Re: speed of light of different colours

[Geoff Nunes <gnunes@MAILAPS.ORG>]

> > why is the speed of light for red bigger that , say, blue, when both are
> > in an optcally denser medium?

Here is a picture that I have had good luck using to explain this phenomenon to freshman.  It is very classical, but describes the process quite well.

Light in a medium propagates by excitation and re-radiation.  You can think of the molecules in the glass as little electrically charged harmonic oscillators.  The electric field of the incoming light excites a layer of molecules and sets them oscillating.  Since this oscillation involves acceleration, the excited molecules will themselves radiate EM waves.  These waves then act as the "incoming" light for the next layer, and so on through the whole glass.  (See the introductory text by Hecht for some pictures and hand-waving arguments about how this process can result in a beam staying a beam instead of scattering in all directions.)

So why different speeds for different wavelengths?  The harmonic oscillator is being driven at a frequency below its resonant frequency.  So the motion of the oscillator is not in phase with the incoming wave, but reaches it's maximum a little bit after the EM wave does.  That means the radiation that it puts out is also behind.  The cumulative effect of all these little delays is a propagation speed less than c.  The bluer the light, the closer it is to the resonant frequency (which is in the ultraviolet for most glasses).  The closer to the resonance, the bigger the "phase lag," and the slower the wave travels.

Close to the resonance, the oscillators are absorbing a lot of energy, but not radiating it all back out as EM waves---the damping term in the harmonic oscillator equation becomes important.  For these wavelengths the glass is no longer transparent (standard window glass does a pretty good job of stopping UV light).  Instead the enery is lost as.........oops, better not go there.

Geoff Nunes


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