Question

A glass slab, of thickness t, has a refractive index 3/2. A point source is kept at the bottom of the slab. The fraction of light, emitted by S, that emerges out of the upper face of slab, is

(1) 0.5

(2) \([1-\frac{\sqrt{3}}{2}](\frac{1}{2})\)

(3) \([1-\frac{\sqrt{5}}{3}](\frac{1}{2})\)

(4) 0.25

Answer 1

 (3) \([1-\frac{\sqrt{5}}{3}](\frac{1}{2})\)

Fig. shows that only those incident rays from S, that lie within the cone OAA´, emerge out of the upper surface of glass. Also

The area S; from which light emerges out is

The total light, emitted by S, gets spread over the surface of a sphere of radius R, i.e., 4πR² . Therefore Fraction of total light (emitted by the source S) that passes out of the slab, is