The first lecture during the South West Physics Teacher Conference was entitled "Warping Electromagnetic Space: The Quest for Invisibility" by Dr Alastair Hibbins from the University of Exeter.
Dr Hibbins is part of a team trying to build metamaterials that will hide objects or make them more visible. To do that he has to use elements on the surface of materials to alter the refractive index.
What is the refractive index?
When I teach this at secondary school I just teach that light slows down in a different medium, and this is what causes the wavelength to change. There is a complicated proof involving drawing a diagram with lots of lines and comparing angles using trigonometry that generates snells law.
The idea that waves just slow down has never sat well with me. I haven't considered what really causes the effect of refraction; I didn't study this at university.
Dr Hibbins described refraction as the change in phase speed of the wave cause by the electrons in the medium being forced to vibrate by the incoming electromagnetic wave. A vibrating electron generates another electromagnetic wave, which is out of phase to the incoming wave, these two superimpose and give a wave with a shorter wavelength.
This would explain why different frequencies have different refractive indexes.
Something else that I had not considered is that you can prove snell's law using momentum as well as differentiation and how I would normally demonstrate it via trigonometry.