Physics
Physics
Problem
A plane mirror is mounted on a rotational stage so that its surface can be rotated through a small angle about a vertical axis. A fixed laser beam strikes the mirror before and after the rotation, and in both cases the reflected beams are observed on a distant screen. (a) Derive an expression for the angle through which the direction of the reflected beam is deflected on the screen in terms of the mirror’s rotation angle . (b) The mirror is rotated through . Calculate the corresponding angular deflection of the reflected beam. (c) Provide a qualitative explanation, using geometrical reasoning, for why the reflected beam’s direction changes by a factor of two compared with the mirror’s rotation.Intuitive explanation
When a mirror rotates, its surface normal rotates by the same angle, and the law of reflection tells us the reflected beam must rotate by twice that amount. The key insight is that the angle between the incident ray and the surface normal determines the reflection geometry—so a small rotation of the mirror causes the reflected beam to deflect by on the distant screen. This 2:1 magnification is why mirrors are so sensitive for detecting small angular changes.
Intuitive explanation
When a mirror rotates, its surface normal rotates by the same angle, and the law of reflection tells us the reflected beam must rotate by twice that amount. The key insight is that the angle between the incident ray and the surface normal determines the reflection geometry—so a small rotation of the mirror causes the reflected beam to deflect by on the distant screen. This 2:1 magnification is why mirrors are so sensitive for detecting small angular changes.