Question

If one face of a prism of angle ${30}^{\circ }$ and refractive index $\mu =\sqrt{2}$ is silvered, the incident ray retraces its initial path. The angle of incidence is

• A. ${45}^{\circ }$
• B. ${30}^{\circ }$
• C. ${60}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is A ${45}^{\circ }$



If the incident ray retraces its path, then angle of incidence at the silvered surface $={90}^{\circ }$
From the property of $\Delta AED$, we can find $\angle ADE={60}^{\circ }$
Then, angle of refraction $r={90}^{\circ }-{60}^{\circ }={30}^{\circ }$
Now, using Snell’s law,
$1\times \sin i=\mu \times \sin {30}^{\circ }$
$\Rightarrow \sin i=\frac{1}{\sqrt{2}}$
$\therefore i={45}^{\circ }$