Question

A light beam is travelling from Region $I$ to Region $IV$ (Refer Figure). The refractive index in Regions $I, II, III$ and $IV$ are $n_0,\frac{n_0}{2},\frac{n_0}{6} \, \, and \, \, \frac{n_0}{8},$ respectively.The angle of incidence $\theta$ for which the beam just misses entering Region $IV$ is

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

Answer 1

Answer: (B)

$sin^{-1}\big(\frac{1}{8} \big)$

Answer 2

Critical angle from region III to region IV
$20\,mm sin \, \theta_C=\frac{n_0 / 8}{n_0 / 6}=\frac{3}{4}$
Now, applying Snell's law in region I and region III
$20\,mm n_0 sin \, \theta=\frac{n_0}{6} sin \, \theta_C$
or $20\,mm sin \, \theta=\frac{1}{6} sin \, \theta_C=\frac{1}{8}$
$\therefore 20\,mm \theta=sin^{-1}\big(\frac{1}{8} \big)$
$\therefore$ Correct option is (b)