(d) Consider a plane-mirror and a fixed incident ray of light. 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 f 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 is 2ϕ. Thus for a fixed incident ray, the angle of the reflection is twice the angle through which the mirror has rotated.
