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)

$45{}^\circ$

Answer 2

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, $n=\sqrt{2}, r=30^{\circ}$ $\therefore \sin i =\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}$ $\Rightarrow i=45^{\circ}$