Prove that when a mirror rotates through an angle θ a beam of light reflected from it will rotate through an angle of 2θ.

Consider a ray of light incident on a plane mirror at angle i and we assume it is fixed. Now, we know that the angle of reflection r is equal to i. This means the angle between these two rays is 2i.

But when we rotate the angle i further through q and now the angle of incidence will become i+q and the angle between the two becomes 2i+2q. This means the ray reflected also gets reflected twice.

Thus, on rotating a mirror through an angle, the reflected beam rotates through double the angle of rotation given to the mirror.