What We Learn(ed) from Rainbows

What can rainbows teach us about physics and mathematics? As well as describing the beautiful physics of a dramatic natural phenomenon, rainbow studies over several centuries have uncovered unexpected connections with other areas of physics and the practice of science more generally. The connections encompass the rainbow as an illusion—there is no arc in the sky—rainbow-related waves in water, and the historical role of rainbows in shaping colour theory. These connections extend even further, to the deeper conceptual transition from ray to wave optics. The talk will explore a variety of physics concepts, from wave optics to quantum mechanics, and how they link to rainbows: the universal wave decoration of smooth focal lines, decoherence—wave interference blurred by imperfect resolution, and Gell-Mann’s totalitarian principle. Finally, the lecture will explore how rainbow bridges physics and advanced mathematics, serving as a laboratory for numerical experimentation when analytical solutions are insufficient and delve into the mathematics of divergent series.