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 $B$
$\mu =\frac{\sin i}{\sin r_2}\Rightarrow \sqrt{2}=\frac{\sin i}{\sin 30^{\circ }}$
$\Rightarrow i=45^{\circ }$