A ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism. If `mu` is the refractive index of the material of the prism, the maximum value of the base angle for which light is totally reflected from the hypotenuse is

Options

A. `sin^(-1) ((1)/(n))`
B. `tan^(-1) ((1)/(n))`
C. `sin^(-1) ((n-1)/(n))`
D. `cos^(-1) ((1)/(n))`

Answer

D

Explanation

If `alpha ` is maximum ,
TIR occurs between base and hypotenuse
`(90 - alpha) = i_(c ) = `minimum value of angle of incidence

`sin(90 - alpha ) = sin i_(c ) = (1)/(n)`
`rArr " " cos alpha = (1)/(n) rArr alpha = cos^(-1) ((1)/(n)) `.