🌅 Water Caustics — Light Refraction on a Pool Floor
Sunlight refracts as it enters water (Snell's law: n₁·sin θ₁ = n₂·sin θ₂, nwater=1.333). The undulating surface focuses and defocuses rays, creating the familiar shimmering caustic patterns on the floor of a swimming pool or sunlit sea-bed.
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Physics
The water surface is modelled as a superposition of N sinusoidal waves: h(x,y,t) = Σ A·sin(kx·x + ky·y − ωt + φ). At each grid point, the surface normal is computed by finite differences, and Snell's law n₁·sin θ₁ = n₂·sin θ₂ (n₁=1.0, n₂=1.333) gives the refracted ray direction. Each refracted ray is traced to the pool floor, accumulating photon density to form the caustic intensity map.
Where surface curvature focuses many rays onto a small floor area, the intensity spikes — producing the bright caustic lines. Deeper water spreads the pattern; shallower water makes it sharper and more chaotic.
Did you know?
"Caustic" comes from the Greek καυστική meaning "burning" — a focusing mirror or lens can create a caustic hot enough to ignite fire. The shimmering network you see on pool floors, the bright ring inside a coffee cup, and the light patch at the bottom of a glass of water are all everyday caustics.