Announcements

1
Announcements

• HW8 (finally) posted on WebCT, due Wed. April 19

2
Electromagnetic Waves in Matter

• We have previously solved Maxwells equations to
  find electromagnetic waves that propagate through
  vacuum
• Constant speed of propagation c
• Electric and magnetic fields perpendicular to
  each other and the direction of propagation
• Power given by Poynting vector, with equal energy
  densities in electric and magnetic fields
• A number of interesting things happen when
  electromagnetic waves interact with matter
• Conductors will have free charges that move in
  response to the fields
• Dielectrics will develop bound charge densities
• We need to take these effects into account to
  describe the propagation of light through matter

3
Mirror, Mirror, on the Wall

• Mirrors generally have a good conductor that
  reflects the light impinging on the mirror
• In a perfect conductor, the electric field would
  vanish inside the conductor
• What happens to an EM wave hitting a conductor?
• We want E0 inside the conductor
• Charges on the surface of the mirror can create
  normal fields, but not fields parallel to the
  mirror
• To get E0 at the surface, there must be a
  reflected EM wave whose parallel component of
  electric field is opposite that of the incident
  electric field
• The only way to get E0 over the surface is to
  have a reflected EM wave with angle of incidence
  equal to angle of reflectance

4
EM Waves in Linear Dielectric

• We previously saw that for linear dielectrics,
  we could replace e0 by e
• For linear materials, Maxwells equations become
• Velocity of EM wave changes!

5
EM Waves in Dielectrics

• Transparent materials generally have m m0, so
  index of refraction is determined by dielectric
  properties
• Some common materials
• Water n 1.33
• Glass n 1.52
• Plastic n 1.55
• Diamond n 2.42
• When EM wave hits dielectric, frequency is
  unchanged, but wavelength becomes shorter
• Somehow need to match incident wave with shorter
  wavelength wave propagating through dielectric

6
Refraction

• Refracted wave traveling through the dielectric
  changes direction!
• We will show (next week?) week that the refracted
  wave obeys Snells Law
• Suppose material 1 is vacuum or air, material 2
  has an index of refaction n
• Total internal reflection occurs when Snells law
  cant be satisfied, which occurs when

7
Prisms

• Prisms are generally made of glass, so light
  passing through them is refracted
• Index of refraction for glass actually depends on
  frequency of the light
• Thus, different colors are bent by different
  amounts
• White light is made up of EM waves with
  frequencies spread across the visible spectrum
  (and beyond)
• When white light is sent through a prism, each
  frequency of visible light is bent by a different
  amount (higher frequency light is bent more than
  low frequency light), causing the different
  colors the light to be separated out
• Same thing happens with water drops in a rain
  storm, giving rise to a rainbow under the right
  conditions