Rays and Reflection

Law of Reflection

equal angles

When a ray reflects from a plane mirror, the outgoing ray makes the same angle with the normal as the incoming ray.

Example

When a ray reflects from a plane mirror, the outgoing ray makes the same angle with the normal as the incoming ray. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A plane mirror has a normal

At the point where the ray hits, draw the normal: the line perpendicular to the mirror. The reflection rule compares both rays to that normal, not to the mirror surface itself.

normal⊥mirror\text{normal} \perp \text{mirror}
Reflection in a plane mirrorAn incoming ray reflects from a plane mirror symmetrically about the normal.mirrornormal

The two angles match

The incoming ray and outgoing ray are symmetric about the normal. The incoming angle equals the outgoing angle, so the mirror does not choose a new direction at random.

θin=θout\theta_{\text{in}} = \theta_{\text{out}}
Reflection in a plane mirrorAn incoming ray reflects from a plane mirror symmetrically about the normal.mirrornormal

The equality is row-by-row

The exact angle value can change from setup to setup, but the mirror rule keeps the outgoing angle equal to the incoming angle in each row. The diagram shows one symmetric case; the table shows the rule, not extra drawn rays.

θinθout20∘20∘35∘35∘50∘50∘\begin{array}{c|c}\theta_{\text{in}}&\theta_{\text{out}}\\20^\circ&20^\circ\\35^\circ&35^\circ\\50^\circ&50^\circ\\\end{array}
Reflection in a plane mirrorAn incoming ray reflects from a plane mirror symmetrically about the normal.mirrornormal
optics The mirror drawing is a model surface. The angle rule is exact for an ideal plane mirror.