​ A ray of light is falling on a glass sphere of μ=root(3) such that the incident ray and the emergent ray, when produced, intersect ​

Question

A ray of light is falling on a glass sphere of μ=\(\sqrt 3\) such that the incident ray and the emergent ray, when produced, intersect at a point on the surface of the sphere. The angle of incidence in degrees is found to be \(2π\over k\). Find the value of k.

Answer 1

The ray diagram for the situation is shown in figure.

According to Snell’s Law, we have

Rejecting the negative value, we get,

\(sini=\frac{\sqrt3}{2}\Rightarrow i= 60^\circ\)