A ray of light passing through a prism having refractive index `sqrt2` suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. What is the angle of prism?

Options

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

Answer

C

Explanation

For the refraction at the first surface of the prism , `n = (sin i)/( sin r)` but i= 2r
`therefore n = (sin 2r)/(sin r) = ( 2 sin r cos r)/(sin r) = 2 cos r `
`therefore (sqrt2)/(2) = cos r therefore r = (1)/(sqrt2)`
`therefore r = 45^(@)`
But when the ray suffers minimum deviation,
`A = 2r therefore A = 2 xx 45^(@) = 90^(@)`