Question

A ray of light strikes a transparent rectangular slab of refractive index $\sqrt 2$ at an angle of incidence of $45^{\circ}$. The angle between the reflected and refracted rays is

• A. $75^{\circ}$
• B. $90^{\circ}$
• C. $105^{\circ}$
• D. $120^{\circ}$

Answer 1

Answer: (C)

Applying Snell's law at air-glass surface, we get

$1sin i = \sqrt{2} sin r' $
$sin r' = \frac{1}{\sqrt{2}} sin i$
$= \frac{1}{\sqrt{2}} sin 45^{\circ} \left(\because i = 45^{\circ}\right) $
$\Rightarrow sin r' = \frac{1}{2}$ or $r' = sin^{-1}\left(\frac{1}{2}\right) = 30 ^{\circ}$
From figure,
$i + \theta +30^{\circ} = 180^{\circ} \quad (\because i = r = 45^{\circ})$
$45^{\circ} + \theta + 30^{\circ} = 180^{\circ}$ or
$\theta = 180^{\circ} - 75^{\circ} = 105^{\circ}$
Hence, the angle between reflected and refracted rays is $105^{\circ}$