Question

A ray of light refracts from medium $1 $ into a thin layer of medium $2$ , crosses the layer and is incident at the critical angle on the interface between the medium $2$ and $3$ as shown in the figure. If the angle of incidence of ray is $\theta$, the value of $\theta$ is

• A. $\sin ^{-1}\left(\frac{8}{9}\right)$
• B. $\sin ^{-1}\left(\frac{13}{18}\right)$
• C. $\sin ^{-1}\left(\frac{13}{16}\right)$
• D. $\sin ^{-1}\left(\frac{8}{13}\right)$

Answer 1

Answer: (C)

As the light ray incident at critical angle,
$\sin C=\frac{\mu_{3}}{\mu_{2}}=\frac{1.3}{1.8}$ and $C=r$
$\therefore \sin r=\frac{1.3}{1.8}$
$\Rightarrow \sin \theta=\frac{1.8}{1.6} \times \frac{1.3}{1.8}=\frac{13}{16}$
$\theta=\sin ^{-1}\left(\frac{13}{16}\right)$