This simulator aims a light ray at a flat mirror and lets you sweep the angle of incidence and the mirror's own tilt. The incident ray, the surface normal and the reflected ray always lie in a single plane, with the incident and reflected angles measured from the normal always exactly equal.
• A live ray diagram with the mirror surface, a dashed surface normal, the incoming ray and the outgoing reflected ray, each angle marked with its own arc. • Two live controls: incidence angle (1°-89°) and mirror tilt (-40° to +40°), so you can confirm the law holds regardless of how the mirror itself is oriented. • Four preset scenarios spanning grazing incidence, a default 40° angle, steep incidence, and near-normal incidence. • Live numeric readouts for the angle of incidence, the angle of reflection, and their difference — which stays at exactly zero.
The law of reflection, θᵢ = θᵣ, follows from Fermat's principle of least time: for a flat, smooth (specular) surface, the path light actually takes between two points is the one that takes the least time, and geometry shows that path is exactly the one where the angles from the normal match. This holds independent of wavelength, intensity, or the angle chosen — only surface roughness (producing diffuse rather than specular reflection) breaks the clean single-ray picture.
Optics conventionally measures incidence and reflection angles from the normal (the line perpendicular to the surface) rather than from the surface itself — this convention makes the law of reflection and Snell's law for refraction directly comparable, since both describe angles relative to the same reference line.
The angle of incidence equals the angle of reflection, both measured from the surface normal, with the incident ray, reflected ray and normal all lying in the same plane. This simulator lets you confirm it holds at any incidence angle and any mirror tilt.
It is the standard optics convention, chosen because it keeps the law of reflection and Snell's law for refraction expressed the same way — both compare angles to the perpendicular at the point where light meets the surface.
No. Tilting the mirror rotates the normal along with it, but the incident and reflected angles measured from that (now-rotated) normal remain exactly equal — the law holds regardless of the mirror's orientation in space.
It models an ideal specular (mirror-like) flat surface only — it does not model diffuse reflection off rough surfaces, partial transmission through semi-transparent mirrors, or curved mirror surfaces (see the Concave & Convex Mirrors lab for curved-surface ray tracing).