Property 5: Refraction

$Page 1: Property 5: Refraction$
Property 5: Refraction

Experiment ?

Particle (photon)?

Wave (E&M) ?


• Experiment: objects in water seem closer than they really are when viewed from air

air

water

real object

apparentlocation

eye


• Particle (photon) explanation?

water

air

surface

incident ray

refracted ray


• Particle (photon) explanation:

water

air

surface

incident ray

refracted ray

vxair

vyair

vxwater

vywater

vxair = vxwater

vyair < vywater

thereforevair < vwater


• Wave (E&M) ?

surface

air

water

incident wave

refracted wave

normal line

normal line

surface


• Wave (E&M) explanation:

surface

air

water

incident wave

refracted wave

crest of wave

crest of preceding wave

x

air

water

normal line

crest of following wave

air


• Particle (photon) theory: vwater > vair

• Wave (E&M) theory: vwater < vair

• Experiment ?


• Particle (photon) theory: vwater > vair

• Wave (E&M) theory: vwater < vair

• Experiment: vwater < vair

wave theory works!

particle theory fails!

Properties 1, 2 & 5Speed, Color and Refraction

• Speed of light changes in different materials

• Speed is related to frequency and wavelength: v = f

• If speed changes, does wavelength change, frequency change, or BOTH?

• Does color change?

Properties 1, 2 & 5Speed, Color and Refraction

• Speed of light changes in different materials• Speed is related to frequency and wavelength:

v = f• What changes with speed?

– Frequency remains constant regardless of speed

– Wavelength changes with speed– Color remains the same regardless of speed

– so color depends on frequency, not wavelength

Refraction and Thin Lenses

We can use refraction to try to control rays of light to go where we want them to go.

Let’s see if we can FOCUS light.


What kind of shape do we need to focus light from a point source to a point?

lens with some shape for front & back

screen

pointsourceof light

s = object distances’ = image distance


Let’s try a simple (easy to make) shape: SPHERICAL.

Play with the lens that is handed out (either in lecture or in lab)

Does it act like a magnifying glass?


Let’s try a simple (easy to make) shape: SPHERICAL.

Play with the lens that is handed out (either in lecture or in lab)

Does it act like a magnifying glass?

Does it focus light from the night light?


Let’s try a simple (easy to make) shape: SPHERICAL

Play with the lens that is handed outDoes it act like a magnifying glass?

Does it focus light from the night light?

Does the image distance depend on the shape of the lens? (trade with your neighbor to get a different shaped lens)


Spherical shape is specified by a radius.

The smaller the sphere (smaller the radius),

the more curved is the surface!

RR

R1

R2

Focal lengthA lens is made from a transparent material, and it has a front and back curvature.The material has its own speed for light and so it has its own ability to bend light due to refraction. We assign a parameter called the index of refraction to this material based on its ability to bend light.

The front and back sides of the lens are specified by the radius of curvature.

If we put this all together, we come up with a single number called the focal length, f, that describes each lens.

Focal Length

The focal length describes how strongly the lens will bend the light. A small focal length will bend the light more than a larger focal length.

A lens with a small focal length will then perform as a strong magnifying lens, and a large focal length lens will only weakly magnify.

These type lenses can be used to correct far sightedness (where the eye has a too weak of a lens).

Focal Lengths

Focal lengths can be negative if we have opposite curvatures for the two sides.

These lenses will de-magnify.

These can be used to correct near sightedness (where the eye has too strong of a lens).

Focal Length

A lens’ ability to bend the light, described by its focal length, will connect the distance an object is from the lens (called the object distance, s) to the distance the image formed by the lens is from the lens (called the image distance, s’). This is shown in the next several slides. The next slide shows a strong lens that bends the light a lot; the following slides show a weaker lens that does not bend the light as much.

Refraction and the Lens-users Eq.

1

f =

1

s +

1

s'

f f

ss’

s > 0 AND s > f

s’ > 0 AND s’ > f

f > 0

Example: f = 5 cm; s = 10 cm; s’ = 10 cm: 1/10 cm + 1/10 cm = 1/5 cm

A strong lens with a small focal length bends the light a lot


1

f =

1

s +

1

s'

f f

ss’

s > 0 AND s > f

s’ > 0 AND s’ > f

f > 0


A weaker lens with a larger focal length bends the light less. (We’ll use this same weaker lens in all of the following slides.)


1

f =

1

s +

1

s'

f f

ss’

For the same focal length, as s gets bigger, s’ gets smaller.

Example: f = 10 cm; s = 40 cm; s’ = 13.3 cm: 1/40 cm + 1/13.3 cm = 1/10 cm


1

f =

1

s +

1

s'

f f

s s’

as s approaches infinitys’ approaches f

Example: f = 10 cm; s = 100 cm; s’ = 11.1 cm: 1/100 cm + 1/11.1 cm = 1/10 cm


1

f =

1

s +

1

s'

f f

ss’

s > 0 AND s > f

s’ > 0 AND s’ > f

f > 0



1

f =

1

s +

1

s'

f f

s

s’

as s gets smaller, s’ gets larger

Example: f = 10 cm; s = 13.3 cm; s’ = 40 cm: 1/13.3 cm + 1/40 cm = 1/10 cm


1

f =

1

s +

1

s'

f f

ss’

as s approaches f,s’ approaches infinity

Example: f = 10 cm; s = 11.1 cm; s’ = 100 cm: 1/11.1 cm + 1/100 cm = 1/10 cm


Before we see what happens when s gets smaller than f, let’s use what we already know to see how the lens will work.


f f

– Any ray that goes through the focal point on its way to the lens, will come out parallel to the optical axis. (ray 1)

ray 1


f f

– Any ray that goes through the focal point on its way from the lens, must go into the lens parallel to the optical axis. (ray 2)

ray 1

ray 2


f f

– Any ray that goes through the center of the lens must go essentially undeflected. (ray 3)

ray 1

ray 2

ray 3

object

image


f f

– Note that a real image is formed.

– Note that the image is up-side-down.

ray 1

ray 2

ray 3

object

image


f f

– By looking at ray 3 alone, we can see

by similar triangles that M = h’/h = -s’/s.

ray 3

object

image

s

h s’

h’<0

note h’ is up-side-downand so is <0

Example: f = 10 cm; s = 40 cm; s’ = 13.3 cm:

M = -13.3 cm/40 cm = -0.33 X


f f

This is the situation when the lens is used

in a camera or a projector. Image is REAL.

ray 1

ray 2

ray 3

object

image


f f

What happens when the object distance, s, changes?

ray 1

ray 2

ray 3

object

image


f f

Notice that as the object distance, s, gets bigger, the image distance, s’, gets closer to f, and the image height gets smaller.

ray 1

ray 2

ray 3

object

image

Example: f = 10 cm; s = 100 cm; s’ = 11.1 cm:

M = -11.1 cm/100 cm = -0.11 X

Focusing

To focus a camera, we need to change s’ as s changes. To focus a projector, we need to change s as s’ changes. We do this by screwing the lens closer or further from the film or slide.

But what about the eye? How do we focus on objects that are close and then further away with our eyes? Do we screw our eyes in and out like the lens on a camera or projector?

Focusing

But what about the eye? How do we focus on objects that are close and then further away with our eyes? Do we screw our eyes in and out like the lens on a camera or projector? - NO, instead our eyes CHANGE SHAPE and hence change their focal length, f, as s changes, keeping s’ the same!


f f

Let’s now look at the situation where

s < f (but s is still positive):

s


f f

We can still use our three rays. Ray one goes

through the focal point on the left side.

s

ray 1


f f

Ray two goes through the focal point on the

right side (and parallel to the axis on the left).

s

ray 1

ray 2


f f

Ray three goes through the center of the lens

essentially undeflected.

s

ray 1

ray 2

ray 3

s’

h’


f f

Notice that: s’ is on the “wrong” side, which

means that s’ < 0 , and that |s’| > |s| so f > 0.

s

ray 1

ray 2

ray 3

s’

h’

Example: f = 10 cm; s = 7.14 cm; s’ = -25 cm: 1/7.14 cm + 1/(-25 cm) = 1/10 cm


f f

Notice that the image height, h’, is right-side-up and so h’ > 0, and it is bigger than the object height, h. M = h’/h so M > 0 .

s

ray 3

s’

h’

Example: f = 10 cm; s = 7.14 cm; s’ = -25 cm: M = - (-25 cm)/ 7.14 cm = 3.5 X


f f

This is the situation when the lens is used

as a magnifying glass! Image is VIRTUALsince the light does not actually go through the image position.

s

ray 1

ray 2

ray 3

s’

h’


The same lens can be used as:

• a camera lens: s >> f, s > s’,

M < 0, |M| < 1

• a projector lens: s > f, s’ > s,

M < 0, |M| > 1

• a magnifying glass: s < f, s’ < 0,

M > 0, M > 1


Notes on using a lens as a magnifying glass:

• hold lens very near your eye

• want IMAGE at best viewing distance

which has the nominal value of 25 cm

so that s’ = -25 cm.


Are there any limits to the magnifying power

we can get from a magnifying glass?


• Magnifying glass has limits on its magnifying ability due to size since a small focal length (strong magnifying lens) demands a small radius for its curvature – which means a small lens.

• Since a magnifying glass causes “diffraction” spots, with the smaller lens causing bigger spots, the magnifying glass has limits due to its resolving ability.

Need a two lens system

Since a single lens can’t effectively magnifying beyond about 30 power, we need to go to a two lens system.

We need a MICROSCOPE (two lens system) for near and small things;

We need a TELESCOPE (two lens system) for far away things.

Telescope Basics

Light from far away is almost parallel.

objectivelens eyepiece

fo

fe

Telescope Basics:Get More Light

The telescope collects and concentrates light.


fo

fe

Telescope Basics

Light coming in at an angle, in is magnified to out .


fofe

x

Magnification

in = x/fo, out = x/fe; M = out/in = fo/fe


fofe

x

Limits on Resolution

telescopes– magnification: M = out/in = fo /fe – light gathering: Amt D2

– resolution: 1.22 = D sin(limit) so

in = limit and out = 5 arc minutes

so limit 1/D implies Museful = 60/in * D where D is in inches– surface must be smooth on order of

Limits on Resolution:calculation

Mmax useful = out/in = eye/limit

= 5 arc min / (1.22 * / D) radians

= (5/60)*(/180) / (1.22 * 5.5 x 10-7 m / D)

= (2167 / m) * D * (1 m / 100 cm) * (2.54 cm / 1 in)

= (55 / in) * D

Example

What diameter telescope would you need to read letters the size of license plate numbers from a spy satellite?

Example

• need to resolve an “x” size of about 1 cm

• “s” is on order of 100 miles or 150 km

• limit then must be (in radians)

= 1 cm / 150 km = 7 x 10-8

• limit = 1.22 x 5.5 x 10-7 m / D = 7 x 10-8

so D = 10 m (Hubble has a 2.4 m diameter)

Limits on Resolution: further examples

• other types of light– x-ray diffraction (use atoms as slits)– IR– radio & microwave

• surface must be smooth on order of

Review of Telescope Properties

1. Magnification: M = fo/fe depends on the focal lengths of the two lenses.

2. Light gathering ability: depends on area of objective lens, so depends on diameter of objective lens squared (D2).

3. Resolution ability: depends on diameter of objective lens: Max magnification = 60 power/in * D.

Types of Telescopes

The type of telescope we have looked at so far, and the type we have or will have made in the lab is called a refracting telescope, since it uses the refraction of light going from air to glass and back to air. This is the type used by Galileo.

There is a second type of telescope invented by Newton. It is called the reflecting telescope since it uses a curved mirror instead of a curved lens for the objective. There are three main sub-types of reflectors that we’ll consider: Prime focus, Newtonian, and Cassegranian.

Refracting Telescope

Two lenses (as we had or will have in the lab)


fo

fe

Reflecting Telescope

Light from far away mirror

focuses light

problem: how do we get to focused light without blocking incoming light?

Reflecting TelescopePrime Focus

Light from far away mirror

focues light

Solution #1: If mirror is big enough (say 100 to 200 inches in diameter), we can sit right in the middle and we won’t block much light - this is called the prime focus.

eyepiece

Reflecting TelescopeNewtonian Focus

Light from far away primary

mirror focuses

light

Solution #2: Use secondary mirror to reflect light out the side of the telescope- this is called the Newtonian focus.

mirror

eyepiece

Reflecting TelescopeCassegranian Focus

Light from far away primary mirror

focuses light

eyepiece

Solution #3: Use secondary mirror to reflect light out the back of the telescope- this is called the Cassegranian focus.

mirror

Refracting versus Reflecting

One advantage that a refracting telescope has, especially for a small telescope such as a telescope for a rifle, is that a refracting telescope is the simplest to make and easiest to aim. We did (or will do) this in lab.


One advantage that a reflecting telescope has over a refracting one is that a mirror reflects all the colors the same, whereas a lens bends light slightly differently for different colors – called chromatic aberration. This effect is useful in a prism, but causes a blurry image in a lens.

Chromatic aberration can be minimized for a lens if we use two different lenses made of different materials. For small lenses, this adds to the cost, but is quite do-able. For large lenses, this is very expensive!


A second major advantage that a reflecting telescope has over a refracting one is that a mirror only has one side that needs to be polished, while a lens has two sides that need to be polished. This greatly reduces the cost of a large telescope.


A third major advantage that a reflecting telescope has, especially for large telescopes, is that a mirror is much easier to mount than a lens. You can mount a mirror and hold it from the back, while a lens has to be held only by the edges. Almost all large telescopes are reflecting for this reason.

Property 5: Refraction

Documents

s approaches infinitye

ffssas s approaches

lensusers eq

night light

rays of light

vwater vairwave em theory

particle theory

lensesspherical shape