Question

A point source is placed at the bottom of a tank containing a transparent liquid (refractive index n) to a depth H. The area of the surface of the liquid through which light from the source can emerge out is

(A) \(\frac {\pi H^2}{(n-1)}\)

(B) \(\frac {\pi H^2}{(n^2-1)}\)

(C) \(\frac{\pi H^2}{\sqrt{n^2+1}}\)

(D) \(\frac{\pi H^2}{(n^2 +1)}\)

Answer 1

Correct option is : (A) \(\frac{\pi H^2}{(n-1)}\)

For a point source placed at the bottom of a tank, the emergent area through which light escapes depends on total internal reflection and Snell’s Law. The area of the liquid surface through which light emerges is given by:

\(A = \frac { \pi H^2 }{(n^2-1)}\) 

\(= \frac{\pi H^2}{(n-1)}\)