C appears as a constant in Maxwell's equations (they describe the behaviour of electromagnetic field).
Have a look here:
http://en.wikipedia.org/wiki/Electro..._wave_equation
It depends on e0 and u0, electrical and magnetic permeability constants of vacuum, presented and explained in a table lower on the page.
Not as simple as
eh
?
And, we do have V for other mediums, but this is not fundamental, nor it is a constant.
BTW, by knowing electric and magnetic properties of the medium, the velocity of light in it can be calculated with the same formula (v=1/SQRT(e0*u0)). of course, the medium have to be transparent too, and obviously those relations will not cover the issue of transparency, for this there are others.
So, optical behaviour (refraction index) of media are determined by their related electromagnetic properties.. strange but true.