Effect of Rotation of Plane Mirror on Reflected Ray

Topic Content:

If the direction of an incident ray is kept constant and the mirror is rotated, the angle of rotation of the reflected ray will be twice the angle of rotation of the mirror.

We can prove this using the laws of reflection.

Proof:

Let AB be a ray incident on angle i on the mirror PQ (in green) at B. BN₁ is the normal to the mirror at B. According to the laws of reflection , The angle of incidence (i) of light is equal to the angle of reflection (r). The reflected ray is BR₁ and ∠r = ∠i. Let’s draw a new diagram with r = i.

Let’s say the mirror is turned clockwise to a new position by angle θ to a new position RS. If the source of the ray of light does not change, the incident ray will stay the same and travel in the same direction but there will be a new normal BN₂ since the normal