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Physics 117B02 — March 22
“Ray Optics: Reflection, Refraction, Polarization”
Previous lecture: Chapter 32
• Major theme:
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electromagnetic waves
Predicted by Maxwell, verified by Hertz
Radiation from accelerated charges (e.g., dipoles)
Harmonic (sinusoidal) disturbance of E and B fields
Travel with speed c in vacuum, c/n in matter
E  c B in vacuum, E  c n B in matter
EM waves transport energy and momentum
Poynting vector S  1 0 E  B gives power/unit area
• Applications
o Solar heating, laser cutting, welding, surgery
o Radiation
 pressure (e.g., solar “wind”)
Physics 117B— March 22, 2006
Today’s lecture: Chapter 33
• Major themes:
reflection, refraction, polarization
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Rays and wavefronts: Huygens’ principle
Reflection and scattering from interfaces
Dispersion and total internal reflection (rainbows)
Refraction of transmitted rays at interfaces
Polarization effects due to reflection and scattering
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Why the sky looks blue (Rayleigh scattering)
Why double rainbows exhibit reversed colors
Why cataracts cause blurred vision
Telecommunication through optical fibers
Medical endoscopes and fiberscopes
• Applications
Physics 117B— March 22, 2006
Terminology
• Light rays travel perpendicular to phase fronts
• Each point on wave front acts as source of
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secondary spherical or circular “wavelets” … and
Phase fronts are the tangents to those spheres or
circles (Huygens’ principle)
Physics 117B— March 22, 2006
Limits of ray optics
• When observing EM waves at great distances from
their source, it is useful to assume that light travels
in a straight line (perpendicular to the wavefronts)
unless it encounters an obstacle.
Physics 117B— March 22, 2006
Specular vs diffuse
Light incident on smooth reflecting surfaces
is reflected at a specular angle; if the surface
is rough, the light scatters in many directions
from the asperities in the surface, and there
is both specular and diffuse reflection.
Physics 117B— March 22, 2006
Fermat’s principle: reflection
Fermat’s idea was that light follows the geometrical path that minimizes the
transit time. Consider the case of reflection from a surface in air. The total
transit time from point A to point B is
1
t
c

2
h12  y2  h22  w  y

The minimum travel time is found by taking
the derivative with respect to y and setting
it equal to zero:





dt 1
y
wy
 

 0
2
2
2
dy c 
h12  w  y 
 h1  y

And that implies the law of reflection. QED!
y

h12  y2
 sin  i 
Physics 117B— March 22, 2006
wy
2
h12  w  y
 sin  r
The critical angle for TIR
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Consider light incident from glass
(n=1.5) to air (n=1.0) at several
different angles (see figure).
Snell’s law relates the angle of
incidence to the angle of refraction.
n1 sin 1  n2 sin  2

1
15˚
25˚
35˚
45˚
2
At the critical angle …
???
 c  sin1 n2 n1
Physics 117B— March 22, 2006
Application of TIR: prisms
• Total internal reflection in glass or crystalline quartz
prisms are frequently used in optical systems
instead of mirrors. The prisms below all are cut at
angles of 45˚ and 90˚. Why?
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EXAMPLES
Cameras
Binoculars
Periscopes
High-power laser beams
Can you think of others?
Physics 117B— March 22, 2006
Optical fibers
• Why communicate with light? (in a word, bandwidth!)
• Added advantage: not subject to electrical interference
• Fiber transmission works because of total internal
reflection at core-cladding interface
• Fibers can support multiple transmission paths (multimode) or only one (single-mode)
Physics 117B— March 22, 2006
How are fibers made?
• A triumph of modern materials science and engineering!
• Requires exquisite purity and precision during the melting
and drawing process…
• While making the fibers economically by the ton
Physics 117B— March 22, 2006
Polarization by Polaroid®
Malus’s law for polarized
light passing through a
polarizer-analyzer pair
I pol  I max cos2 

• Polarizers work by preferred
direction of absorption
• Long, stringy molecules work for visible light
• If you have owned a pair of polarizing sunglasses …
• Have you noticed a change in brightness of sky
when you put them on? What does this mean?
Physics 117B— March 22, 2006
Polarization by reflection
The Brewster angle …
tan  pol
ninc

ntrans

• Reflections can polarize light that was initially not
polarized … (Brewster’s angle)
• Since scattering is a form of reflection, what happens
to polarized light scattered from a rough surface?
• Then why is it smart to wear polarizing sunglasses
when driving in bright sunlight?
Physics 117B— March 22, 2006
Summing up …
• Light rays travel in straight lines until they run into
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something
Even when they bump into something, light rays
travel the path that takes the shortest time
In material media (e.g., glass) the speed of light
depends on its color (dispersion)
When light is reflected from, scattered from or
transmitted through a surface, it may be polarized
The degree of polarization caused by reflection
depends on the angle of incidence
Physics 117B— March 22, 2006