# Lecture 5 by S9t150h

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```									Physics 212
Lecture 25

Physics 212 Lecture 25, Slide 1
Main Point 1

First, we introduced the law of reflection, that the angle of incidence equals the
angle of reflection. We offered a derivation of this relation for plane waves by
requiring the phase of the reflected wave across a wavefront perpendicular to the
ray to be constant.                                         Physics 212 Lecture 25, Slide 2
Main Point 2

Second, we introduced the modifications to Maxwell’s equations that are necessary
to describe electromagnetic fields in matter. By simply replacing e0 and m0 with e
and m, we determined that the speed of an electromagnetic wave in matter is less
than the speed of light in vacuum. We defined the index of refraction n of a
material as the ration of the speed of light in that material to the speed of light in
vacuum. For non-magnetic materials, the index of refraction is simply related to
the dielectric constant.                                    Physics 212 Lecture 25, Slide 3
Main Point 3

Third, we obtained Snell’s law that relates the angle of refraction to the angle of
incidence by requiring the phase of the refracted wave across a wavefront
perpendicular to the ray to be constant.
Physics 212 Lecture 25, Slide 4
Main Point 4

Finally, we discussed intensities and polarizations of these rays for some special
cases. In particular, we determined that for light moving from a medium with
higher index of refraction to one with a lower index of refraction, there is a
critical angle of incidence, qc equal to the arcsine of the ratio of the indices of
refraction, such that for all angles greater than this angle, no light will be
refracted; all light will be reflected. We also discussed the partial polarization
perpendicular to the plane of incidence of the reflected ray and introduced
Brewster’s angle , defined as the arctangent of the ratio of the indices of
refraction, for which the polarization is total.

Physics 212 Lecture 25, Slide 5

Physics 212 Lecture 25, Slide 6
The speed of light in a medium
is slower than in empty space:

vmedium = c / nmedium
Since l = v/f, if v decreases then so does l
Physics 212 Lecture 25, Slide 7
Physics 212 Lecture 25, Slide 8
A      x1
l1
y1
Same Principle
works for Light !!                              D

y2         l2
x2        B
2    2    2     2
x1  y1   x2  y 2
Time from A to B :              l  l
t 1 2                
v1 v2          v1        v2
To find minimum time,      dt      x1         x2     dx2
differentiate t wrt x1                   
and set = 0          dx1 v1 x1  y1 v2 x2  y2 dx1
2    2      2   2

dx2
How is x2 related to x1?   x2  D  x1              1
dx1

Setting           x1   x                sin 1 sin  2
 2 0                                   v = c/n   n1 sin 1  n2 sin  2
dt/dx1 = 0        v1l1 v2l2                v1     v2
Physics 212 Lecture 25, Slide 9
Physics 212 Lecture 25, Slide 10
A ray of light passes from air into water with an angle of incidence of 30 degrees.

Checkpoint 1a

Which of the following quantities does not change as the light enters the water?
A. wavelength                   B. frequency                  C. speed of propagation

Physics 212 Lecture 25, Slide 11
A ray of light passes from air into water with an angle of incidence of 30 degrees.

Checkpoint 1b

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

Physics 212 Lecture 25, Slide 12
Physics 212 Lecture 25, Slide 13
The path of light is bent as it passes from medium 1 to medium 2.

Checkpoint 2a

Compare the indices of refraction in the two media.
A. n1 > n2                     B. n1 = n2                   C. n1 < n2

Physics 212 Lecture 25, Slide 14
A light ray travels in a medium with n1 and completely reflects from the surface of
a medium n2.

Checkpoint 2b

The critical angle depends on:
A. n1 only                     B. n2 only                     C. both n1 and n2

Physics 212 Lecture 25, Slide 15
Physics 212 Lecture 25, Slide 16
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.

Checkpoint 3

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

Physics 212 Lecture 25, Slide 17
Physics 212 Lecture 25, Slide 18
Reflection

Physics 212 Lecture 25, Slide 19
Refraction: Snell’s Law

Physics 212 Lecture 25, Slide 20
Physics 212 Lecture 25, Slide 21
Total Internal Reflection

1 > c    Total Internal Reflection
Physics 212 Lecture 25, Slide 22
Intensity

Anything looks like a mirror        If two materials have the same n
if light is just glancing off it.   then its hard to tell them apart.
Physics 212 Lecture 25, Slide 23
Exercise                            45o

A meter stick lies at the bottom of a                                nwater = 1.33
rectangular water tank of height 50cm.
You look into the tank at an angle of
45o relative to vertical along a line that   50 cm
skims the top edge of the tank.

What is the smallest number on the
0   20    40     60     80    100
ruler that you can see?

Conceptual Analysis:

Strategy:

Physics 212 Lecture 25, Slide 24
Physics 212 Lecture 25, Slide 25
Physics 212 Lecture 25, Slide 26

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