Math Playground
Physics

Reflection (waves)

Angle in equals angle out — for light, sound or any wave.

When a wave hits a boundary, the angle of incidence equals the angle of reflection — measured from the normal.

Quick check

A light ray hits a mirror 30° from the surface. What angle does the reflected ray make with the surface?

Ray box — reflection & refraction at a surface
air (n = 1)medium (n = 1.50)θᵢ = 40°θᵣ = 40°θₜ = 25.4°

Snell's law sin θᵢ = n · sin θₜ — light entering a denser medium bends toward the normal and slows down; some always reflects too. (Going the other way, past a critical angle it can't escape at all — total internal reflection, the trick behind fibre optics.)

Law of reflection

Angles measured from the normal — the line perpendicular to the surface at the point of contact. The incoming ray, outgoing ray, and normal all lie in one plane.

Two kinds of reflection

  • Specular — smooth surface (mirror, still water): parallel rays stay parallel, you get a clear image.
  • Diffuse — rough surface (paper, a wall): rays scatter every way, which is how you see ordinary objects from any angle.
  • Same law applies to each tiny facet — rough just means the normals point all over.
Watch out

Always measure angles from the normal, not from the surface itself. Mixing the two is the classic ray-optics slip-up.