How is refractive index a function of frequency?

[vhbelvadi]

I recently came across the representation of n(ω) for refractive indices.
I also scouted the internet for explanations but could find none, except one on 'complex refractive index' but I don't think that's quite it.

So how exactly is refractive index a function of frequency?

 

[Dadface]

Cauchy came up with an empirical equation with constants characteristic of the media used.I'm assuming that advances have been made since Cauchys time and if so a search starting with something like "Cauchy's dispersion formula" might lead you in the right direction.