Ray Optics and Optical Instruments - Result Question 52
54. 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) $60^{\circ}$
(b) $45^{\circ}$
(c) Zero
(d) $30^{\circ}$
[2018]
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Answer:
Correct Answer: 54. (b)
Solution:
- (b) For retracing the path, light ray should be normally incident on silvered face.
$A=r+O \Rightarrow r=30^{\circ}$
Applying Snell’s law at point M,
$\frac{\sin i}{\sin 30^{\circ}}=\frac{\sqrt{2}}{1}$
$\Rightarrow \sin i=\sqrt{2} \times \frac{1}{2}$
or, $\quad \sin i=\frac{1}{\sqrt{2}}$ i.e., $i=45^{\circ}$
