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 $A=2r$
$=2\times 45{}^{\circ }=90{}^{\circ }$