Question

Angle of a prism is ${30}^{\circ }$ and its refractive index is $\sqrt{2}$and one of the surface is silvered. At what angle of incidence, a ray should be incident on one surface so that after reflection from the silvered surface, it retraces its path

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. $si{n}^{-1}\sqrt{1.5}$

Answer 1

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

This is the case when a light ray is falling normally the second surface.
Hence by using:
$\mu =\frac{sini}{sinA}\Rightarrow \sqrt{2}$
$=\frac{sini}{sin{30}^{\circ }}\Rightarrow sini$
$=\sqrt{2}\times \frac{1}{2}\Rightarrow i={45}^{\circ }$