Physics 2112
Unit 25
What happens at boundaries
- Reflection
- Refraction
- Snell’s Law
- Critical Angle
Polarization
- Brewster’s Angle
Topic 25, Slide 1
Boundaries
Recall from 2111:
When wave hits a boundary where speed changes
- part is transmitted
- part is reflected
DEMO
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
Topoc 25, Slide 2
Speed of Light in media
Relative speeds given by index of refraction, n
n=
speed of light in vacuum
speed of light in media
Media
vacuum
air
water
alcohol
glass
diamond
=
V
C
n
1.0
~1.0
1.33
1.36
1.5
2.4
Recall:
c 1
 o o
So can think of n as:
 o  o / 
Topic 25, Slide 3
Reflection
Measured from
normal
Topic 25, Slide 4
CheckPoint 2: Changes at Boundary
A ray of light passes from air into water with an angle of incidence of
30 degrees.
30o
Which of the following quantities does not change as the light
enters the water?
A.
B.
C.
D.
E.
wavelength
frequency
speed of propagation
(A) and (B)
(B) and (C)
Topic 25, Slide 5
Refraction: Snell’s Law
tab=Dxab/v1
tab = tdc
a
D
b
c
d
D sin  2 D sin 1

c / n2
c / n1
n2 sin 2  n1 sin 1
Unit 25, Slide 6
Think of it another (weird) way…
Minimum Travel Time
What's the fastest path to the ball knowing
you can run faster than you can swim?
This one is better
Not the quickest route…
Topic 25, Slide 7
Not on test….
A
x1
l1
Same Principle
works for Light!
y1
D
y2
l2
x2
Time from A to B :
To find minimum time,
differentiate t wrt x1 and set  0
How is x2 related to x1?
Setting
dt/dx1  0
l
l
t 1  2 
v1 v2
x12  y12

v1
B
x22  y22
v2
dt
x1
x2
dx2


dx1 v1 x12  y12 v2 x22  y22 dx1
x2  D  x1
x1
x
 2 0
v1l1 v2l2
dx2
 1
dx1
sin 1 sin  2

v1
v2
v  c/n
n1 sin 1  n2 sin 2
Topic 25, Slide 8
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
minimum value.
“Principle of Least
Action”
 ( KE  PE )ds
has
“Lagranginan”
CheckPoint 2: Refraction
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
Example 25.1: Cube of Glass
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?
?
?
How much is the beam shifted by the
cube?
Topic 25, Slide 11
Example 25.2: Fish in the water
The light from a fish is
incident from below on the
boundary between water and
air with an incident angle of
30o.
30o
At what refracted angle does
it leave the boundary?
What if the incident angle had been 60o?
Topic 25, Slide 12
Phet Demo
Click Here for Demo
Topic 25, Slide 13
Total Internal Reflection
NOTE: n1 > n2 implies 2 > 1
1 > c
BUT: 2 has max value = 90o!
Total Internal Reflection
Unit 25, Slide 14
Example 25.3: Diver’s Ilusion
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?
Unit 25, Slide 15
Checkpoint 2
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
Electricity & Magnetism Lecture 25, Slide 16
How much is reflected?
When going from n1>n2, some is reflected, some is transmitted
(refracted)
How much goes into each?
Complex. We can do extremes.
 i  90
i  0
o
o
R 1
n 2 n1 2
R(
)
n2  n1
Unit 25, Slide 17
Example 25.3: Reflection from Window
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?
Topic 25, Slide 18
Polarization
Unpolarized
Intensity decreased
in plane of incidence
Partially polarized
plane of incidence
Topic 25, Slide 19
Polarization
Completely polarized
when Q1 + Q2 = 90o
Brewster’s Angle:
QB = tan-1(n2/n1)
1  2  90

sin 2  sin(90  1 )  cos1
Snell’s Law: n2 sin 2  n2 cos1  n1 sin 1
tan1 
n2
n1
Unit 25, Slide 20
Example 25.4: Brewster’s Angle
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?
Q
B
Qr
Topic 25, Slide 21
CheckPoint 4
A ray of light passes from air into water with an angle of incidence of
30 degrees.
30o
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
Topic 25, Slide 22
CheckPoint 3
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
Electricity & Magnetism Lecture 25, Slide 23
Dispersion
Speed of E&M wave in media decreases in
media slightly with frequency dispersion
n is slight frequency (wavelength) dependent
Topic 25, Slide 24
Rainbows
Refraction (dispersion)
Rain
drops
Mixed (white) light
reflection
Refraction (dispersion)
84o
Topic 25, Slide 25
Example 25.4: Meter Stick in Tank
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.
45o
nwater  1.33
50 cm
0
20
40
60
meter stick
80
100
What is the smallest number on the meter stick that
you can see?
Unit 25, Slide 26
Summary
from n2 to n1
Unit 25, Slide 27