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

Critical angle from region III to region IV
`sintheta_(c)=(n_(0)//8)/(n_(0)//6)=(3)/(4)`
Now, applying Snell's law in region I and region III
`n_(0)sintheta =(n_(0))/(6)sintheta_(c)`
`sintheta =(1)/(6)sintheta_(c)=(1)/(6)((3)/(4))=(1)/(8)rArr theta=sin^(-1)((1)/(8))`
`:.` Correct option is (b).`