A ray of light is incident normally on one face of a prism as shown in figure. The refractive index of the material of the prism is `(5)/(3)` and the prism is immersed in water of refractive index `(4)/(3)`, then

Options

A. a. The angle of emergence `theta_(2)` of the ray is `sin^(-2)((5)/(8))`
B. b. The angle of emergence `theta_(2)` of the ray is `sin^(-1)((5)/(4sqrt(3)))`
C. c. The angle of emerrgence `theta_(2)` of the ray is `sin^(-1)((7)/(3sqrt(4)))`
D. d.Total internal reflection will not occur at P if the refractive index of water increases to a value greater than `(5)/(2sqrt(3))` by dissolving some substance.

Answer

A, D

Explanation

Initially at `P` there is TIR, there force at Q (snell's law)
`(5)/(3)sin30^(@)=(4)/(3)sintheta_(2)`
`implies sintheta_(2)=(5)/(8)impliestheta_(2)=sin^(-1)((5)/(8))`
if `mu_(W)(5)/(2sqrt(3))implies sinCgt(5//2sqrt(3))/(2//3)impliesCgt60^(@)`
therefore now TIR will not occur at P.