Ray Optics and Optical Instruments - Result Question 61
64. 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 mirror surface if its angle of incidence of the prism is
(a) $30^{\circ}$
(b) $45^{\circ}$
(c) $60^{\circ}$
(d) $0^{\circ}$
[2004, 1992]
Show Answer
Answer:
Correct Answer: 64. (b)
Solution:
- (b) $\angle r=30^{\circ}$ (using law of triangle)
$ \begin{aligned} & \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} $
