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The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is $30^{0}$ .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

For retracing the path, light ray should be normally incident on silvered face.

$A = r + O r = 30 °$

Applying Snell’s law at point M,

$\frac{sini}{\sin 30^{0}} = \frac{\sqrt{2}}{1}$ $\Rightarrow sini = \sqrt{2} \times \frac{1}{2}$

or $sini = \frac{1}{\sqrt{2}} i . e ., i = 45^{0}$

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