A ray of light is incident normally on one of the faces of a prism of apex angle `30^(@)` and refractive index `sqrt(2)`. The angle of deviation through prism is

Options

A. `0^(@)`
B. `12.5^(@)`
C. `15^(@)`
D. `22.5^(@)`

Answer

C

Explanation

For normal incidence,
`i=0^(@), r_(1)=0^(@)`
As `:.r_(2)=A-r_(1)=30^(@)`
As `mu=(sine)/(sinr_(2))`
`:.sine=musinr_(2)=sqrt(2)sin30^(@)-(1)/(sqrt(2))`
or `e=sin^(-1)((1)/(sqrt(2)))=45^(@)`
or `delta=i+e-A=0^(@)+45^(@)-30^(@)=15^(@)`