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)/(sqrt(2)`

Answer

B

Explanation

i= `45^(@) , delta_(m) = 2i - A = 90^(@) - 60^(@) = 30^(@)`
`n = (sin ((A + delta_(m))/(2) ) )/(sin A //2) = (sin 45^(@))/(sin 30^(@)) = sqrt(2)`.