Two tuning forks vibrating close together affect each other: the air they push makes them sound different. Physicists used this simple analogy to calculate optical resonators — devices that trap light between mirrors. But the analogy falls apart when the mirrors become flat, like window panes.

For half a century, nobody noticed the error because flat resonators skillfully pretended to be three-dimensional. The new theory exposed the deception: it precisely describes how light darts around inside a trap of any shape — from tiny laser pits to multi-layered mirrors. It turns out that even a slight curvature of the walls dramatically changes the light's behavior. This discovery will help build supersensitive sensors and lasers with record-breaking efficiency.