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)

${sin}^{-1}\left(\frac{13}{16}\right)$

Applying Snell's Law at interface 2:

$\frac{{\mu }_3}{{\mu }_2}=sin\left({\theta }_c\right)......\left(i\right)$

Using equality of alternate angles,

${\theta }_2={\theta }_c$

Applying Snell's Law at interface 1:

$\frac{{\mu }_2}{{\mu }_1}=\frac{sin\left(\theta \right)}{sin\left({\theta }_c\right)}..........\left(ii\right)$

From (i) and (ii), $sin\left(\theta \right)=\frac{{\mu }_3}{{\mu }_1}=\frac{1.3}{1.6}=\frac{13}{16}$

$\theta =si{n}^{-1}\left(\frac{13}{16}\right)$