Loughborough Applied Mathematics Seminar (Christmas Lecture)

The rainbow is an often observed yet striking phenomenon whose quantitative explanation requires a surprisingly high degree of mathematical sophistication. Professor Linton will begin by providing a brief history of theories that were developed to explain this atmospheric phenomenon from the ancient Greeks to Newton, Young and Airy. It was in his efforts to provide a quantitative description of rainbow phenomena that Airy created what we know call the Airy function Ai(x). They will then outline the full solution to the problem of electromagnetic scattering by a sphere and say a little about the difficulties that one encounters at high frequencies (as is the case in the light-raindrop problem). Finally, they will discuss one technique, the Watson transformation, that can be used to overcome some of these difficulties and describe an example of its application.