In the shown figure, mirror is rotated by an angle theta. Find theta if

ray of light retraces its path after reflection from M
ray of light MP turns in the direction of MN.

Answer

A, C

Explanation

in this case, A and `i_1` are small. Therefore,
deviation by prism can be obtained by
`delta=(mu-1)A=(1.5-1)(2^@)=1^@`
Hence, the prism will deviate the ray of light by `1^@` from its
original path as shown in fig. `31.116`.

In the absence of prism, ray of light was falling normal
to the mirror. So, ray of light was already retracing its
path. Prism has rotated the ray by `1^@` in
cloakwise direction, then ray of light will further fall
normal to the mirror and it again retraces its path. Therefore, the correct answer is
`theta=1^@,`cloakwise
If we rotate a plane mirror by theta in clockwise direction, then reflected ray also rotates in
clockwise direction by an angle `2theta.`
Here, we have to rotate reflected ray MP by `1^@` in clockwise direction to make it in the
direction if MN. Therefore, we will have to rotate the mirror by `0.5^@` in clockwise direction.
Therefore, the correct answer is
`theta=0.5^@,` clockwise