Different frequencies of light travel at different speeds through solids, which along with Snell's law allows for rainbows. Has this phenomenon of variable speeds been predicted through derivations? What does it tell us about the interactions that occur when light travels through a solid?
The index of refraction is found to be a function of the frequency in an analysis of radiation scattering in a medium: for example in the book of Panofsky and Philips "classical electricity and magnetism" chapter 22, radiation scattering and dispersion ,on paragraph 7. The book seems to be available for a free download here.
Here is a link with Feynman lectures on light to to get the extended framework on light.