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I've been studying in optics the macroscopic maxwell's equations, and how electromagnetic fields propagate through different mediums. Over there, the index of refraction appears, as a complex function that generally depends on $\omega$, with both refraction and absorbtion terms: $n_c=n+i\kappa$.

I understand how this affects the speed at which light propagates, both macro and microscopically, and how this affects to how light is absorbed when it transmits through the medium, but I don't get yet how this index changes the direction of light, producing dispersion. I mean, all time I'm seeing those effects as something that separates dispersive from non dispersive mediums and all that stuff, and I don't know how light is actually dispersed. As it's something that happens when changing medium, I guess it's an interface effect, and we haven't seen those effects yet, but I would like to know an explanation.

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Are you looking for an explanation of the refraction of single-wavelength light or for an explanation of the dispersion of multi-wavelength light? –  Glen The Udderboat Apr 4 '13 at 21:20
@Gugg Isn't it the same? I guess that when studying the refraction of a single-wavelenght wave, you will get that the angle depends on the frequency, and there fore the multiwavelength light is dispersed. –  MyUserIsThis Apr 4 '13 at 21:27
The easiest way to answer this is, of course, with Fermat's Principle. But that may not be what you're looking for. –  jld Apr 4 '13 at 21:30

2 Answers 2

up vote 6 down vote accepted

Here is an analogy that I like to use: (even though it is not really a correct physical explanation)

Imagine that you are out riding your segway over some strange surfaces, that each have a number $n_i$ that controls the speed that a segway wheel travels over it according to the formula $v_i=v_0/n_i$. Now imagine that you cross a straight boundary between two surfaces at an angle. Because of the angle, one wheel will cross the boundary before the other. If $n_i$ is higher for the entered surface this wheel will go slower than the other until it too crosses the boundary, which will cause the segway to turn towards the normal of the boundary. Similarly, if $n_i$ is lower for the entered surface, the first wheel to enter will go faster, and the segway will turn from the normal.

If you do the calculations for the segway you will get the the same results as for the wavefront explanation (basically Snell's law), but I really like how this analogy works with your intuition.

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Alternatively, the light ray will take the path that reduces the total time - the question being, "how does it know?" –  Martin Beckett Apr 5 '13 at 3:52
@MartinBeckett That question can be found here. –  Glen The Udderboat Apr 5 '13 at 8:21
Thank you very much, that analogy ir really good. –  MyUserIsThis Apr 5 '13 at 17:18

The direction a wave travels is due to its self-interference. This shows a series of wave fronts encountering an interface where the speed of propagation is slower:

enter image description here

EDIT for @Alec S: Suppose you have a pond of water, and you simultaneously drop in 100 stones, all in a line, 1 inch apart. What does the wave look like? It looks like a line, because the circular wave from each stone interferes with those from its neighbors, so you don't see a bunch of circular waves, you see a line wave.

That's what a planar wave in 3D is. As the wave propagates, it is acting like an infinite number of sources spread out on a plane. The only place all those waves reinforce is in a plane, so the wave looks planar. Otherwise it would be a mish-mash of spherical waves from all the points, all jumbled together.

When such a wave front encounters a medium where the waves travel slower, guess what? The distance between succeeding wave fronts decreases, and the self-interference takes off in a new direction.

There is nothing about a wave that keeps it going in one direction, other than the pattern of its own self-interference.

ANOTHER way to look at it is in terms of time. The locus of points on the wave front, whether it is above or below the interface, are simultaneous.

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Thanks I got it. that picture opened my eyes (even when I have seen that picture like a trillion times) –  MyUserIsThis Apr 4 '13 at 21:29
I don't understand this picture. –  santa claus Apr 5 '13 at 0:10

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