Nature’s optics and our understanding of light

Abstract

Optical phenomena visible to everyone have been central to the development of, and abundantly illustrate, important concepts in science and mathematics. The phenomena considered from this viewpoint are rainbows, sparkling reflections on water, mirages, green flashes, earthlight on the moon, glories, daylight, crystals and the squint moon. And the concepts involved include refraction, caustics (focal singularities of ray optics), wave interference, numerical experiments, mathematical asymptotics, dispersion, complex angular momentum (Regge poles), polarisation singularities, Hamilton’s conical intersections of eigenvalues (‘Dirac points’), geometric phases and visual illusions.

Keywords:

• refraction
• reflection
• interference
• caustics
• focusing
• polarisation

Acknowledgements

I thank Professor Roy Bishop for permission to reproduce Figure 1, Professor Zeev Vager and Mr. Omer Abramson for introducing me to the squint moon illusion and a helpful correspondence, Professor Andrew Young for advice on mirages, and Professors Mark Dennis and Pragya Shukla for their careful readings of the first draft and helpful suggestions.