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

$1sini=\sqrt{2}sin{r}^{\prime }$
$sin{r}^{\prime }=\frac{1}{\sqrt{2}}sini$
$=\frac{1}{\sqrt{2}}sin45^{\circ }\left(\because i=45^{\circ }\right)$
$\Rightarrow sin{r}^{\prime }=\frac{1}{2}$ or $r^{\prime }=si{n}^{-1}\left(\frac{1}{2}\right)=30^{\circ }$
From figure,
$i+\theta +30^{\circ }=180^{\circ }(\because i=r=45^{\circ })$
$45^{\circ }+\theta +30^{\circ }=180^{\circ }$ or
$\theta =180^{\circ }-75^{\circ }=105^{\circ }$
Hence, the angle between reflected and refracted rays is $105^{\circ }$