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 monchromatic light will retrace it path it its angle of incidence on the unsilvered refracting surface of the prism is

Options

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

Answer

D

Explanation

In `DeltaAPM,/_APM=180^(@)-(30^(@)+90^(@))=60^(@)`
`:. r=90^(@)-/_APM=90^(@)-60^(@)=30^(@)`
Now applying Snell law at `P`

`1.sin i=sqrt(2)sin 30^(@)=(1)/(sqrt(2))`
Hence `i=45^(@)`