By what angle the mirror must be rotated such that the reflected ray becomes vertical. Let the light ray incident on the plane mirror with an angle of incidence theta with respect to horizontal

Explanation

The diagram below shows the four ways in which the reflected ray can become vertical.

For case 1 : Angle by which the Reflected ray rotates `= 30^(@)`
Angle by which the mirror rotates `=30^(@)/2 =15^(@)`
(Anticlockwise)

For case 2 : Angle by which the Reflected ray rotates `= 150^(@)`
Angle by which the mirror rotates `= 75^(@)` (clockwise)
For case 3 : Angle by which the Reflected ray rotates `= 300^(@)`
Angle by which the mirror rotates `= 150^(@)` (clockwise)
For case 4 : Angle by which the Reflected ray rotates `= 210^(@)`
Angle by which the mirror rotates `= 105^(@)` (Anticlokwise)
But case (2) & case (3) are not possible as the I.R. falls on the polished part of mirror. after rotation of mirror.
`:.` Answer is `15^(@)` (Anticlockwise) and `105^(@)` (Anticlockwise)