A ray of light strikes a plane mirror at an angle of incidence `45^@` as shown in Figure . After reflection,l the ray passes through a prism of refractive indes 1.5 whos apex angle is `4^@`. Through what angle must the mirror be rotated it total deviation of the ray be `90^@` ?

Explanation

The deviation produced by small angled prism,
`delta_(1)=(mu-1)alpha=(1.5-1)4^@=2^@` (always)
Deviation caused by mirror,
`delta_(2)=180^@-2i=180^@-2xx45^@=90^@`
Net deviation produced by system `=delta_(1)+delta_(2)=2^@+90^@=92^@`
This is more than `90^@`
Greater is angle of incidence on the mirror, smaller is the deviation.
If `beta` is the angle of rotation of mirror is clockwise direction mirror will be `180^@-2(45^@+beta)=90^@-2beta`
Therefore, total deviation produced `=90^@-2beta+2^@=92^@-2beta`
Given, `92^@-2beta=90^@rArrbeta=1^@`