Question

A light beam is travelling from region I to region IV (Refer figure). The refractive indices in regions I, II, III and IV are ${\mu }_0,\frac{{\mu }_0}{2},\frac{{\mu }_0}{6}$ and $\frac{{\mu }_0}{8}$, respectively. The angle of incidence $\theta$ for which the beam just misses entering region IV is

• A. ${\sin }^{-1}\left(\frac{3}{4}\right)$
• B. ${\sin }^{-1}\left(\frac{1}{8}\right)$
• C. ${\sin }^{-1}\left(\frac{1}{4}\right)$
• D. ${\sin }^{-1}\left(\frac{1}{3}\right)$

Answer 1

Answer: (B)

As the beam just misses entering region IV, the angle of refraction in the region IV must be $90^{\circ }$.

Application of Snell's law successively at different interfaces gives
${\mu }_0\sin \theta =\frac{{\mu }_0}{2}\sin {\theta }_1=\frac{{\mu }_0}{6}\sin {\theta }_2=\frac{{\mu }_0}{8}\sin 90^{\circ }$
$\Rightarrow \sin \theta =\frac{1}{8}$ or $\theta ={\sin }^{-1}\left(\frac{1}{8}\right)$