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This question already has an answer here:

Lights entering the prism with different wavelengths at the same angle. why go to different directions? what happens step to step between the protons&electrons in glass and the photons? what is the wavelength of interest in the direction the light goes? please don't tell they have different index of refraction.

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marked as duplicate by Kyle Kanos, Yashas, John Rennie visible-light Jul 27 '18 at 16:31

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ Different wavelengths of light have different indices of refraction. (You asked not to tell you that, but that is the explanation.) $\endgroup$ – David Hammen Jul 17 '18 at 21:11
  • $\begingroup$ The polarisability of dielectrics depends on frequency. This of course is the same as saying that the RI does so. :-). $\endgroup$ – my2cts Jul 17 '18 at 21:22
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    $\begingroup$ With respect to the comment by David Mannen: When you wrote "Please don't tell [me] they have different index[es] of refraction," is it fair to assume that you understand what the index of refraction is, and that you're really asking why the different wavelengths of light have different indexes of refraction in glass? See physics.stackexchange.com/questions/65812/… $\endgroup$ – Randall Stewart Jul 18 '18 at 0:02
  • $\begingroup$ I thought it was clear enough. The answer of this question will also work ''why the different wavelengths of light have different indexes of refraction in glass? '' $\endgroup$ – evet buyrun Jul 18 '18 at 0:18
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There are two ways to describe this:

  1. Here is the classical view:

Every material has some wavelength dependence, and this is dispersion.

In glass, the dispersion curve is described by the Sellmeier equation:

$$ n^2(\lambda) = 1 + \sum_k \frac{B_k \lambda^2}{\lambda^2 - C_k} $$

  1. Now in the QM view

You can derive the Sellmeier equation by using a set of independent harmonic osciallators, giving the Lorenz curve, where ω=2πc/λ and where polarization and n2 are linearly dependent.

Now imagine the glass as a lattice. The space between the atoms is constant (on average) and so the photons will see this average spacing between atoms.

If you look at the same case in the double slit experiment, you will see that the different wavelength photons will create a different spacing between the interference patterns. This is because the photon, as it is shot towards the screen has to go through both slits and as a wave will interfere with itself. The darker areas are destructive interferences, and the brighter ones are constructive interferences.

Now in your case, when the photon interacts with the lattice, the atoms in the glass will act like the slits. The slits will cause the photon (wave) to go through all spaces, and will interfere with itself. Now in this case it will be constructive in only one angle, the angle of refraction. And it will be destructive in all other angles.

Now the only one constructive angle will depend on the wavelength, because, depending on the wavelength, the wave will interact with itself in different angles constructively.

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