Question

A ray of light passing through a prism having $ \mu =\sqrt{2} $ suffers minimum deviation. If the angle of incidence is double the angle of refraction within the prism, then the angle of the prism is

• A. $ 45{}^\circ $
• B. $ 90{}^\circ $
• C. $ 60{}^\circ $
• D. None of these

Answer 1

Answer: (B)

We know that
$ \frac{\sin i}{\sin r}=\mu $
or $ \sin i=\mu \sin r $
Given, $ i=2r $ and $ \mu =\sqrt{2} $
$ \therefore $ $ \sin 2r=\sqrt{2}\sin r $
$ \Rightarrow $ $ 2\sin r\cos r=\sqrt{2}\sin r $
Or $ 2\cos r=\sqrt{2} $
Or $ r=45{}^\circ $
In minimum deviation,
$ r=\frac{A}{2} $
Or $ A=2r $
$ =2\times 45{}^\circ =90{}^\circ $