Question

A ray of monochromatic light is incident on one refracting face of a prism of angle $75^{\circ}$. It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is $\sqrt{2}$, the angle of incidence on the first face of the prism is

• A. $30^{\circ}$
• B. $45^{\circ}$
• C. $60^{\circ}$
• D. $0^{\circ}$

Answer 1

Answer: (B)

From figure

$A=r_{1}+c=r_{1}+\sin ^{-1}\left(\frac{1}{\mu}\right) $
$\Rightarrow r_{1}=75-\sin ^{-1}\left(\frac{1}{\mu}\right)$
$\Rightarrow 75-45=30^{\circ}$
From Snell's law At $B$
$\mu=\frac{\sin i}{\sin r_{2}} \Rightarrow \sqrt{2}=\frac{\sin i}{\sin 30^{\circ}} $
$\Rightarrow i=45^{\circ}$