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((4)/(3))`
D. `cot^-1((4)/(3))`

Answer

B

Explanation

Let the light suffers 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_2)/(mu_1) = (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)`.
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