Q.What is the angle of incidence if a ray incident normally on a plane mirror?

Reflection Angle Deflection

Shine a laser at a plane mirror and watch the spot it makes on the far wall. Tilt the mirror just a little and the spot jumps a surprisingly large distance. This is reflection angle deflection: a small rotation of the mirror produces a doubled change in the direction of the reflected ray.

Why the deflection is double

When light strikes a plane mirror, the angle of incidence (measured from the normal — the line perpendicular to the mirror) equals the angle of reflection. This is the law of reflection.

Now keep the incident ray fixed and rotate the mirror by a small angle $\theta$. Because the normal is always perpendicular to the surface, it also turns by $\theta$. So:

• The angle of incidence (measured from the shifted normal) changes by $\theta$.
• By the law of reflection, the reflected ray moves by $\theta$ on the other side of the new normal.

Both shifts add, so the reflected ray swings through $\theta + \theta = 2\theta$.

In words: rotating a plane mirror by $\theta$ (about an axis in the mirror surface, perpendicular to the plane of incidence) rotates the reflected ray by $2\theta$ in the same sense, while the incident ray stays put.

The geometry

Let the initial normal $N_1$ make angle $i$ with the incident ray, so the reflected ray also makes angle $i$ on the other side of $N_1$. After rotating the mirror by $\theta$, the new normal $N_2$ makes angle $i+\theta$ with the incident ray, and the new reflected ray makes angle $i+\theta$ on the opposite side of $N_2$. The angle between the old and new reflected rays is

The $2i$ terms cancel — the result does not depend on the initial angle of incidence. Whether light strikes at $30^\circ$ or $60^\circ$, a mirror rotation of $\theta$ always deflects the reflected ray by $2\theta$.

A worked example

A vertical mirror sends a horizontal beam straight back. Rotate the mirror $5^\circ$ clockwise and the reflected ray now points $10^\circ$ clockwise from its original path. Likewise, "a mirror is rotated by $10^\circ$" ⟹ the reflected ray turns by $20^\circ$. …