64. The refractive index of the material of a prism is √2 and the angle of the prism is 30°. One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is ?

64. The refractive index of the material of a prism is √2 and the angle of the prism is 30°. One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is ?

(a) 60°

(b) 45°

(c) 0°

(d) 30°

Answer :  (b) 45°

\(\frac{\sin i}{\sin r} = \mu\)

\(\frac{\sin i}{\sin 30^\circ} = \sqrt{2}\)

\(\sin i = \frac{1}{\sqrt{2}}\)

\(i = 45^\circ\)