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It is written in our physics textbook that $$\mu = A+\frac{B}{\lambda^2}+\ldots.$$ However no reason has been provided .. Even on wikipedia no reason is mentioned. I do not want to know exactly what model led to this formula but I simply want to know why the index of refraction decreases on increasing wavelength. Can you suggest any intuitive reason for this?

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This is an empirical formula, according to your wiki link , fitted to the individual material.

In this Feynman lecture a formula is derived which connects the effect of the incoming frequency of light to the inherent frequencies of the material and the index of refraction:

a formula for the index of refraction in terms of the properties of the atoms of the material—and of the frequency of the light:

enter image description here

where

q_e =charge on an electron

m =mass of an electron

ω0 =resonant frequency of an electron bound in an atom

There resonant frequencies depend on the bindings of the atoms and molecules and the Cauchy function describes how.

An index of refraction of 1 means that light goes through without interaction with the molecules , i.e the difference between ω^2 and ω0^2 is very large and there is no change in the direction of the light.

So the Cauchy formula is a fit to the observed functional variations between the incoming frequency and the material frequencies due to the charges which have a resonant frequency . As feynman says

We still have the problem, of course, of knowing how many atoms per unit volume there are, and what is their natural frequency ω0. We do not know this just yet, because it is different for every different material, and we cannot get a general theory of that now.

I think the above still holds, so one is left with the empirical Cauchy formula.

The discussion on dispersion in the lecture may help in intuition.

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A lot of material's absorption line is in the UV , so the shorter the wavelength, the closer you get to the absorption line, which means the material is doing more interaction with the light - thus slowing it down in the medium.

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