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

Answer

B

Explanation

As the beam just suffers `TIR` at interface of region `III` and `IV`

`n_(0) sintheta=(n_(0))/(2)sintheta_(1)=(n_(0))/(6)sintheta_(2)=(n_(0))/(8)sin 90^(@)`
`sintheta=(1)/(8)`
`theta=sin^(1)((1)/(8))`