Final answer:
In the law of reflection, when a mirror rotates by angle θ, the normal to its surface also rotates by θ. This causes the reflected light ray's direction to change by 2θ, doubling the angular shift for the reflected light.
Step-by-step explanation:
According to the law of reflection, the angle of incidence (the angle at which the incoming light hits a surface) is equal to the angle of reflection (the angle at which the light reflects off the surface). When a mirror is rotated by a certain angle θ, the normal to the surface of the mirror (the line perpendicular to the mirror surface) also rotates by the same angle. This changes the angle of incidence and, therefore, the angle of reflection.
To visualize this, consider the incoming ray of light and the line perpendicular to the mirror before it is rotated. This line is known as the 'normal'. When the mirror is rotated by angle θ, the normal rotates by θ as well. However, since the angles of incidence and reflection are measured from the normal, the reflected ray now is angled 2θ away from its original direction, as it will deflect θ in the opposite direction to the rotation of the mirror. This happens because the incident angle and the normal rotate together, but the reflected angle moves in the opposite direction to maintain the law of reflection.
Therefore, if a mirror is rotated by an angle θ, the reflected light ray changes direction by 2θ, creating new and dynamic effects in light shows with lasers.