Consider the ray diagram for the refraction given Fig. The maximum value of angle `theta` for which the light suffers total internal reflection at the vertical surface, is

Options

A. `cos^(-1)((3)/(4))`
B. `sin^(-1)((3)/(4))`
C. `tan^(-1)((3)/(4))`
D. `cot^(-1)((3)/(4))`

Answer

B

Explanation

Let the light sufferes total internal reflection at the vertical surface where the critical angle is `theta_(c )` as shown in Fig.

`sin theta_(c ) = (mu_(1))/(mu_(2)) = (1)/(1.25) = (4)/(5)`
Here, `theta_(1) = 90^(@) - theta_( c)`
so `sin theta_(1) = sin 90^(@) - theta_( c) = cos theta_( c) = (3)/(5)`
For refraction at the horizontal surface
`(mu_(1))/(mu_(2)) = (sin theta)/(sin theta_(1))`
or `(1.25)/(1) = (sin theta)/(3//5)`
or `sin theta = (3)/(5) xx 1.25 = (3)/(4)`
or `theta = sin^(-1)(3//4)`