A parallel beam of light is incident from air at an angle `alpha` on the side of right angled triangular prism of refractive index `mu = sqrt(2)`. Light undergoes total internal reflection in the prism at the face `PR` when `alpha` has a minimum value of `45^@`. The angle `theta` of the prism is.
.

Options

A. (a)`15^(@)`
B. (b)`22.5^(@)`
C. (c)`30^(@)`
D. (d)`45^(@)`

Answer

A

Explanation

`1 "sin"45^(@) = sqrt(2) "sin" r_(1)`
`r_(2) - r_(1) = theta`
` theta = 45^(@) - 30^(@)`
`implies theta = 15^(@)`