Geometrical Optics • Reflection • Refraction • Critical angle • Total internal reflection Lecture 16: Polarisation of light waves
Geometrical Optics
• Reflection
• Refraction
• Critical angle
• Total internal reflection
Lecture 16:
Polarisation of light waves
Geometrical Optics- subset of optics concerning
interaction of light with macroscopic material
Geometrical Optics
Optics—Branch of Physics,
concerning the interaction of light with matter
Dimension larger than a human hair ≈ 50mm
Light can travel through
•empty space,
•air, glass, water,
•cornea,
•eye lens etc.
each one referred to as a medium
Geometrical Optics ray optics
Light Ray –beam of light
Light rays will travel in a straight line if they
remain in the same medium
At the boundary between two media, the light
ray can change direction by
Reflection or Refraction
Reflection
For a mirror (smooth metal surface)
“all” light will be reflected
Reflection
Normal
Incident Ray Reflected Ray
qi qr
Smooth
Metal surface
Rough Surface
No unique angle of reflection for all rays
Light reflected in all directions
Diffuse reflection
Reflection
Majority of objects (clothing, plants, people, etc)
are visible because they reflect light in
a diffuse manner.
Normal
Incident Ray Reflected Ray
qi qr
Refraction At the surface of transparent media, glass,
water etc both reflection and refraction occur.
Normal Incident Ray
Reflected Ray
Refracted Ray
Medium 1
Medium 2
q1
q2
q1
Light ray changes direction going from one
medium to another.
Which way does it bend and by how much?
Is q2<q1 or is q2>q1
Refraction (deflection from a straight path in
passing obliquely from one medium
( such as air) into another (such as glass)
Answer
Depends on the speed of light in both media
q2
speed of light in
the material = v
Index of refraction (n) of the medium
cn
v
The amount by which a medium reduces the
speed of light is characterised by
Vacuum 1(by definition)
Air 1.0003
Glass 1.52
Water 1.33
Diamond 2.42
Indices of Refraction
Refraction
Speed of light in a vacuum: c = 3x108 ms-1
Example
Calculate the speed of light in diamond
8 18 13 10
1.24 102.42
c msv ms
n
Refraction
Example
How long does it take light to travel
394cm in glass
8 18 13 10
1.97 101.52
msv ms
8
8 1
3.942 10
1.97 10
mt s
ms
dt
v
Calculate the speed of light in glass
cv
n
Normal
q1
q2
Incident
Ray
Medium 1
Medium 2
q1
q2
n2 > n1 n2 < n1
1 1
2 2
Sin v
Sin v
q
q
1 1
2 2
/
/
Sin c n
Sin c n
q
q
1 2
2 1
Sin n
Sin n
q
q
1 1 2 2n Sin n Sinq q
where v1 and v2 are the
speeds of light in media
1 and 2 respectively
Monochromatic light (one colour or frequency)
Refraction
Normal
Incident
Ray
cn
v
Refraction
product nSinq remains constant as
light crosses a boundary from
one medium to another
Incident and refracted rays and the normal
are all in the same plane
1 1 2 2n Sin n Sinq q
Law of refraction or Snell’s law
Example
A laser beam is directed upwards from below
the surface of a lake at an angle of 35º to the
vertical. Determine the angle at which the light
emerges into the air. n1(air) =1.0003 and
n2 (water) =1.33
1 1 2 2n Sin n Sinq q
0
11.0003 1.33 35Sin Sinq
Normal
air
water
q1 n1
n2
Snell’s law
0
1
1
0
1
1.33 35
1.0003
0.76
49.7
SinSin
Sin
q
q
q
35º
If light enters the water at an angle of 49.70,
what is its refraction angle in the water?
Normal
Incident
Ray
Medium 1
Medium 2
q1
q2
n2 > n1
n2 < n1
1 1 2 2n Sin n Sinq q
Monochromatic light (one colour or frequency)
n2 > n1
or
Normal incidence q1 = 0
therefore q2 = 0.
transmitted ray is not deviated
independent of the materials on either
side of the interface.
Refraction
Incident
Ray
End of ruler
air
water
ruler
Apparent position
of ruler end
Refraction
Real and apparent depth
Ruler partially immersed in water
Setting sun appears flattened (top to bottom)
because light from lower part of the sun
undergoes greater refraction upon passing
through denser air (higher refractive index)
in lower part of the Earth’s atmosphere.
Refraction
2
2 1
cSin n
Sin n
q
q
Angle of incident for which refracted ray emerges
tangent to the surface is called the critical angle
Refraction
Critical Angle
as q1 is increased q2 increases
q1
q2
n2 < n1
q2 900
qc >qc
qc is critical angle
1
2
in this case q2 = 90o or Sin q2 =1
2
1
c
nSin
nq
2
1
c
nSin
nq
1 cq q>
incident ray undergoes total internal
reflection at boundary and cannot
pass into the material with the lower
refractive index
Refraction
Total internal reflection
q1
q2
n2 < n1
q2 900
qc >qc
qc is critical angle
1
2
Ray undergoes
total internal
reflection
maximum value of the sine of any angle is 1
total internal reflection occurs at interface only
when n2 < n1
when
1cSinq
Example
1 1 02
1
1.0003sin sin 49
1.33c
n
nq
Determine the critical angle for both water and
diamond with respect to air.
1 1 02
1
1.0003sin sin 24.4
2.42c
n
nq
water
diamond
Refraction
2
1
c
nSin
nq
45º
1 1 02
1
1.33sin sin 61
1.52c
n
nq
Refractive index of glass =1.52
Refractive index of air =1.0003
Total internal reflection
at glass air interface if
incident angle is >410
Glass prism
(right angled
isosceles triangle)
What happens the beam if the prism is immersed
in water? Refractive index of water =1.33
1 1 02
1
1.0003sin sin 41
1.52c
n
nq
Example
qc > 45º
Total internal reflection
at glass-water interface does not occur
What happens to light ray at the glass-air
interface in prism as shown.
Critical angle given by
45º
Applications
Fibre optic cables used for telecommunications
and for diagnostic tools in medicine
Refraction
Total internal reflection
Optical fibre
(end on)
Refractive index of core greater than
refractive index of clading
Light coupled into core will travel extremely
long distances along fibre, undergoing
total internal reflection at core-cladding
interface and exit only at the other end.
diameter of core 8mm
350
q4
glass
q2
q3
air
air
Light in air is incident on a glass block at an
angle of 350 The sides of the glass block are
parallel. At what angle does the light emerge
into the air from the lower surface of the glass
block?
glass block has
parallel sides,
therefore
q2 q3 =
0
4
0
4
35
35
Sin Sinq
q
Example
Let n1 = refractive index of air
& n2 = refractive index of glass Using Snell’s
Law 0
1 2 235n Sin n Sinq
2 3 1 4n Sin n Sinq q
2 2 1 4n Sin n Sinq q q2 Since q3 =
0
1 135 4n Sin n Sinq
Infrared Ultra violet Wavelength
Visible spectrum
v f Electromagnetic wave
Transverse wave
V: velocity
f: frequency
: wavelength
Light: Electromagnetic wave
Electromagnetic wave
Unpolarised light
viewed along
direction of
propagation
Polarised Light
polarised light
viewed along
direction of
propagation
Light source
Light beam Polariser
Light waves
vertically polarised
Schematic representation
Polaroid
filter Unpolarised
light
Polarised
light
Polarised Light
Unpolarised
light
Schematic representation
Polarised
light
Vertically polarised
light wave
Unpolarised
Incident beam
Horizontal
polariser
Vertical
polariser
Polarising
filter
Light can become polarised by
•Reflection •refraction •scattering
Unpolarised incident
light
Polarised reflected
light
Polarised incident
light
Polarised reflected
light
Polarised incident
light No reflected
light
Polarised Light
?
?
Polarised Light
Applications 3D movies
2 slightly different images projected on screen
2 cameras, a short distance apart,
photograph original scene
Each image linearly polarised in
mutually perpendicular direction
3D glasses have perpendicular polarisation axis
Each eye sees a different image associated with
different viewing angle from each camera
Brain perceives the compound image
as having depth or three dimensions.
Polarisation of light : application
Demineralised enamel is polarisation sensitive
shading may be seen, indicating the early
stages of caries at the tooth’s surface
Application to dentistry
Early detection of caries
Demineralised enamel viewed directly with
unpolarised light
No information
Polarised light incident on the dental tissue
Visual, mechanical probing, x rays???
The wavelength of red light from a HeNe laser is 633 nm
but is 474 nm in the aqueous humor inside an eyeball.
Calculate the index of refraction of the aqueous humor and
the speed and frequency of the light in the substance.
0
0
633
6331.34
474
n
nmn
nm
8 18 13 10
2.25 101.34
c x msv x ms
n
8 114
9
2.25 104.75 10
474 10
v x msf x Hz
x m
8 114
0 9
0
3.00 104.75 10
633 10
c x msf x Hz
x m
Refractive index
Speed in aqueous humor
Frequency of the light in aqueous humor
Frequency of the light in air
Example
0fcn
v f
0c f