A light beam is traveling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are $\mathrm{n}_0, \frac{\mathrm{n}_0}{6}$ and $\frac{\mathrm{n}_0}{8}$, respectively. The angle of incidence $\theta$ for which the beam just misses entering Region IV is
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$\begin{aligned} & \therefore \sin \theta=\frac{\sin \alpha}{2}=\frac{\sin \phi}{6}=\frac{1}{8} \\ & \therefore \theta=\sin ^{-1}\left(\frac{1}{8}\right)\end{aligned}$