Problems on Light in Dense Media
Problem 3.1:
If there were no atmosphere, what color would be sky appear?
[Solution]
Problem 3.2:
Use a dimensional argument to show that the proportion of the electric field of a light ray scattered by an
atomic oscillator is proportional to
λ-2. Let
Ei and
Es be the incident and scattered
amplitudes, respectively, with
Es corresponding to a distance
d from the scatterer. Assume
Es∝EI,
Es∝1/r and also that the scattered amplitude is proportional to the volume of the
scatterer.
[Solution]
Problem 3.3:
Derive an expression for the time taken by light to travel through a substance consisting of
m layers of
material each with thickness
di and index of refraction
ni.
[Solution]
Problem 3.4:
Propose a simple argument to show that for reflection from a planar surface, Fermat's principle
demands that the incident and reflected rays share a common plane with the normal to the surface.
[Solution]
Problem 3.5:
Derive the law of reflection
θi = θr using Fermat's principle.
[Solution]
