A light ray enters through a right angled prism at point P with the angle of incidence \( 30^\circ \) as shown in figure. It travels through the prism parallel to its base \( BC \) and emerges along the face \( AC \). The refractive index of the prism is:

At the first surface AB, \( \sin 30^\circ = \mu \sin r_1 \implies \sin r_1 = \frac{1}{2\mu} \). At surface AC, grazing emergence gives \( \sin r_2 = \frac{1}{\mu} \). Since the ray inside is parallel to base BC, \( r_1 + r_2 = 90^\circ \), so \( \cos r_1 = \sin r_2 = \frac{1}{\mu} \). Using \( \sin^2 r_1 + \cos^2 r_1 = 1 \), we get \( \frac{1}{4\mu^2} + \frac{1}{\mu^2} = 1 \implies \mu = \frac{\sqrt{5}}{2} \).