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

`:'n_0 gt (n_0)/(2) gt (n_0)/(6) gt (n_0)/(8)` , the ray of the light is travelling from a denser medium to rare media. For each refraction , we use the relation `n_1 sin theta_1= n_2 sin theta_2 `

In this problem ` theta_1 gt theta , theta_2 gt theta_1, theta_3 gt theta_2 ` and the beam of light will not enter region IV, if the angle of refraction in region IV is `90^(@)` .
For successive refractions, we get
`n_0 sin theta =(n)/(2) sin theta_1 =(n)/(4) sin theta_2=(n_(0))/(8) sin90^(@)`
` or n_0 sin theta =(n_0)/(8) sin 90^(@)`
`:. sin theta =(1)/(8) or theta = sin^(-1)""((1)/(8))`
Thus (b) is the correct choice.