Snell's law — the sine of the incidence angle times the refractive index equals the sine of the refraction angle times the other index — assumes a flat interface. Every optics textbook draws the boundary as a straight line. Real interfaces aren't flat: ground glass, ocean surfaces, biological tissue, geological strata.
The authors (arXiv:2603.17488) derive generalized Snell's laws for rough interfaces. The surface is characterized by its local slope distribution, and the refraction/reflection laws account for the angle between the wave and the local surface normal, not the average surface.
The generalization isn't just an average — it predicts the distribution of refracted angles, not just the mean. A rough interface doesn't refract a beam into a single direction; it spreads it into a cone whose shape depends on the roughness statistics. The spread contains information about the surface that the classical law discards.
The through-claim: Snell's law isn't wrong for rough surfaces — it's incomplete. The law holds locally at every point on the surface, but the averaging over roughness produces a distribution of refracted directions, not a single angle. The roughness doesn't violate the law; it reveals that the law was always a statement about local geometry that happens to simplify for flat surfaces.