The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is $30^{o}$ . 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

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zero

$45^{0}$

$60^{0}$

$30^{0}$

answer is B.

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Detailed Solution

The light ray retraces the path of second
surface. That is light ray falls normally on
mirror, i.e., i₂= r₂ = 0.
But for any prism, r₁ + r₂ = A
r₁ = A
Applying Snell’s Law,
$\begin{aligned} 1 \times \sin i_{1} = \sqrt{2} \cdot \sin r_{1} \\ \Rightarrow \sin i_{1} = \sqrt{2} \sin A \\ \Rightarrow \sin i_{1} = \sqrt{2} \sin 30^{\circ} \\ \Rightarrow \sin i_{1} = \frac{1}{\sqrt{2}} \Rightarrow i_{1} = 45^{\circ} \end{aligned}$