Why does the angle of light through a prism change based on its wavelength?

[Ambidext]

Just a general question on the EM spectrum.

angle deviation of the light wave as it passes through a prism seems to be inversely related (looks like a 1/x graph) to its wavelength. So my question, why?

My guess is that the deflected path is shorter than the undeflected by cos A, where
0 < A < 90
and the bigger wavelength is, the longer the path it can travel and thus a bigger wavelength corresponds to a longer path x cos A?

 

[Claude Bile]

The ordinary dispersion relation that we observe in glasses such as silica is due to the strong absorption in the ultraviolet region (which, in turn, is due to the size of the energy band gap of the material; that is, the energy difference between the valence and conduction band).

The analytical form is given by the Kramers-Kronig relations. http://en.wikipedia.org/wiki/Kramers–Kronig_relation.

Claude.