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

Answer

A

Explanation

`r_(2)=0` (`because` no refraction is there at second surface)
`thereforer_(1)=A=30^(@)`
`n=(sini_(1))/(sinr_(1))=(sini_(1))/(sin30^(@))`
`=sqrt(2)xx(1)/(2)=(1)/(sqrt(2))`
`sini_(1)=(1)/(sqrt(2))`
`i_(1)=45^(@)`