A prism is shown in the figure with prism angle `75^(@)` and refractive index `sqrt(3)`. A light ray incidents on a surface at incident angle `theta`. Other face is coated with a medium of refractive index n. for ` theta le 60^(@)` ray suffers total internal reflection find value of `n^(2)`.

Answer

1.5

Explanation

It is given that when ray is incident on one of the surface at an angle `60^(@)` then it falls on the front surface at critical angle.

Let `r_(1)` be the angle of refraction then we can write the following Snell.s law.
`sin 60^(@) = sqrt(3) sin r_(1)`
`rArr (sqrt(3))/(2) = sqrt(3) sin r_(1) = 30^(@)`.
We know that, `r_(1) = A rArr 30 +r_(2) = 75 rArr r_(2) = 45^(@)`.
Since `r_(2)` is increased angle hence angle mirror and this location be taken as `90^(@)`. We can apply Snell.s law as follows :
`sqrt(3) sin 45^(@) = n sin 90^(@) rArr n_(2) = 3//2`.