A ray of monochromatic light is incident on the refracting face of a prism (angle `75^(@)0` . It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the prism is `sqrt(2)` , then the angle of incidence on the first of the prism is

Options

A. `15^(@)`
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Answer

c.

Explanation

`sini_(c)=(1)/(sqrt(2))i_(c)=45^(@)`
Now, `75^(@)=r+45^(@)`
or `r=30^(@)`
Now, `(sini)/(sin30^(@))=sqrt(2)`
or `sini=sqrt(2)xx(1)/(2)=(1)/(sqrt(2))`
`:. i=45^(@)`