Question

A light beam is propagating, from region I to region IV [refer to Fig. The refractive indices of region I, II, III and IV are (n₀), \((\frac{n_0}{2}),(\frac{n_0}{6})\) and \((\frac{n_0}{8})\) respectively. The angle of incidence, θ , in region I, for which the beam would just miss entering region IV, is

(1) sin^-1 (3/4)

(2) sin^-1 (1/8)

(3) sin^-1 (1/4)

(4) sin^-1 (1/3)

Answer 1

(2) sin^-1 (1/8)

Fig. shows the ray OA incident, from region I, at an angle of incident θ . Since the incident ray at C, i.e, region III just fails to enter region IV, the angle of incidence at C, must equal the critical angle of incidence between regions III and IV. Hence

Using Snell’s law at point A and B, we have