A light beam is travelling from Region I to IV (figure). The refractive index in regionals 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 -

• A. \[si{{n}^{-1}}(3/4)\]
• B. \[si{{n}^{-1}}(1/8)\]
• C. \[si{{n}^{-1}}(1/4)~~\]
• D. \[si{{n}^{-1}}(1/3)\]