A ray of monochromatic light is incident on one refracting face of a prism of angle `75^(@)`. It passes thorugh the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is `sqrt(2)`, the angle of incidence on the first face of the prism is

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `0^(@)`

Answer

B

Explanation

`r_(2)=sin^(-1)((1)/(mu))=45^(@)`
`r_(1)=A-r_(2)=75^(@)-45^(@)=30^(@)`
`(sin i)/(sin r_(1))=sqrt2`
`implies sin I =sqrt2sin 30^(@)=sqrt2xx(1)/(2)`
`implies i=45^(@)` .