
medium at any angle other than normal to the boundary then
the change in the waves speed will also change its direction
A material is transparent if you can see through it If you can
see through it it means that light can travel through it
Transparent materials include air glass Perspex and water
Light travels at different speeds in different materials because
they have different densities The higher the density the
slower light travels Light travels fastest in space (a vacuum)
and a little slower in air Light moves noticeably more slowly in
glass than in air because glass is obviously more dense
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
12
A line drawn at right
angles to the
boundary between the
two media (air and
glass) is called a
normal
Light which enters a glass block along a normal (at 90 degrees) does not change direction but it does travel more slowly
through the glass When a ray of light enters a glass block at
an angle other than the normal it changes speed wavelength
and direction as shown below
Conditions of Refraction
The angle i is called the angle of incidence while
angle r is called angle of
refraction The light must
change speed when
crossing the boundary
In going from a less dense medium (air) to a more dense
medium (glass) light bends towards the normalThis means
that i gt r (the angle i is greater than the angle r)
In going from a more dense to a less dense medium (glass to
air) light bends away from the normal How much the light
bends depends on its colour
The change in angle of the light ray is the same when it enters
and leaves the glass If the incident ray had continued without
changing direction then the emergent ray would be parallel to
it Like any wave the speed of a light wave is dependent
upon the properties of the medium
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
13
Refractive Index - n
Index of refraction values (represented by the symbol n) are
numerical index values which are expressed relative to the
speed of light in a vacuum The index of refraction value of a
material is a number which indicates the number of times
slower that a light wave would be in that material than it is in a
vacuum
ή = Speed of light in air
Speed of light in medium
Material Index of Refraction
Vacuum 100
Water 133
Glass 150
Diamond 240
The index of refraction values thus provide a measure of the
relative speed of a light wave in a particular medium
Real and Apparent Depth
To an observer standing at
the side of a swimming pool
objects under the water
appear to be nearer the
surface than they really are
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
14
A fish appears to be nearer to
the surface than it really is
A straight stick appears to be
bent when part in and part
out of water
Both these effects are caused by
refraction of light at the surface of the water Therefore this
effect is related to the refractive
index of the media involved
The real depth of the fish is R and its apparent depth is A It is
clear that n represents the refractive index of light going from
air to water we have
Refractive index n = Real Depth Apparent depth
When light emerges from glass or water into air it speeds up
again As it meets the glass-air boundary at any angle greater than 0o it will refract away from the normal If you look at a
stick that is poking into some water at an angle the stick looks
bent because of refraction The bottom of the stick seems to be
nearer the surface of the water than it really is It also explains
why flat-based swimming pools appear to get shallower as you
look towards the end furthest from you
Total Internal Reflection - Critical Angle
When a light ray emerges from glass into air it is refracted and bends away from the normal so i lt r As i is made bigger the
refracted ray gets closer and closer to the surface of the glass
When the refracted ray is just touching the glass surface that is angle r = 90 degrees than angle i is called the critical
angle
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
15
The critical angle is different for different materials for glass it is about 42 degrees Total internal reflection happens when i is
bigger than the critical angleWhen a light ray tries to move
from glass to air at an angle greater than the critical angle the
refracted ray cannot escape from the glass and total internal
reflection occurs
Refraction cannot happen and all
of the light is reflected
at the glass air boundary as if it
had hit a mirror i = r
It is called internal reflection
because it occurs inside the glass
and total because all the light must
be reflected
Total Internal Reflection (TIR) can occur in prisms and optical
fibres
Total Internal Reflection - Prisms
A right angle prism can be used to
change the direction of a light ray by
90 degrees or 180 degrees
The light ray enters along a normal
and continues straight on until it hits
the back face of the prism Total
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
16
internal reflection occurs here because light strikes the surface
at 45 degrees which is greater than the critical angle
The light ray then emerges from the
prism along a normal and so continues
straight through This type of prism
can be used in a periscope Two right
angle prisms can be used to form a periscope as shown below Total
internal reflection occurs at the back
face of the prisms
A periscope may be used by people
(i) in a submarine to see above the
sea surface
(ii) to see over the heads of people in a crowd
A right angle prism can be used to change
the direction of light by 180
degrees as shown below
The same effect can result from two prisms arranged as shown
belowEither of these arrangements may be used in
binoculars or reflectors on the rear of cars and bicycles
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
12
A line drawn at right
angles to the
boundary between the
two media (air and
glass) is called a
normal
Light which enters a glass block along a normal (at 90 degrees) does not change direction but it does travel more slowly
through the glass When a ray of light enters a glass block at
an angle other than the normal it changes speed wavelength
and direction as shown below
Conditions of Refraction
The angle i is called the angle of incidence while
angle r is called angle of
refraction The light must
change speed when
crossing the boundary
In going from a less dense medium (air) to a more dense
medium (glass) light bends towards the normalThis means
that i gt r (the angle i is greater than the angle r)
In going from a more dense to a less dense medium (glass to
air) light bends away from the normal How much the light
bends depends on its colour
The change in angle of the light ray is the same when it enters
and leaves the glass If the incident ray had continued without
changing direction then the emergent ray would be parallel to
it Like any wave the speed of a light wave is dependent
upon the properties of the medium
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
13
Refractive Index - n
Index of refraction values (represented by the symbol n) are
numerical index values which are expressed relative to the
speed of light in a vacuum The index of refraction value of a
material is a number which indicates the number of times
slower that a light wave would be in that material than it is in a
vacuum
ή = Speed of light in air
Speed of light in medium
Material Index of Refraction
Vacuum 100
Water 133
Glass 150
Diamond 240
The index of refraction values thus provide a measure of the
relative speed of a light wave in a particular medium
Real and Apparent Depth
To an observer standing at
the side of a swimming pool
objects under the water
appear to be nearer the
surface than they really are
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
14
A fish appears to be nearer to
the surface than it really is
A straight stick appears to be
bent when part in and part
out of water
Both these effects are caused by
refraction of light at the surface of the water Therefore this
effect is related to the refractive
index of the media involved
The real depth of the fish is R and its apparent depth is A It is
clear that n represents the refractive index of light going from
air to water we have
Refractive index n = Real Depth Apparent depth
When light emerges from glass or water into air it speeds up
again As it meets the glass-air boundary at any angle greater than 0o it will refract away from the normal If you look at a
stick that is poking into some water at an angle the stick looks
bent because of refraction The bottom of the stick seems to be
nearer the surface of the water than it really is It also explains
why flat-based swimming pools appear to get shallower as you
look towards the end furthest from you
Total Internal Reflection - Critical Angle
When a light ray emerges from glass into air it is refracted and bends away from the normal so i lt r As i is made bigger the
refracted ray gets closer and closer to the surface of the glass
When the refracted ray is just touching the glass surface that is angle r = 90 degrees than angle i is called the critical
angle
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
15
The critical angle is different for different materials for glass it is about 42 degrees Total internal reflection happens when i is
bigger than the critical angleWhen a light ray tries to move
from glass to air at an angle greater than the critical angle the
refracted ray cannot escape from the glass and total internal
reflection occurs
Refraction cannot happen and all
of the light is reflected
at the glass air boundary as if it
had hit a mirror i = r
It is called internal reflection
because it occurs inside the glass
and total because all the light must
be reflected
Total Internal Reflection (TIR) can occur in prisms and optical
fibres
Total Internal Reflection - Prisms
A right angle prism can be used to
change the direction of a light ray by
90 degrees or 180 degrees
The light ray enters along a normal
and continues straight on until it hits
the back face of the prism Total
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
16
internal reflection occurs here because light strikes the surface
at 45 degrees which is greater than the critical angle
The light ray then emerges from the
prism along a normal and so continues
straight through This type of prism
can be used in a periscope Two right
angle prisms can be used to form a periscope as shown below Total
internal reflection occurs at the back
face of the prisms
A periscope may be used by people
(i) in a submarine to see above the
sea surface
(ii) to see over the heads of people in a crowd
A right angle prism can be used to change
the direction of light by 180
degrees as shown below
The same effect can result from two prisms arranged as shown
belowEither of these arrangements may be used in
binoculars or reflectors on the rear of cars and bicycles
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
13
Refractive Index - n
Index of refraction values (represented by the symbol n) are
numerical index values which are expressed relative to the
speed of light in a vacuum The index of refraction value of a
material is a number which indicates the number of times
slower that a light wave would be in that material than it is in a
vacuum
ή = Speed of light in air
Speed of light in medium
Material Index of Refraction
Vacuum 100
Water 133
Glass 150
Diamond 240
The index of refraction values thus provide a measure of the
relative speed of a light wave in a particular medium
Real and Apparent Depth
To an observer standing at
the side of a swimming pool
objects under the water
appear to be nearer the
surface than they really are
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
14
A fish appears to be nearer to
the surface than it really is
A straight stick appears to be
bent when part in and part
out of water
Both these effects are caused by
refraction of light at the surface of the water Therefore this
effect is related to the refractive
index of the media involved
The real depth of the fish is R and its apparent depth is A It is
clear that n represents the refractive index of light going from
air to water we have
Refractive index n = Real Depth Apparent depth
When light emerges from glass or water into air it speeds up
again As it meets the glass-air boundary at any angle greater than 0o it will refract away from the normal If you look at a
stick that is poking into some water at an angle the stick looks
bent because of refraction The bottom of the stick seems to be
nearer the surface of the water than it really is It also explains
why flat-based swimming pools appear to get shallower as you
look towards the end furthest from you
Total Internal Reflection - Critical Angle
When a light ray emerges from glass into air it is refracted and bends away from the normal so i lt r As i is made bigger the
refracted ray gets closer and closer to the surface of the glass
When the refracted ray is just touching the glass surface that is angle r = 90 degrees than angle i is called the critical
angle
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
15
The critical angle is different for different materials for glass it is about 42 degrees Total internal reflection happens when i is
bigger than the critical angleWhen a light ray tries to move
from glass to air at an angle greater than the critical angle the
refracted ray cannot escape from the glass and total internal
reflection occurs
Refraction cannot happen and all
of the light is reflected
at the glass air boundary as if it
had hit a mirror i = r
It is called internal reflection
because it occurs inside the glass
and total because all the light must
be reflected
Total Internal Reflection (TIR) can occur in prisms and optical
fibres
Total Internal Reflection - Prisms
A right angle prism can be used to
change the direction of a light ray by
90 degrees or 180 degrees
The light ray enters along a normal
and continues straight on until it hits
the back face of the prism Total
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
16
internal reflection occurs here because light strikes the surface
at 45 degrees which is greater than the critical angle
The light ray then emerges from the
prism along a normal and so continues
straight through This type of prism
can be used in a periscope Two right
angle prisms can be used to form a periscope as shown below Total
internal reflection occurs at the back
face of the prisms
A periscope may be used by people
(i) in a submarine to see above the
sea surface
(ii) to see over the heads of people in a crowd
A right angle prism can be used to change
the direction of light by 180
degrees as shown below
The same effect can result from two prisms arranged as shown
belowEither of these arrangements may be used in
binoculars or reflectors on the rear of cars and bicycles
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
14
A fish appears to be nearer to
the surface than it really is
A straight stick appears to be
bent when part in and part
out of water
Both these effects are caused by
refraction of light at the surface of the water Therefore this
effect is related to the refractive
index of the media involved
The real depth of the fish is R and its apparent depth is A It is
clear that n represents the refractive index of light going from
air to water we have
Refractive index n = Real Depth Apparent depth
When light emerges from glass or water into air it speeds up
again As it meets the glass-air boundary at any angle greater than 0o it will refract away from the normal If you look at a
stick that is poking into some water at an angle the stick looks
bent because of refraction The bottom of the stick seems to be
nearer the surface of the water than it really is It also explains
why flat-based swimming pools appear to get shallower as you
look towards the end furthest from you
Total Internal Reflection - Critical Angle
When a light ray emerges from glass into air it is refracted and bends away from the normal so i lt r As i is made bigger the
refracted ray gets closer and closer to the surface of the glass
When the refracted ray is just touching the glass surface that is angle r = 90 degrees than angle i is called the critical
angle
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
15
The critical angle is different for different materials for glass it is about 42 degrees Total internal reflection happens when i is
bigger than the critical angleWhen a light ray tries to move
from glass to air at an angle greater than the critical angle the
refracted ray cannot escape from the glass and total internal
reflection occurs
Refraction cannot happen and all
of the light is reflected
at the glass air boundary as if it
had hit a mirror i = r
It is called internal reflection
because it occurs inside the glass
and total because all the light must
be reflected
Total Internal Reflection (TIR) can occur in prisms and optical
fibres
Total Internal Reflection - Prisms
A right angle prism can be used to
change the direction of a light ray by
90 degrees or 180 degrees
The light ray enters along a normal
and continues straight on until it hits
the back face of the prism Total
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
16
internal reflection occurs here because light strikes the surface
at 45 degrees which is greater than the critical angle
The light ray then emerges from the
prism along a normal and so continues
straight through This type of prism
can be used in a periscope Two right
angle prisms can be used to form a periscope as shown below Total
internal reflection occurs at the back
face of the prisms
A periscope may be used by people
(i) in a submarine to see above the
sea surface
(ii) to see over the heads of people in a crowd
A right angle prism can be used to change
the direction of light by 180
degrees as shown below
The same effect can result from two prisms arranged as shown
belowEither of these arrangements may be used in
binoculars or reflectors on the rear of cars and bicycles
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
15
The critical angle is different for different materials for glass it is about 42 degrees Total internal reflection happens when i is
bigger than the critical angleWhen a light ray tries to move
from glass to air at an angle greater than the critical angle the
refracted ray cannot escape from the glass and total internal
reflection occurs
Refraction cannot happen and all
of the light is reflected
at the glass air boundary as if it
had hit a mirror i = r
It is called internal reflection
because it occurs inside the glass
and total because all the light must
be reflected
Total Internal Reflection (TIR) can occur in prisms and optical
fibres
Total Internal Reflection - Prisms
A right angle prism can be used to
change the direction of a light ray by
90 degrees or 180 degrees
The light ray enters along a normal
and continues straight on until it hits
the back face of the prism Total
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
16
internal reflection occurs here because light strikes the surface
at 45 degrees which is greater than the critical angle
The light ray then emerges from the
prism along a normal and so continues
straight through This type of prism
can be used in a periscope Two right
angle prisms can be used to form a periscope as shown below Total
internal reflection occurs at the back
face of the prisms
A periscope may be used by people
(i) in a submarine to see above the
sea surface
(ii) to see over the heads of people in a crowd
A right angle prism can be used to change
the direction of light by 180
degrees as shown below
The same effect can result from two prisms arranged as shown
belowEither of these arrangements may be used in
binoculars or reflectors on the rear of cars and bicycles
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
16
internal reflection occurs here because light strikes the surface
at 45 degrees which is greater than the critical angle
The light ray then emerges from the
prism along a normal and so continues
straight through This type of prism
can be used in a periscope Two right
angle prisms can be used to form a periscope as shown below Total
internal reflection occurs at the back
face of the prisms
A periscope may be used by people
(i) in a submarine to see above the
sea surface
(ii) to see over the heads of people in a crowd
A right angle prism can be used to change
the direction of light by 180
degrees as shown below
The same effect can result from two prisms arranged as shown
belowEither of these arrangements may be used in
binoculars or reflectors on the rear of cars and bicycles
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
17
Optical fibres
An optical fibre is a long thin strand of glass which has an outer
plastic coating
Light from a laser enters at one end of the fibre striking the
surface of the glass at an angle greater than the critical
angle Total internal reflection occurs at the glass surface
and the light cannot escape until it reaches the other end of the
fibre The plastic coating prevents the glass surface from
getting scratched which might allow the light to escape
through the side of the fibre
Optical fibres are used in endoscopes and for
telecommunications
Telecommunications
Information is transmitted (sent) using electromagnetic waves
light in optical fibres This information can be used in many
ways including telephone television fax and internet
A digital signal has a higher quality than an analogue signal
An endoscope is an instrument used by Doctors and
Surgeons A bundle of very thin optical fibres is used with
lenses to see inside a body
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
18
Dispersion of Light
A glass prism of angle 60 degrees can
disperse white light
into its different colours (called a
spectrum)
The seven colours of light are
Red Orange Yellow Green Blue Indigo and violet
Different colours of light have each a different frequency and wavelength The different colours are refracted by different
amounts Red light has the longest wavelength and is
refracted least Violet light has the shortest wavelength and is
refracted most
The source of light may
also emit infra-red and
ultraviolet light
Infra-red light is heat
radiation with a longer wavelength than red light A
thermometer placed at IR will show a rise in temperature Ultraviolet light has a shorter wavelength than violet light A
fluorescent material will glow when placed at UV
Lenses
A lens is a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an
image
First consider a convex lens Suppose that several rays of
light approach the lens and suppose that these rays of light
are traveling parallel to the principal axis (The line that passes
from the optical centre the centre of the lens)
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
19
Upon reaching the front face of the lens each ray of light will
refract towards the normal to the surface Once the light ray
refracts across the boundary and enters the lens it travels in a
straight line until it reaches the back face of the lens At this
boundary each ray of light will refract away from the normal to
the surface it will bend away from the normal line
The principal focus is that point on the principal axis through
which all rays pass after passing through the lens
Refraction for Diverging Lenses (concave lens)
The incident rays diverge upon refracting through the lens For
this reason a concave lens can never produce a real image
Concave lenses produce images which are virtual
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
20
Refraction Rules for a Converging Lens
There are three rules of refraction for converging lenses by
which we can predict the formation of an image
1 Any incident ray traveling
parallel to the principal axis
of a converging lens will refract through the lens and
travel through the focal point
on the opposite side of the
lens
2 Any incident ray traveling through the focal point on
the way to the lens will
refract through the lens
and travel parallel to
the principal
axis
3 An incident ray which passes through
the center of the lens will in affect
continue in the same direction that it
had when it entered the lens
Converging Lenses - Ray Diagrams
Step-by-Step Method for Drawing Ray
Diagrams
The method of drawing ray diagrams for
a convex lens is described below
1 Pick a point on the top of the object
and draw three incident rays traveling
towards the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
21
Using a straight edge accurately draw one ray so that it passes
exactly through the focal point on the way to the lens Draw
the second ray such that it travels exactly parallel to the
principal axis Draw the third incident ray such that it travels
directly to the exact center of the lens Place arrowheads upon the rays to indicate their direction of travel
2 Once these incident rays strike the lens refract them
according to the three rules of refraction for converging lenses
3 Mark the image of the top of the object
The image point of the top of the object is the point where the
three refracted rays intersect If the object is a vertical line
then the image is also a vertical line and its bottom is located
upon the principal axis
Converging Lenses - Object-Image Relations
Case 1 The object is located beyond 2F
When the object is located beyond the 2F point the
image will always be located
somewhere in between the 2F
point and the focal point (F)
on the other side of the lens In this case the image will be an
inverted image That is to say the image is upside down In this case the image is reduced in size in other words the
image dimensions are smaller than the object dimensions
Finally the image is a real image
Case 2 The object is located at 2F
When the object is located at the
2F point the image will also be
located at the 2F point on the other side of the lens In this case the
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
22
image will be inverted The image dimensions are equal to
the object dimensions Finally the image is a real image
Case 3 The object is located between 2F and F
In this case the image will be inverted (ie a right-side-up object
results in an upside-down image)
The image dimensions are larger than
the object dimensions(Magnified)
Finally the image is a real image
Case 4 The object is located at F
When the object is located at the
focal point no image is formed After
refracting the light rays are traveling parallel to each other and cannot
produce an image
Case 5 The object is located
in front of F
When the object is located at a location in front of the focal
point the image will always be
located somewhere on the same side of the lens as the object
The image is located behind the object In this case the image
will be an upright image That is to say if the object is right-
side up then the image will also be right-side up In this case
the image is magnified Finally the image is a virtual image
Light rays diverge upon refraction for this reason the image location can only be found by extending the refracted rays
backwards on the objects side the lens
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
23
Object at Image at Size Orientation Nature Use
Infinity F Diminished Inverted Real Image on a
film (at infinity)
gt2F Between F
and 2F Diminished Inverted Real
Image on a film
(close up)
2F 2F Same size Inverted Real Photocopier
Between 2F and F
gt2F Magnified Inverted Real Projector
F Infinity Magnified Inverted Real Spot light
ltF ltF (on same
side) Magnified Upright Virtual
Magnifying glass
Magnification
The magnification is the ratio of the height of the object to
the height of the image If the magnification is greater than 1 than the image is greater than object (magnified) If the
magnification is a number with an absolute value less than 1
than the image is smaller than object (diminished)
Magnification = height of image = image distance
height of object object distance
The Electromagnetic and Visible Spectra
Electromagnetic waves are waves which are capable of traveling through a vacuum unlike mechanical waves which
require a medium
Electromagnetic waves exist with an enormous range of
frequencies This continuous range of frequencies is known as
the electromagnetic spectrum The longer wavelength
lower frequency regions are located on the far right of the
spectrum and the shorter wavelength higher frequency regions
are on the far left
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
24
Remember also that its the high frequency waves that are the
most dangerous (Gamma rays)
All electro-magnetic waves travel in a straight line
Electromagnetic waves are transverse waves which have
both an electric and a magnetic effect All electromagnetic waves travel at the same speed (in a
vacuum)
Electromagnetic waves travel very quicklyThere is
nothing which can travel faster Their speed is
300000000 ms in a vacuum
They can have a wide variety of wavelengths and
frequencies which form the electromagnetic spectrum
Radio Waves
These are the longest of all the electro-magnetic waves and are used in telecommunications (radio and TV broadcasts as
well as portable phones and walkie talkies)
Microwaves
These are really just very short radio waves and are very
useful in communications Uses
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
25
Satellite Dishes - Microwaves are used to transmit
television signals to satellites in orbit microwaves are also
able to travel through the atmosphere This means we can
transmit signals back to the ground
Microwave Ovens - Microwave ovens also use microwaves as
they can be tuned (all microwaves use a frequency of 2450
MHz no matter what their power) to match the vibrations of
water molecules The waves just make the molecules vibrate
with a larger amplitude which heats the food up
Microwaves in Cars - Microwaves reflect well off metal
objects - this fact is put to good use in speed guns and speed
traps Some cars are fitted with low power microwave emitters
at the back to help drivers park safely
Infra Red
Beyond the red end of the visible spectrum is infra red This is
detectable by our skin as heat radiation
A filament lamp emits light and infra red radiation (heat
radiation) We can see the red light and feel the warmth on
our skin
The sun also emits huge amounts of infra-red radiation It is
this that keeps the Earth warm and can also heat our homes
for free
Visible Light
There are many millions of colours which we can distinguish with our eyes Each colour of light we see has a different
wavelength (and frequency) The longest wavelength light we
can see is red at about 700 nm (700 times 10-9 m) Any longer
than this and we cannot see it The shortest wavelength light
we can see is violet at about 400 nm (400 times 10-9 m) Any
shorter than this and we see nothing
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
Form 4 ndash Unit 1 ndash Theme 3 ndash Nature of Waves
26
Ultra Violet
Beyond violet is a dangerous type of radiation called ultra violet UV is also emited from the Sun It is to this that our
bodies respond when out in the sunshine for too long
A brown pigment is produced in the skin to help protect our
living cells from destruction - or even cancer UV is partly
absorbed by the ozone layer but it is still important to apply
sunscreen as an extra layer of protection
X-Rays
An X-ray photograph is taken to examine broken bone or of the teeth X-rays are even more dangerous than UV but are
amazingly useful X-rays are absorbed by bone but pass
almost perfectly through flesh
Gamma Waves
These are the most dangerous and penetrating form of electro-
magnetic waves Gamma rays are emitted by some radioactive
nuclei so have to be stored in lead-lined boxes
Gamma waves have the shortest wavelengths and highest
frequency They are also produced during supernova
explosions Despite the apparent danger they can be amazingly useful Amongst others they are widely used in
hospitals Some medical imaging equipment involves the use of
gamma rays Gamma waves can also be used to kill cancerous
cells by direct exposure
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