A prism is made up of material of refractive index `sart3`. The angle of prism is `A`. If the angle of minimum deviation is equal to the angle of the prism, then the value of A is

Options

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

Answer

C

Explanation

(c ) Given `mu = sqrt3` and `delta_(m) = A`
Now `mu = (sin ((A + delta_(m))/(2)))/(sin ((A)/(2))) = (sin ((A + A)/(2)))/(sin ((A)/(2))) = (sin A)/(sin (A)/(2))`
`= (2 sin ((A)/(2)) cos ((A)/(2)))/(sin ((A)/(2))) = 2 cos ((A)/(2))`
Now, `2 cos ((A)/(2)) = mu = sqrt3`
or `cos ((A)/(2)) = (sqrt3)/(2) implies (A)/(2) = 30^(@)`
`A = 60^(@)`