Question

A sphere with index of refraction, n2, is embedded in a material with index of refraction, n1. A ray of light is incident the sphere at an angle theta. If when the ray of light leaves the sphere, it has subtended an angle gamma=pi?theta, what must the ratio, n2/n1, be. Assume that theta is small, and make use of small angle approximations.

Answer 1

Snell's Law states that the ratio of the sines of the angles of incidence and refraction of a wave are constant when it passes between two given media. And can we expressed as,

Now given the angle at which the light is incident on the sphere is

And when the ray of light leaves the sphere it is

Refractive index of sphere = n2

Refractive index of material = n1

Thus by using Snell's Law we can conclude that,

  

n2/n1 = sin / sin