Refraction · Fermat → Snell simulation

Light goes from a point in air to a point in glass. Of all the paths it could take, which does it follow — the straight line, or something else?

▶ Run the simulation See the measured result

Measured by the lab

1.500272

Known value

1.5

Relative error

1.81e-4

Units: sinθ₁/sinθ₂ = n₂/n₁ for air (n₁ = 1.000) → crown glass (n₂ = 1.500); Hecht, Optics 5e, Table 4.1

How the lab tests it

Race photon pulses from A (air, index n₁) to B (glass, n₂) down several broken paths A→(x,0)→B, each travelling at c/n₁ above the interface and the slower c/n₂ below, and time the arrivals; then read the winning path's angles, and across a sweep of incidence angles find each least-time path numerically and measure (sinθ₁, sinθ₂).

What it checks

FERMAT'S PRINCIPLE — light takes the path of LEAST time, which BENDS at the interface (the straight geometric line is slower), and the bend obeys SNELL'S LAW n₁ sinθ₁ = n₂ sinθ₂ (i.e. sinθ₁/sinθ₂ = v₁/v₂ = n₂/n₁); across angles the measured (sinθ₁, sinθ₂) fall on a straight line of slope n₁/n₂

This simulation has a catalogued, oracle-checked result: Fermat → Snell: no-oracle → validated — the bent path, found by a stopwatch: with NOTHING coded but the travel time of broken….