Question

A light beam is traveling from Region I to Region IV (refer figure). The refractive indices in Regions I, II, III, and IV are $n_0,n_0/2,n_0/6$, and $n_0/8$, respectively. The angle of incidence $\theta$ for which the beam just misses entering Region IV is

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

Answer 1

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

by applying snell's law at every interface we get ,

${\mu }_{1}sin{\alpha }_1={\mu }_{2}sin{\alpha }_2={\mu }_{3}sin{\alpha }_3...................$

so $n_{o}sin\theta =\frac{n_0}{8}sin90$ (for just to prevent entering )

$\theta =si{n}^{-1}\frac{1}{8}$

option $B$ is correct