Question

A point source of power 4W is placed 1m below the free surface of liquid whose refractive index is $\frac{2}{\sqrt{3}}$Find the rate of transfer of energy (in watt) from the liquid surface to air. Ignore any absorption or scattering of light energy.

Answer 1

The light escape is confined within a cone of apex angle $2{\theta }_c$where ${\theta }_c$is the critical angle. Imagine a sphere with source of light as its centre and the surface area abc is A. Here A = ${\int }_0^{{\theta }_c}2\pi R^{2}sin\theta d\theta =2\pi R^2(1-cos{\theta }_c)$ = $\pi R^2[\therefore {\theta }_c=si{n}^{-1}(\frac{\sqrt{3}}{2}={60}^{\circ })]$ $\therefore$Power transfer = P $\times \frac{A}{4\pi R^2}$ = 4 $\times \frac{1}{4}$ = 1 W