Question

The angle of incidence for an equilateral prism of refractive index $\sqrt{3}$ so that the ray is parallel to the base inside the prism is

• A. $30^{\circ }$
• B. $20^{\circ }$
• C. $60^{\circ }$
• D. $45^{\circ }$
• E. $75^{\circ }$

Answer 1

Answer: (C)

Given, $\mu =\sqrt{3}$
Here, $r=\frac{A}{2}=\frac{60^{\circ }}{2}=30^{\circ }$ $(\because$ equilateral prism )
So, $\frac{\sin i}{\sin r}=\mu$
$\sin i=\sqrt{3}\sin 30^{\circ }$
$\sin i=\sqrt{3}\times \frac{1}{2}$
$\sin i=\frac{\sqrt{3}}{2}$
$i={\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)$
$i=60^{\circ }$