# Light in a medium

Could someone please explain how the speed of light, a supposed constant, can be slowed down in a medium? I checked Wikipedia and all they had to offer was this

"In passing through materials, the observed speed of light differs from c. When light enters materials its energy is absorbed. In the case of transparent materials (dielectrics) this energy is quickly re-radiated. However, this absorption and re-radiation introduces a delay. As light propagates through dielectric material it undergoes continuous absorption and re-radiation. Therefore when the speed of light in a medium is said to be less than c, this should be read as the speed of energy propagation at the macroscopic level. At the microscopic level electromagnetic waves always travel at c."

I guess all I need is a clearer explanation.

Thanks.

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CompuChip
Homework Helper
So first let's talk about light in vacuum. Its speed (magnitude of the velocity) is a constant value, which we conventionally call c (for celeritas). This means that with whatever velocity you move, you always see a light ray pass at c. From the theory of special relativity it is a consequence, that massive matter can only travel at a speed strictly smaller than c and light must always travel precisely at c.

In matter, the situation is a bit different. For simplicity, let us consider light as built up from little energy packets called photons. If we zoom in on a material very closely, then we mostly see a vacuum, with for example an electron or atomic nucleus spread out here and there. Now if you send a photon in, it will mostly just travel at the "speed of light", i.e. the vacuum speed c, through the big empty space in between the particles. However, occasionally the photon will hit a particle. Since the photon is just a packet of energy, the particle can absorb this, thereby going into a higher energy state. So now the photon is gone and the particle carries a little bit of extra energy compared to its "normal" state.

If the photon has precisely the right energy, the particle will feel fine and stay that way. Since photon energy is directly related to the color of the light we see, we won't see the photon coming out and we say that the material absorbs the light of that color. For most energies (colors) however, the particle doesn't really feel at ease carrying around that extra energy. Therefore, after some time, it will get rid of it. How? Well, it simply puts it in a new energy packet (photon) and shoots it off to propagate at c through the vacuum. If you repeat this process, say, 1023 times, then you will see that each absorption and re-emission takes a little bit of time. So when you average that out over the whole passage through the medium, you will find that the nett speed (I would say: of the photon, although it is technically not the "same" photon as the one that went in -- insert discussion about quantum mechanics and discernability here -- anyway, the nett speed) is a little less than c, because it took more time than it would in vacuum to propagate through.

Now you can imagine that depending on the properties of the matter, the velocity gets reduces a little or a lot (but never increased). Actually I think there have been experiments where they have succeeded in "capturing" a photon inside the material (reducing the velocity to 0). As a consequence, it is possible to let something move through the material which exceeds the speed of light! This is not a contradiction with special relativity, but a consequence of the sloppy "popular" formulation that "nothing can travel faster than light", which usually leaves out "in vacuum".

Does that help?

jtbell
Mentor
This comes up so often that we have an FAQ about it:

https://www.physicsforums.com/showpost.php?p=899393&postcount=4 [Broken]

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thanks, yea i understand it better now.