One face of prism of refracting angle `30^@` and refractive index `1.414` is silvered. At what angle must a ray of light fall on the unsilvered face so that it retraces its path out of the prism ?

Options

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

Explanation

At second surface, therefore is no refraction, so
`r_(2)=0`
`therefore r_(1)=A=30^(@)`
From Snell's law,
`n=(sini_(1))/(sinr_(1))`
`implies n=(sini_(1))/(sin30^(@))`
`implies sini_(1)=sqrt(2)xx(1)/(2)=(1)/(sqrt(2))`
`implies sin_(1)=(1)/(sqrt(2))`
`implies i_(1)=45^(@)`