By how much the mirror should be rotated to make the given reflected ray incident

Dear student , Consider a plane-mirror and a fixed incident ray of light reflecting from the surface at an angle θ. Before the mirror has rotated, the angle of incidence is θ as is the angle of reflection. If the mirror is rotated through an angle φ the normal is rotated by an angle φ and thus the angle of incidence increases to θ +φ. Therefore, the angle of reflection must also increase by φ to θ+φ The difference between the final angle of reflection and the initial angle of reflection and is 2φ. For a fixed incident ray, the angle of reflection is twice the angle through which the mirror has rotated and θf = 2φ. now back to question... 2x30° = 60 ° . Regards