A light beam is traveling 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

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