What we learn(ed) from rainbows

Abstract As well as describing the beautiful physics of a dramatic natural phenomenon, rainbow studies over centuries have illustrated unexpected connections with other areas of physics and the practice of science more generally. The connections include: • Numerical experiments when mathematics is too difficult • Illusions: no arc in the sky • A theory (light rays) being replaced by a deeper one (light waves) • Decoherence: suppressing wave interference • Ubiquity of rainbow interference decorating caustics • Colour science • Mathematics of divergent series • The totalitarian principle: refractionless rainbows and gravitational lensing Physics students would benefit from encountering all or some of these connections.