# Light

### Problems on Light in Dense Media

Problem : If there were no atmosphere, what color would be sky appear?

Problem : 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 E i and E s be the incident and scattered amplitudes, respectively, with E s corresponding to a distance d from the scatterer. Assume E sâàùE I , E sâàù1/r and also that the scattered amplitude is proportional to the volume of the scatterer.

Problem : Derive an expression for the time taken by light to travel through a substance consisting of m layers of material each with thickness d i and index of refraction n i .

Problem : 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.

Problem : Derive the law of reflection θ i = θ r using Fermat's principle.

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