Question

A prism of refractive index $\sqrt{2}$ has a refracting angle of $60^{\circ}$. At what angle must a ray be incident on it so that it suffers a minimum deviation?

• A. $30^{\circ}$
• B. $45^{\circ}$
• C. $60^{\circ}$
• D. $75^{\circ}$

Answer 1

Answer: (B)

$\mu=\sqrt{2}, A=60^{\circ}$
At for minimum deviation:
$i=i_{e} $ and $ r_{1}=r_{2}$
Also, $r_{1}+r_{2}=A$
or $2 r=60^{\circ}$
$r=30^{\circ}$
$\mu=\frac{\sin i}{\sin r}$
$\sqrt{2}=2 \sin i$
$\left[\right.$ Putting $\left.r=30^{\circ}\right]$
$\sin i=\frac{1}{\sqrt{2}}$
$i=45^{\circ}$