Ray Optics And Optical Instruments Ques 62
62. The refractive index of the material of a prism is $\sqrt{2}$ and its refracting angle is $30^{\circ}$. One of the refracting surfaces of the prism is made a mirror inwards. A beam of monochromatic light enters the prism from the non-mirror surface if its angle of incidence of the prism is
[1992, 2004]
(a) $30^{\circ}$
(b) $45^{\circ}$
(c) $60^{\circ}$
(d) $0^{\circ}$
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Answer:
Correct Answer: 62.(b)
Solution:
$\angle r=30^{\circ}$ (using law of sines)
$ \begin{alignedat} & \Rightarrow \mu=\frac{\sin i}{\sin r} \\ & \Rightarrow \sqrt{2} \times \sin 30^{\circ}=\sin i \\ & \Rightarrow \sin i=\frac{1}{\sqrt{2}} \Rightarrow i=45^{\circ} . \end{aligned} $
BETA
