A glass prism has refractive index `sqrt(2)` and refracting angle `30^(@)` . One of the refracting surface of the prism is silvered. A beam of monochromatic light will retrace it path it its angle of incidence on the unsilvered refracting surface of the prism is

Options

A. 0
B. `pi//6`
C. `pi//4`
D. `pi//3`

Answer

c.

Explanation

`A=r_(1)+r_(2)`
`30^(@)=r_(1)+0`
or `r_(1)=30^(@)`
Now, `(sini)/(sin30^(@))=sqrt(2)`
or `sini=sqrt(2)xx(1)/(2)`
or `i=45^(@)`