For an angle of incidence `theta` on an equilateral prism of refractive index `sqrt(3)`, the ray refracted is parallel to the base inside the prism. The value of `theta`is

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `75^(@)`

Answer

C

Explanation

Here, angle of prism, A= `60^(@)`
Refractive index, `mu=sqrt(3)`
At the minimum deviation `delta_(m)`, the refracted ray inside the prism becomes parallel to its base.
`mu=(sin((A+delta_(m))/(2)))/(sin(A/(2)))` or `sqrt(3)=(sin((60^(@)+delta_(m))/(2)))/(sin((60^(@))/(2)))`
`sqrt(3)sin30^(@)=sin((60^(@)+delta_(m))/(2))` or `(sqrt(3))/(2)=sin((60^(@)+delta_(m))/(2))`
`sin60^(@)=sin((60^(@)+delta_(m))/(2))` or `60^(@)=(60^(@)+delta_(m))/(2)impliesdelta_(m)=60^(@)`
As `delta_(m)=2i-A`, where i is the angle of incidence
Here, `i=theta`
`:.theta=(delta_(m)+A)/(2)=(60^(@)+60^(@))/(2)=60^(@)`