Physics 2112

Unit 25

Topic 25, Slide 1

What happens at boundaries

- Reflection

- Refraction

- Snell’s Law

- Critical Angle

Polarization

- Brewster’s Angle

Recall from 2111: When wave hits a boundary where speed changes - part is transmitted - part is reflected DEMO

Boundaries

Topoc 25, Slide 2

Same with E&M: Think of window. Can see through it Can see reflection in it

Speed of light is different in

vacuum and glass

Relative speeds given by index of refraction, n

Speed of Light in media

Topic 25, Slide 3

n = speed of light in vacuum

speed of light in media

Media n

vacuum 1.0

air ~1.0

water 1.33

alcohol 1.36

glass 1.5

diamond 2.4

= V

C

oo

c

1

Recall:

/oo

So can think of n as:

Reflection

Topic 25, Slide 4

Measured from

normal

CheckPoint 2: Changes at Boundary

Topic 25, Slide 5

Which of the following quantities does not change as the light

enters the water?

A. wavelength

B. frequency

C. speed of propagation

D. (A) and (B)

E. (B) and (C)

A ray of light passes from air into water with an angle of incidence of

30 degrees.

30o

Refraction: Snell’s Law

Unit 25, Slide 6

1122 sinsin nn 1

1

2

2

/

sin

/

sin

nc

D

nc

D

D

a

b c

d

tab = tdc

tab=Dxab/v1

Not the quickest route…

This one is better

What's the fastest path to the ball knowing you can run faster than you can swim?

Think of it another (weird) way…

Topic 25, Slide 7

Minimum Travel Time

A

B

x1

y1

l1

x2

y2 l2

Setting dt/dx1 0

Same Principle works for Light! D

Topic 25, Slide 8

v c/n 2211 sinsin nn 2

2

1

1 sinsin

vv

0

22

2

11

1 lv

x

lv

x

How is x2 related to x1? 12 xDx 1

1

2 dx

dx

To find minimum time, differentiate t wrt x1 and set 0

1

2

2

2

2

22

2

2

1

2

11

1

1 dx

dx

yxv

x

yxv

x

dx

dt

Time from A to B : 2

2

2

2

2

1

2

1

2

1

2

2

1

1

v

yx

v

yx

v

l

v

lt

Not on test….

REALLY(!) weird (….but not on test)

This business of “minimum travel

time” is everywhere in nature!

Remember from 2111? When you kick a soccer

ball up at 30o, where does it land?

It lands so that the integral has

minimum value. dsPEKE )(

“Principle of Least Action” “Lagranginan”

A ray of light is bent as it passes from medium 1 to medium 2.

Compare the indices of refraction in

the two mediums.

A. n1 > n2

B. n1 = n2

C. n1 < n2

Topic 25, Slide 10

CheckPoint 2: Refraction

How much is the beam shifted by the

cube?

Example 25.1: Cube of Glass

Topic 25, Slide 11

25o

?

A beam of laser light hits a cube of glass

that is 4cm on a side with a angle that is

25o to the normal. The index of

refraction for glass is n= 1.5.

At what angle will it leave the cube?

?

The light from a fish is

incident from below on the

boundary between water and

air with an incident angle of

30o.

At what refracted angle does

it leave the boundary?

Example 25.2: Fish in the water

Topic 25, Slide 12

What if the incident angle had been 60o?

30o

Topic 25, Slide 13

Phet Demo

Click Here for Demo

1 > c Total Internal Reflection

NOTE: n1 > n2 implies 2 > 1 BUT: 2 has max value = 90o!

Total Internal Reflection

Unit 25, Slide 14

Example 25.3: Diver’s Ilusion

Unit 25, Slide 15

If a scuba diver looks straight up towards the

surface from underwater, he see a bright circle of

light.

Why? What is the size of that circle?

Checkpoint 2

Electricity & Magnetism Lecture 25, Slide 16

A light ray travels in a medium with n1 and

completely reflects from the surface of a medium

with n2.

The critical angle depends on:

A. n1 only

B. n2 only

C.both n1 and n2

How much is reflected?

Unit 25, Slide 17

When going from n1>n2, some is reflected, some is transmitted

(refracted)

How much goes into each? Complex. We can do extremes.

o

i 90

2

12

12 )(nn

nnR

o

i 0

1R

Example 25.3: Reflection from Window

Topic 25, Slide 18

If you looked straight into a

window made of regular

glass, you would see a

reflection of the things behind

you.

What refraction of the

intensity of the original waves

would in that reflected

image?

Polarization

Topic 25, Slide 19

Unpolarized Intensity decreased

in plane of incidence

Partially polarized

plane of incidence

Polarization

Unit 25, Slide 20

112 cos)90sin(sin 9021

Snell’s Law: 111222 sincossin nnn

1

21tan

n

n

Completely polarized

when Q1 + Q2 = 90o

Brewster’s Angle:

QB = tan-1(n2/n1)

Example 25.4: Brewster’s Angle

Topic 25, Slide 21

A light beam is incident on a piece of glass

(n=1.5) at the minimum angle for which to

reflected beam is completely polarized.

What is Qr for the portion of the beam that

is refracted? QB

Qr

CheckPoint 4

Topic 25, Slide 22

Some of the light also reflects off the surface of the water. If the

incident light is initially unpolarized, the reflected light will be

A. Unpolarized

B. Somewhat horizontally polarized

C. Somewhat vertically polarized

A ray of light passes from air into water with an angle of incidence of

30 degrees.

30o

CheckPoint 3

Electricity & Magnetism Lecture 25, Slide 23

A light is shining at the bottom of a swimming pool

(shown in yellow in the figure). A person is standing at

the edge of the pool as shown.

Can the person standing on the edge of the pool be prevented from

seeing the light by total internal reflection at the water-air surface?

A. yes

B. no

Dispersion

Topic 25, Slide 24

Speed of E&M wave in media decreases in

media slightly with frequency

n is slight frequency (wavelength) dependent

dispersion

Rainbows

Topic 25, Slide 25

Mixed (white) light

Refraction (dispersion)

reflection

Refraction (dispersion)

Rain

drops

84o

50 cm

20 0 40 60 80 100

45o

A meter stick lies at the bottom of a rectangular water tank of height 50cm. You look into the tank at an angle of 45o relative to vertical along a line that skims the top edge of the tank.

nwater 1.33

Example 25.4: Meter Stick in Tank

Unit 25, Slide 26

What is the smallest number on the meter stick that

you can see?

meter stick

from n2 to n1

Summary

Unit 25, Slide 27