The Victor L. Shapiro Distinguished Lecture in Mathematics

Sir Michael Berry

Four geometrical-optics illusions

Thursday, March 16, 11:00am - 12:30pm

To be given jointly with the Seminar on Fractal Geometry, Dynamical Systems and Mathematical Physics.

Zoom Link: https://ucr.zoom.us/j/94882864345

Biosketch

Sir Michael V. Berry was born in Surrey, in 1941.  He holds a BSc in physics from the University of Exeter (1959-62) and was awarded his doctorate in 1965 from the University of St. Andrews, under the supervision of Professor R.B. Dingle.  He is known for the Berry phase as well as the Berry connection and curvature.  He has been awarded the Wolf prize in physics, the Dirac medal, the Onsager Medal, the Lorentz medal, and many other prestigious honors for his academic achievements.  

Professor Berry began his career at the University of Bristol as a postdoctoral researcher in 1965 and remained at Bristol thereafter.  He was elected a Fellow of the Royal Society (FRS) in 1982 and was knighted in 1996.  From 2006 onwards, he has been the Melville Wills Professor of Physics at Bristol University.

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.