Physics 117B02

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Physics 117B02 March 22

• Ray Optics Reflection, Refraction,
  Polarization

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Previous lecture Chapter 32

• Major theme 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
• in vacuum, in
  matter
• EM waves transport energy and momentum
• Poynting vector gives
  power/unit area
• Applications
• Solar heating, laser cutting, welding, surgery
• Radiation pressure (e.g., solar wind)

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Todays lecture Chapter 33

• Major themes reflection, refraction,
  polarization
• 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
• Applications
• 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

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Terminology

• Light rays travel perpendicular to phase fronts
• Each point on wave front acts as source of
  secondary spherical or circular wavelets and
• Phase fronts are the tangents to those spheres or
  circles (Huygens principle)

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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.

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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.
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Fermats principle reflection
Fermats 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
The minimum travel time is found by taking the
derivative with respect to y and setting it equal
to zero
And that implies the law of reflection. QED!
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The critical angle for TIR

• Consider light incident from glass (n1.5) to air
  (n1.0) at several different angles (see figure).
  
• Snells law relates the angle of incidence to the
  angle of refraction.

J1 J2
15
25
35
45 ???
At the critical angle
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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?

• EXAMPLES
• Cameras
• Binoculars
• Periscopes
• High-power laser beams
• Can you think of others?

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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
  (multi-mode) or only one (single-mode)

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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

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Polarization by Polaroid
Maluss law for polarized light passing through
a polarizer-analyzer pair

• 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?

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Polarization by reflection
The Brewster angle

• Reflections can polarize light that was initially
  not polarized (Brewsters 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?

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Summing up

• Light rays travel in straight lines until they
  run into 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