Title: Four geometrical-optics illusions
Abstract:
Centuries after the laws of geometrical optics were established, they still have nontrivial and varied applications. Illustrating this are some illusions:
- Mirages, and Raman’s error. Understanding why he denied the applicability of geometrical optics requires careful exploration of the continuum limit of a discretely-stratified medium, to reveal its nonuniform convergence.
- Oriental magic mirrors and the Laplacian image. The optics of these several-millennia-old objects involves the unfamiliar regime of pre-focal brightening. The transmission analogue (‘Magic windows’) raises a challenge for freeform optics.
- The squint moon and the witch ball. The moon sometimes appears to point the wrong way because we perceive the sphere of directions as a distorted ‘skyview’, on which geodesics appear curved. This can be conveniently viewed and analysed by viewing the sky in a reflecting sphere.
- Distorted and topologically disrupted reflections in curved mirrors. Mirror-reflected rays from each point of a continuous object form caustic surfaces in the air. Images are organised by those points whose caustics intersect our eyes, and can be systematically understood in terms of the elementary catastrophes of singularity theory.
Bio:
Sir Michael Berry is a theoretical physicist at the University of Bristol, where he has been for more than twice as long as he has not. His research centres on the relations between physical theories at different levels of description (classical and quantum physics, ray optics and wave optics…). In addition to these deeply mathematical, often geometric, studies, he also delights in finding familiar phenomena illustrating deep concepts – the arcane in the mundane: rainbows, the sparkling of the sun on the sea, twinkling starlight, polarised light in the sky, tidal bores…