Question

The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is $30^{\circ}$. One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is

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

Answer 1

Answer: (D)

$45^{\circ}$

Answer 2

For retracing its path, light ray should be normally incident on silvered face. Applying Snell's law at $M$, $\frac{\sin \, i }{\sin \, 30^{\circ}} = \frac{\sqrt{2}}{1}$ $\Rightarrow \, \, \sin \, i = \sqrt{2} \times \frac{1}{2}$ $\sin \, i = \frac{1}{\sqrt{2}}$ i.e. $i = 45^{\circ}$