Question

If one face of prism is silvered having prism angle $ 30{}^\circ $ and $ \mu =\sqrt{2}. $ What will be the angle of incidence, so that the incident ray retraces its path?

• A. $ 30{}^\circ $
• B. $ 60{}^\circ $
• C. $ 90{}^\circ $
• D. $ 45{}^\circ $

Answer 1

Answer: (D)

The ray retraces its path after reflection from the silvered face $A C$. Therefore, $\angle A R Q=90^{\circ}$. As is clear from the figure, the angle of reflection $RQN$ at face $A B$ is $30^{\circ}$.

Therefore, by Snell's law, we have
$ n =\frac{\sin i}{\sin r} $
Given, $ n=\sqrt{2}, r=30^{\circ} $
$ \therefore \sin i =\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}} $
$ \Rightarrow i=45^{\circ} $