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 6 for which the beam just misses entering Region IV is Region I Region II Region III Region IV \[\frac{{{n}_{0}}}{2}\] \[\frac{{{n}_{0}}}{6}\] \[\frac{{{n}_{0}}}{8}\] 0 0.2 m 0.6 m

• 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. \[{{\sin }^{-1}}\left( \frac{1}{3} \right)\]