62. The angle of incidence for a ray of light at a refracting surface of a prism is 45°. The angle of prism is 60°. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are :

62. The angle of incidence for a ray of light at a refracting surface of a prism is 45°. The angle of prism is  60°. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are :

(a) \(45^\circ , \; \sqrt{\tfrac{1}{2}}\)

(b) \(30^\circ , \; \sqrt{2}\)

(c) \(45^\circ , \; \sqrt{2}\)

(d) \(30^\circ , \; \sqrt{\tfrac{1}{2}}\)

Answer :  (b) \(30^\circ , \; \sqrt{2}\)

\( r = \frac{A}{2} = \frac{60^\circ}{2} = 30^\circ \)

\( \mu = \frac{\sin i}{\sin r} = \frac{\sin 45^\circ}{\sin 30^\circ} = \frac{\tfrac{1}{\sqrt{2}}}{\tfrac{1}{2}} = \sqrt{2} \)

\( \delta_m = 2i - A = 2 \times 45^\circ - 60^\circ = 30^\circ \)