A prism ABC of angle `30^(@)` has its face AC silvered. A ray of light incident at an angle of `45^(@)` at the face AB retraces its path after refraction at face AB and reflection at face AC . The refractive index of the material of the prism is

Explanation

Since rays retrace their path i.e. they are incident normally on mirror.
`r=A=30^@`
`1xxsini=musinr`
`sini=sqrt2sin30^@=1/sqrt2=sin45^@`
`i=45^@` OR
The ray inside the prism is parallel to base i.e. `delta=delta_m`
`mu=(sin((A+delta_m)/(2)))/(sin(A//2))=(sini)/(sin30^@)`
`sqrt2=(sini)/(1//2)impliessini=1/sqrt2=sin45^@`
`i=45^@`