Dispersion of Light

Hi to whoever is reading this. here is my question - In an article , i read that dispersion occurs as the diff. colors of light have diff frequency and hence have diff energy levels and interact with the atoms of the material they are passing through differently and each is slowed by a different extent. The mechanism for such was stated as absorption and re emission of photons where the photon is absorbed and re emitted as its freq does not match that of the electron's and this time delay causes diff speeds for diff colors . SO according this article is the time delay diff for different colors of light ? and why do photons of higher energy take longer to be re emitted? pls forgive me if the question might seem a bit dumb . thanks in advance.
- vignesh (age 15)
Chennai, Tamilnadu, India

That's a subtle question, not dumb at all!.

The light is not really absorbed and re-emitted in the usual sense of the words. That process would be called fluorescence. Fluorescence has a (somewhat random) time delay associated with it. Fluorescent light is emitted at lower frequency than the absorbed light, follows a different directional pattern, etc. 

The interaction you're interested in here is scattering of the light. A classical picture of it works pretty well for most purposes. You can think of the electrons oscillating in response to the electric field of the light. These electrons then do emit light, at just the frequency of the incoming light (since that's the frequency of their response) and in a spatial pattern just matching that of the incoming beam. However, their emitted light is out of phase with the incoming beam, and this has the effect of slowing the propagation of the combined beam. Just as for a classical mass-on-spring oscillator, the amount and phase of the electron's response depends on their resonant frequency and on the driving frequency. (Here there are slight quantum corrections because there are multiple resonant frequencies corresponding to different energy levels.) It's the frequency dependence of the phase-delay and the amplitude of the scattered light that gives rise to the dispersion.

So this has a strong resemblance to what you were thinking, but not quite expressed in the absorption-emission framework.  No single electron absorbs a whole photon in the scattering process. Each goes to a quantum state that is a superposition of the ground state and some (typically small) amplitude of excited states.

It's not always true that the higher frequencies see a bigger index of refraction, although that is typical for light in glass and many other familiar cases. Let's follow the reasoning for our classical picture. Typically, the main absorption lines (like classical resonances) are at frequencies higher than the visible light. That's like driving an oscillator at frequencies well below resonance, so the displacement depends mainly on the force (the electric field) and not on the frequency. Classical electromagnetism gives that the radiated field goes as the square of the oscillation frequency for fixed amplitude charge oscillations. So the scattering effect becomes stronger at higher frequencies.

Mike W.

(published on 01/03/2015)