Magic mirrors and magic windows

Venue: Room Sala "Luigi Stringa" FBK
At: 14.00

• Prof. Michael Berry - Melville Wills Professor of Physics (Emeritus) at the University of Bristol, UK

Abstract:

Ancient oriental mirrors possess a property that seemed magical and was probably unintended by those who made them: the pattern embossed on the back of such a mirror appears in light reflected onto a screen from its apparently featureless front surface.
In reality, the embossed pattern is reproduced on the front, in low relief invisible to direct observation, and analysis shows that the projected image results from pre-focal ray deviation.
In this interesting regime of geometrical optics, the image intensity is given simply by the Laplacian of the height function of the relief. Observation confirms this ‘Laplacian image’ interpretation.
Current research aims to create the transparent analogue of the magic mirror: ‘magic windows’, in which glass sheets, flat to unaided vision, concentrate light onto a screen with intensity reproducing any desired image.
Laplacian image theory implies that the desired surface relief is obtained by solving Poisson’s equation.

Michael Berry, Melville Wills Professor of Physics (Emeritus) at the University of Bristol, UK
After graduating from Exeter and St Andrews, Michael Berry entered Bristol University, where he has been for twice as long as he has not.
He is a physicist, focusing on the physics of the mathematics…of the physics.
Applications include the geometry of singularities (caustics on large scales, vortices on fine scales) in optics and other waves, connections between classical and quantum physics, and the physical asymptotics of divergent series.
He delights in finding the arcane in the mundane – abstract and subtle concepts in familiar or dramatic phenomena:
- Singularities of smooth gradient maps in rainbows and tsunamis;
- The Laplace operator in oriental magic mirrors;
- Elliptic integrals in the polarization pattern of the clear blue sky;
- Geometry of twists and turns in quantum indistinguishability;
- Matrix degeneracies in overhead-projector transparencies;
- Gauss sums in the light beyond a humble diffraction grating.