Snell's law of refraction
1621 (Snellius, unpublished); 1637 (published by Descartes)
The exact rule for how much light bends when it passes from air into glass. With it, the path of every ray through a lens could be calculated.
How it began
Ptolemy and Ibn al-Haytham had measured refraction, but nobody had a rule that fitted every angle. The Persian mathematician Ibn Sahl wrote an equivalent rule in 984; it was forgotten. In 1621 Willebrord Snellius in Leiden found it again, and in 1637 René Descartes published it.
How it works
Light slows down in glass. The sine of the angle at which a ray meets the surface, multiplied by the refractive index, stays the same on both sides: n₁ sin θ₁ = n₂ sin θ₂. A ray entering glass at a slant therefore bends towards the perpendicular.
Why it mattered
With an exact law, lens makers could calculate where each ray would go instead of grinding and testing. Every designed camera lens, from Petzval’s in 1840 to today’s phone lenses, depends on it.
Limits and what replaced it
The refractive index differs slightly for each colour, which is why simple lenses show colour fringes. Correcting that needed the achromatic lens. The wave theory of light later explained why the law holds.
Today
Lens design software still traces millions of rays with Snell’s law to design camera and phone lenses.