A light ray enters a solid glass sphere of refractive index $\mu = \sqrt3$ at an angle of incidence $60^\circ$. The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is ______.
Numerical value type. Enter your answer.
Answer: 90
At entry: $\sin60^\circ = \sqrt3\sin r \Rightarrow r = 30^\circ$.
The chord inside the sphere joins two points on the surface, so the angle of incidence at the far surface is also $30^\circ$.
The reflected ray makes $30^\circ$ with the normal (inside) and the refracted ray makes $60^\circ$ with the normal (outside). These lie on opposite sides of the surface, so the angle between them is
$$180^\circ - 30^\circ - 60^\circ = 90^\circ$$
Solution by Sreeraj P, M.Sc Physics