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. ${\sin }^{-1}\left(\frac{3}{4}\right)$
• 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

The correct option is B ${\sin }^{-1}\left(\frac{1}{8}\right)$

Total internal reflection occurs at the interface of region III and IV as shown in figure.

$n_0\sin \theta =\frac{n_o}{2}\sin {\theta }_1=\frac{n_o}{6}\sin {\theta }_2=\frac{n_o}{8}\sin r$

$n_0\sin \theta =\frac{n_0}{8}\sin {90}^0\Rightarrow \theta ={\sin }^{-1}\left(\frac{1}{8}\right)$