In the figure a beam of parallel light rays from a laser is

In the figure, a beam of parallel light rays from a laser is incident on a solid transparent sphere of index of refraction n. (a) If a point image is produced at the back of the sphere, what is the index of refraction of the sphere? (b) What index of refraction, if any, will produce a point image at the center of the sphere (Input number or 0 if none)? Assume that the index of refraction of the air is 1.

Solution

Refraction at a single surface

n₁/s + n₂/s\' = n₂ - n₁ / r

Parallel incident rays s ---> infinity

n₁ / s ---> 0

image distance s\' = 2 r

n₂/2r = n₂ - 1 / r

n₂ = 2