Ray Optics And Optical Instruments Ques 52
52. 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
[2018]
(a) $60^{\circ}$
(b) $45^{\circ}$
(c) Zero
(d) $30^{\circ}$
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Answer:
Correct Answer: 52.(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, $ \sin i=\frac{1}{\sqrt{2}}$ i.e., $i=45^{\circ}$
BETA
