A ray of monochromatic light is incident on one refracting face of a prism of angle `75^(@)`. It passes through 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

From figure
`A=r_(1)+c=r_(1)+sin ^(-1)((1)/(mu))`
`impliesr_(1)=75^(@)-sin^(-1)((1)/(mu))`
`75^(@)-45^(@)=30^(@)`
From Snell's law, at `B`
`mu=(sin i)/(sin r_(1))=sqrt(2)=(sini)/(sin 30^(@))impliesi=45^(@)`