Q. One of the refracting surfaces of a prism of angle $30{^\circ}$ is silvered. A ray of light incident at an angle of $60{^\circ}$ retraces its path. The refractive index of the material of prism is
A) $\sqrt{3}$
B) 3/2
C) 2
D) $\sqrt{2}$
Explanation
(b) As is clear from figure, $A = 30{^\circ},i_{1} = 60{^\circ}$
As the ray retraces its path on reflection at the silvered face, therefore,
$i_{2} = 0,r_{2} = 0$
As $r_{1} + r_{2} = A$
$\therefore r_{1} + 0 = 30{^\circ}$
Or ${\ r}_{1} = 30{^\circ}$
[image:9_image118.emf]
$\mu = \frac{\sin i_{1}}{\sin r_{1}} = \frac{\sin{60{^\circ}}}{\sin{30{^\circ}}} = \frac{\sqrt{3}/2}{1/2} = \sqrt{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.