# Dispersion: frequency dependent wave speeds

Assuming that light travels through an optically dense medium such as glass slower than in a vacuum:

1. What on the atomic level causes the different changes in speed for different wavelengths?

2. For a light wave incident at the normal (90 degress) of the entry boundary do the different wavelength photons emerge at different times at the exit boundary?

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Transparency needs a photon frequency too low to excite the electrons, and then electron movement is limited by the stiffness of the orbitals rather than the inertia, which implies more electron speed a higher frequency and a higher index.

That was a rough one.

Transparent materials with an index decreasing at higher frequency must be pretty uncommon, since achromatic optics consistently use a convex-concave combination to become frequency-independent despite the indices of both materials increase with frequency. But with metamaterials, one should obtain any unnatural behaviour.

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Photons at one wavelength...

At one single wavelength, a wave has neither a start nor an end, so it has no emergence time nor transit time.

To define start and arrival time, you need a bunch of wavelengths or frequencies. Then the transit time depends on how differently the phase propagates at each frequency. This is called a group speed as opposed to the phase speed.

Whether a bunch centred around a higher frequency emerges later depends on this group speed, which relates to the derivative of the phase speed with respect to the frequency.

You could refer to Wiki, about group speed, dispersion and the like.