If a prism having refractive index `sqrt 2` has angle of minimum deviation equal to the angle of refraction of the prism, then the angle of refraction of the prism is:

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

D

Explanation

Put `A=delta_(min)` and `mu= sqrt(2)`
The relation `mu=(sin ((A+delta_(min))/(2)))/(sin((A)/(2)))`
`sqrt(2)=(sinA)/(sin A//2) rArr sqrt(2)=2 cos A//2`
`rArr cos A//2 =(1)/(sqrt(2)) rArr A//2 =45^(@)`
`rArr A=90^(@)`.