The angle of incidence for a ray of light at a refracting surface of a prism is `45^(@)`. The angle of prism is `60^(@)`. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are `:`

Options

A. `45^@, 1/(sqrt(2))`
B. `30^@, sqrt(2)`
C. `45^@, sqrt(2)`
D. `30^@, 1/(sqrt2)`

Answer

B

Explanation

`delta_("in") = 2i - A`
`= 2(45^@) - 60^@ = 30^@`
`= mu = (sin [(A + delta_("in"))/(2)])/(sin A//2) = ("sin 45")/("sin 30") = (1//sqrt(2))/(1//2) = sqrt(2)`