A prism having refractive index 1.414 and refracting angle `30^(@)` has one of the refracting sufraces silvered .A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is

Options

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

Answer

D

Explanation

It is clear from the figure that the ray will retrace the path when the refracted rat QR is incident normally on the silvered surface AC.
In `DeltaAQR`
`angleARQ=90^(@) thereforeangleAQR=60^(@)`
Angle of refraction ,r=`90^(@)-60^(@)=30^(@)`
Applying the Snell.s law at face AB
`1sini=musinr`
`sini=sqrt(2)xx30^(@)=sqrt(2)xx(1)/(2)=(1)/(sqrt(2))`
`sin^(-1)((1)/(sqrt(2)))=45^(@)`