Question

A point source is placed at a depth h below the surface of water (refractive index $=\mu$).

(a) Show that light escapes through a circular area on the water surface with its centre directly above the point source.

(b) Find the angle subtended by a radius of the area on the source.

Answer 1

(a) Let P is a point source placed at a depth h.

Clearly from figure, the light escapes at a fixed distance r at water surface.

That makes a circle whose centre is just above P.

$\Rightarrow sin\theta =\frac{1}{\mu }$

$\Rightarrow v=si{n}^{-1}\left(\frac{1}{\mu }\right)$