Question

When a plane mirror is rotated through an angle $\varphi$, by what angle will the reflected beam rotate?

Answer 1

Consider a plane-mirror and a fixed incident ray of light reflecting from the surface at an angle $\theta$. Before the mirror has rotated, the angle of incidence is $\theta$ as is the angle of reflection. If the mirror is rotated through an angle $\varphi$, the normal is rotated by an angle $\varphi$ and thus the angle of incidence increases to $\theta +\varphi$. Therefore, the angle of reflection must also increase from $\varphi$ to $\theta +\varphi$. The difference between the final reflected ray and the initial reflected is $2\varphi$.