A light beam is traveling from Region I to region IV (refer figure). The refractive indices in Region 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

Options

A. `sin^(-1)((3)/(4))`
B. `sin^(-1)((1)/(8))`
C. `sin^(-1)((1)/(4))`
D. `sin^(-1)((1)/(3))`

Answer

B

Explanation

As the beam just misses entering region IV, the angle of refraction in the region IV must be `90^(@)`

Application of Snell.s law successive at different interfaces gives `mu_(0)sintheta=(mu_(0))/(2)sintheta_(1)=(mu_(0))/(6)sintheta_(2)=(mu_(0))/(8)sin90^(@)`
`impliessintheta=(1)/(8)` or `theta=sin^(-1)((1)/(8))`