We know that refractive index, for any medium,
Also, according to Cauchy's relation
where $A$ and $B$ are constants related to the medium.
According to the first relation, refractive index isn't in any way related to the wavelength of the light, it is only related to the permitivitty and permeability of the medium. According to the second relation, however, it depends on the wavelength too. Which formula is right? Why does the discrepancy arise?