One face of the glass prism is silver polished. A light ray falls at an angle of `45^@` on the other face. After reflection it is subsequently reflected from the silvered face and then retraces its path. The refracting angle of prism is `30^@`. The refractive index of the prism is

Options

A. `3/2`
B. `sqrt(2)`
C. `sqrt(3)/2`
D. `sqrt(3)`

Answer

B

Explanation

From the above figure,
`implies r= 90^@-[180^@-(90^@+30^@)]=90^@-60^@=30^@`
`impliesi=45^@`
`mu=(sini)/(sinr)=(sin45^@)/(sin30^@)=(1/sqrt(2))/(1/2)=sqrt(2)`