# How can molecules slow down light wave?

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## Main Question or Discussion Point

Imagine light of frequency $\Omega$ enters a liquid and propagates in the z direction. Its velocity is reduced to c/n. This leads to reduction of its wavelength to 1/n of the vacuum wavelength and the wave is described by the macroscopic electric field

$$\mathbf E (\mathbf x,t) = \mathbf E_0 \cos(\Omega t - n\Omega/c z).$$

However, does the reduction of the wavelength and speed occur also at the microscopic level?

Take one molecule of the liquid; it is surrounded by empty space, and is under action of the microscopic electromagnetic field. How would you describe this microscopic field, as a slowed-down wave

$$\mathbf e (\mathbf x,t) = \mathbf e_0 \cos(\Omega t - n\Omega/c z).$$

or as a vacuum wave

$$\mathbf e (\mathbf x,t) = \mathbf e_0 \cos(\Omega t - \Omega/c z).$$

or neither?

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it is not true that light after getting into a medium with a refractive index n,gets retarded at a speed c/n. in fact when light enters a medium then it makes the electrons of that medium move up and down.which in turn create their own electric field which when combines with the original gives a field which can be explained by a handy thing like refractive index with which people were aware before the discovery of electron.a good discussion on it can be found in feynman lectures vol 1, which explains it beautifully.

BobG
Homework Helper
To clarify, if a photon of light were to travel through some substance, between the molecules, making no contact with the substance what so ever, there would be no slowing down.

The "slowing down" is the delay created by photons of light being absorbed by a molecule or atom, raising an electron to a higher orbit due to increased energy, and the electron then falling back down to its lower orbit, releasing a new photon of light. The direction of that new photon could be any direction and it would most likely hit another molecule, and so on. If the geometry created by the molecules is just right, most of the photons eventually come out the other side (in other words, the substance is transparent).

The photons of light always traveled the speed of light when they were between molecules. The "slowing" was caused by how many interactions the photon underwent while passing through the substance.

And, once you consider all of the effects of the interactions (how the entire molecule winds up moving, etc), the outgoing light has lost a little bit of energy, resulting in a lower frequency on the 'output' side than the 'input' side.

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adrien, what you say is right, but the question is, what electric field should we use to describe the force on the atom?

Bob, I am afraid that the description in terms of photons can not beof much help here. I would like to find the wavelength of the microscopic electric field, and this belongs to wave theory.

it is the electrons which will feel the effect,and so far the force on electron can be considered as an restoring force like a harmonic oscillator and the electric field will be the incident electric field without any n.

Gold Member
But what is incident electric field?
I suppose the electric field acting on the atom is given by sum of the electric field due to source E0 and electric fields E_b of the other atoms b in the medium. It is hard to find out what their sum is like - especially, whether it is equivalent to wave with n>1 or with n=1.

it is not true that light after getting into a medium with a refractive index n,gets retarded at a speed c/n. in fact when light enters a medium then it makes the electrons of that medium move up and down.which in turn create their own electric field which when combines with the original gives a field which can be explained by a handy thing like refractive index with which people were aware before the discovery of electron.a good discussion on it can be found in feynman lectures vol 1, which explains it beautifully.
That might be a slightly simplified way to look at it. Instead, you might consider that the parameters $\epsilon$ and $\mu$, electric permittivity and magnetic permeability determine the speed of electromagnetic propagation. The refractive index is a side effect of those parameters having a particular configuration in the vicinity of an atom or molecule (or group of them). What you mention about moving charges is still further a side effect for media that is non-rigid (such as a free electron).

But what is incident electric field?
I suppose the electric field acting on the atom is given by sum of the electric field due to source E0 and electric fields E_b of the other atoms b in the medium. It is hard to find out what their sum is like - especially, whether it is equivalent to wave with n>1 or with n=1.
this is true that the electric field acting will be sum of incident and field from other electrons but the problem is how to find that extra field.in case of low density materials like gases ,it is a good approximation to assume the electric field acting as the incident one to determine the motion of electrons and then finding out the correction due to other electrons to the incident field.in case of isotropic materials having not low density,correction is required.the corrected field will be some local field which depend on the polarization of material.moreover, in this case the incident field will be counted with a n.refractive index of a material is response to a time varying electric field.