Property 5: Refraction

experiment ?

particle (photon)?

wave (E&M) ?

Property 5: Refraction

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

air

water

real object

apparentlocation

eye

Property 5: Refraction

• particle (photon) ?

water

air

surface

incident ray

refracted ray

Property 5: Refraction

• particle (photon) ?

water

air

surface

incident ray

refracted ray

vxair

vyair

vxwater

vywater

vxair = vxwater

vyair < vywater

thereforevi < vr

Property 5: Refraction

• wave (E&M) ?

surface

air

water

incident wave

refracted wave

normal line

normal line

surface

Property 5: Refraction

• wave (E&M) ?

surface

air

water

incident wave

refracted wave

crest of wave

crest of preceding wave

x

air

water

normal line

crest of following wave

air

Property 5: Refraction

• particle (photon) theory: vwater > vair

• wave (E&M) theory: vwater < vair

• experiment ?

Property 5: Refraction

• particle (photon) theory: vwater > vair

• wave (E&M) theory: vwater < vair

• experiment: vwater < vair

wave theory works!

particle theory fails!

Properties 1, 2 & 5

Speed, 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?

Properties 1, 2 & 5• Speed, 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

Refraction and Thin Lenses

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.

Refraction and Thin Lenses

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

Refraction and Thin Lenses

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

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

Refraction and Thin Lenses

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?

Refraction and Thin Lenses

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)

Refraction and Thin Lenses

Spherical shape is specified by a radius.

The smaller the sphere (smaller the radius),

the more curved is the surface!

RR

R1

R2

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 = 10 cm; s = 20 cm; s’ = 20 cm: 1/20 + 1/20 = 1/10

Refraction and the Lens-users Eq.

1

f =

1

s +

1

s'

f f

ss’

as s gets bigger,s’ gets smaller

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

Refraction and the Lens-users Eq.

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 + 1/11.1 = 1/10

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 = 10 cm; s = 20 cm; s’ = 20 cm: 1/20 + 1/20 = 1/10

Refraction and the Lens-users Eq.

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 + 1/40 = 1/10

Refraction and the Lens-users Eq.

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 + 1/100 = 1/10

Refraction and the Lens-users Eq.

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.

Refraction and the Lens-users Eq.

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

Refraction and the Lens-users Eq.

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

Refraction and the Lens-users Eq.

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

Refraction and the Lens-users Eq.

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

Refraction and the Lens-users Eq.

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 = -13.3/40 = -0.33 X

Refraction and the Lens-users Eq.

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

Refraction and the Lens-users Eq.

f f

What happens when the object distance, s, changes?

ray 1

ray 2

ray 3

object

image

Refraction and the Lens-users Eq.

f f

Notice that as s gets bigger, s’ gets closer to f and |h’| gets smaller.

ray 1

ray 2

ray 3

object

image

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

M = -11.1/100 = -0.11 X

FocusingTo 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 f as s changes, keeping s’ the same!

Refraction and the Lens-users Eq.

f f

Let’s now look at the situation where

s < f (but s is still positive):

s

Refraction and the Lens-users Eq.

f f

We can still use our three rays. Ray one goes

through the focal point on the left side.

s

ray 1

Refraction and the Lens-users Eq.

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

Refraction and the Lens-users Eq.

f f

Ray three goes through the center of the lens

essentially undeflected.

s

ray 1

ray 2

ray 3

s’

h’

Refraction and the Lens-users Eq.

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 + 1/(-25) = 1/10

Refraction and the Lens-users Eq.

f f

Notice that: h’ right-side-up and so h’ > 0.,

M = h’/h = -s’/s . M > 0 (s’ < 0 but -s’ > 0).

s

ray 3

s’

h’

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

Refraction and the Lens-users Eq.

f f

This is the situation when the lens is used

as a magnifying glass! Image is VIRTUAL.

s

ray 1

ray 2

ray 3

s’

h’

Refraction and the Lens-users Eq.

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

Refraction and the Lens-users Eq.

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.

Refraction and the Lens-users Eq.

Are there any limits to the magnifying power

we can get from a magnifying glass?

Refraction and the Lens-users Eq.

• Magnifying glass has limits due to size

• As we will see in a little bit, magnifying

glass has limits due to resolving ability

• NEED MICROSCOPE (two lens system) for near and small things; need 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.

objectivelens eyepiece

fo

fe

Telescope Basics

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

objectivelens eyepiece

fofe

x

Magnification

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

objectivelens eyepiece

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 in the lab)

objectivelens eyepiece

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