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

Answer

D

Explanation

Given, `i=45^(@), A=60^(@)`
Since the ray undergoes minimum deviation, therefore, angle of emergence from second face, `e=i=45^(@)`
`:.delta_(m)=i+e-A=45^(@)+45^(@)-60^(@)=30^(@)`
`mu=(sin((A+delta_(m))/(2)))/(sin((A)/(2)))=(sin.((60^(@)+30^(@))/(2)))/(sin((60^(@))/(2)))`
`=(sin45^(@))/(sin30^(@))=(1)/(sqrt(2))xx(2)/(1)=sqrt(2)`