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

Answer

D

Explanation

(d) At second surface, there is no refraction, so
`r_(2)=0`
`therefore` `r_(1)=A=30^(@)`
From Snell's law,
`n=sini_(1)/sinr_(1)`
`rArrn=sin i_(1)/(sin 30^(@))`
`sini_(1)=sqrt2xx1/2=1/sqrt2`
`rArr sin i_(1)=1/sqrt2rArr i_(1)=45^(@)`