Airy equation: y'' − xy = 0. Solution Ai(x): oscillatory for x<0 (classically allowed), exponential decay for x>0 (forbidden).
WKB approximation: ψ≈(p(x))^{-1/2} exp(i∫p dx), fails at turning point (p=0) — Airy function is the exact connection formula.
Caustic: fold catastrophe — envelope of a family of rays. Light intensity ∝ |Ai(ξ)|² near caustic.
Rainbow: deflection angle extremum at ≈138° (Descartes, 1637). Supernumerary bows = interference of Airy-function type.