I don't understand how light slows down in certain materials

[Boltzmannbrain]

This video is trying to explain how an oscillating electric field of light interacts with the oscillating electric field of electrons as the light passes through a material.  He seems to be saying that the wave from the electron is slower than the light wave, and when they combine, the light slows down, though he doesn't say that explicitly.  So my question is: wouldn't the waves of the electric field of electrons also go the speed of light?  If not, what speed does it go?  

Start the video at about 6:20 when he starts to explain what I am trying to understand.

 

[Lorentz Jr]

57 minutes ago, Boltzmannbrain said:

the wave from the electron is slower than the light wave, and when they combine, the light slows down, though he doesn't say that explicitly.

He says at 7:05 that the sum of two waves moving at different speeds is a wave moving at some intermediate speed.

57 minutes ago, Boltzmannbrain said:

  wouldn't the waves of the electric field of electrons also go the speed of light?  If not, what speed does it go?  

Electrons can't escape the glass, so their wave is a standing wave, like the vibration of a guitar string. Its speed is zero. You can think of it as a combination of two waves that move in opposite directions and keep getting reflected internally at the surface of the glass. I'm not sure what the speed of those electron waves is. Offhand, I would guess that it should be less than c because of the mass of the electrons, but don't quote me on that.

Come to think of it, maybe the speed of the "electron" waves is just c/n, where n is the medium's index of refraction. That's the speed of "light" in the medium. Physically speaking, the best way to think about it may be that there isn't a pure "light wave" going through the glass, but a combined light+electron wave that has its own properties.

So the overall wave is still the sum of two waves moving in opposite directions at speed c/n (or at least it can be broken down that way mathematically), but the one going in the direction of the incident light has a larger amplitude than the one going the other way.

Edited February 9, 2023 by Lorentz Jr

[exchemist]

6 hours ago, Boltzmannbrain said:

This video is trying to explain how an oscillating electric field of light interacts with the oscillating electric field of electrons as the light passes through a material.  He seems to be saying that the wave from the electron is slower than the light wave, and when they combine, the light slows down, though he doesn't say that explicitly.  So my question is: wouldn't the waves of the electric field of electrons also go the speed of light?  If not, what speed does it go?  

Start the video at about 6:20 when he starts to explain what I am trying to understand.

 

The electrons of the material can oscillate at certain resonant frequencies that cause them to move between different energy states. This is how absorption and emission of light take place. 

If the frequency of the radiation is close to one of these frequencies but does not match, it can only cause the electrons to move temporarily to the higher state and then return. (If the frequency matches exactly, the electron can absorb a photon and move permanently to the higher energy state.) N.B. The light is not absorbed and re-emitted, as it is something said to be in bad explanations. It is just that the electron "borrows" energy from the wave it and gives it back. The effect is a bit like if you try to run on a trampoline: it absorbs and then releases energy from the wave. This slows down the phase velocity of the light.

The closer to the absorption frequency the light is, the more it gets slowed down. In the limiting case, when the frequency matches exactly, it is absorbed, i.e. it is stopped! This is why glass is a dispersive medium, i.e. the refractive index depends on the frequency. The absorption frequency is in the UV, so as light frequency goes from red to blue, it is getting closer to the absorption frequency and thus the refractive index for blue light is greater than for red light. 

But refractive index is quite a complex phenomenon and really needs QM to explain it properly. It is related to polarisability - the ease with which a material can be polarised by an electric field.

P.S. I actually watched most of your linked YouTube video, something I rarely do. I thought his explanation was good, avoiding the usual pitfalls of non-mathematical analogies.  

 

  

Edited February 9, 2023 by exchemist

[Lorentz Jr]

1 hour ago, exchemist said:

The electrons of the material can oscillate at certain resonant frequencies that cause them to move between different energy states. This is how absorption and emission of light take place.

Yes, but we're talking about transmission. There's a classical theory for calculating the index of refraction. I think the idea (to put it into quantum-mechanical terms) is that the applied potential from the light distorts the electron wave functions (i.e. their energy eigenstates) "smoothly" (so the photon energy must be less than the band gap) so the electrons oscillate without jumping out of their ground states.

Edited February 9, 2023 by Lorentz Jr

[exchemist]

2 minutes ago, Lorentz Jr said:

Yes, but we're talking about transmission. There's a classical theory for calculating the index of refraction. I think the idea (to put it into quantum-mechanical terms) is that the applied potential from the light distorts the electron wave functions smoothly without making them jump out of their ground states.

It's years since I studied this, but my recollection is that the distortion (polarisation) of the electron distribution mixes in some proportion of a higher energy state. Recall that there is a "transition dipole moment" involved in the absorption process that occurs when the frequency is exactly right, involving both states, that is made possible by the perturbation due to the electric vector of the radiation.  

 

[Lorentz Jr]

26 minutes ago, exchemist said:

the distortion (polarisation) of the electron distribution mixes in some proportion of a higher energy state.

A slightly higher energy, but only because the external potential makes that the new ground state. So it's a complete transition, not just partial mixing, and it's to the equivalent state (i.e. S to S, P to P, etc.). I don't think transmission can be based on any mixing or transitions to excited states. As you said, that's how absorption works.

Edited February 9, 2023 by Lorentz Jr

[exchemist]

1 hour ago, Lorentz Jr said:

A slightly higher energy, but only because the external potential makes that the new ground state. So it's a complete transition, not just partial mixing, and it's to the equivalent state (i.e. S to S, P to P, etc.). I don't think transmission can be based on any mixing or transitions to excited states. As you said, that's how absorption works.

Yeah but my understanding is absorption is merely the limiting case of refractive index, not a totally separate phenomenon. That's why the refractive index goes up as you approach the absorption line.  

We may not actually be disagreeing, in that your new externally induced potential can lead to a new ground state that is the equivalent of a mixture of the ground and excited states in the undistorted (spherical potential) case.  

[studiot]

https://www.intechopen.com/chapters/16405

Quote

Interaction of quantums of electromagnetic radiation with substance can be investigated both from a wave position, and from a quantum position. From a wave position under action of an electromagnetic wave there are compelled fluctuations of an electronic orbit and nucleus of atoms. The energy of electromagnetic radiation going on oscillation of nucleus passes in heat. Energy of fluctuations of an electronic orbit causes repeated electromagnetic radiation with energy, smaller, than initial radiation.

Whenever EM radiation passes through a region of space containing matter there are transient (eg Van der Waals) and permanent electric fields present due to the matter.

The strength and nature of these fields depends upon the type and distribution of the matter - solid, liquid, gas, solution etc.

Macro observed effects are dispersion, absorbtion, scattering.

The velocity depends upon the permittivity of the bulk material, and permeability in ferrofluids.

Matter and the space it occupies is mostly empty, which is why some light passes through at all.

 

 

 

 

 

Edited February 9, 2023 by studiot

[exchemist]

30 minutes ago, studiot said:

https://www.intechopen.com/chapters/16405

Whenever EM radiation passes through a region of space containing matter there are transient (eg Van der Waals) and permanent electric fields present due to the matter.

The strength and nature of these fields depends upon the type and distribution of the matter - solid, liquid, gas, solution etc.

Macro observed effects are dispersion, absorbtion, scattering.

The velocity depends upon the permittivity of the bulk material, and permeability in ferrofluids.

Matter and the space it occupies is mostly empty, which is why some light passes through at all.

 

 

 

 

 

Yes, the permittivity being the classical electromagnetic term, equivalent to the polarisability at the molecular level, that is to say the degree to which its electron orbitals distort in response to the oscillating electric field of the radiation.

[studiot]

5 minutes ago, exchemist said:

Yes, the permittivity being the classical electromagnetic term, equivalent to the polarisability at the molecular level, that is to say the degree to which its electron orbitals distort in response to the oscillating electric field of the radiation.

Not only the incoming EM radiation, but also the varying transient fields from other molecules as in VDW forces.

[exchemist]

4 minutes ago, studiot said:

Not only the incoming EM radiation, but also the varying transient fields from other molecules as in VDW forces.

Yes, London forces result from mutual polarisability of the molecules involved.

[Boltzmannbrain]

Thanks everyone.

 

From what the seems to be saying, I am gathering that the light wave and the wave from the electron combine into another wave. Moreover, the wave of the electron speeds up and the light wave slows down, which makes sense energywise. 

 

Is this kind of the just of what he is saying?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Edited February 9, 2023 by Boltzmannbrain

[studiot]

25 minutes ago, Boltzmannbrain said:

Thanks everyone.

 

From what the seems to be saying, I am gathering that the light wave and the wave from the electron combine into another wave. Moreover, the wave of the electron speeds up and the light wave slows down, which makes sense energywise. 

 

Is this kind of the just of what he is saying?

 

Not really. exchemist said distorted not combined or speeded up.

Read these two extracts.

 

[joigus]

16 minutes ago, Boltzmannbrain said:

From what the seems to be saying, I am gathering that the light wave and the wave from the electron combine into another wave.

No, no, no. That's not what they're saying.

[Lorentz Jr]

45 minutes ago, joigus said:

No, no, no. That's not what they're saying.

I suggested that, but I tried not to be too factual or authoritative about it.

Dr. Lincoln said there's a light wave moving at c and a standing electron wave (i.e. not moving at all).

Although he does say (at 7:05) that they produce a more slowly moving wave as a "result", whatever that's intended to mean.

Edited February 9, 2023 by Lorentz Jr

[exchemist]

20 minutes ago, Lorentz Jr said:

I suggested that, but I tried not to be too factual or authoritative about it.

Dr. Lincoln said there's a light wave moving at c and a standing electron wave (i.e. not moving at all).

I think Lincoln is saying the motion of the electrons creates a secondary oscillating electric field (a forced oscillation, actually), moving slower than that of the incoming light and that the resultant speed of light in the medium arises from the superposition of the two electric field waves.

I am unable to say for sure whether this classical-sounding explanation is the equivalent of the QM explanation that I think I recall. But it sounds as if it may be. 

This is actually quite an interesting and tricky subject. 

Edited February 9, 2023 by exchemist

[Lorentz Jr]

6 minutes ago, exchemist said:

I think Lincoln is saying the motion of the electrons creates a secondary oscillating electric field (a forced oscillation, actually), moving slower than that of the incoming light and that the resultant speed of light in the medium arises from the superposition of the two electric field waves.

Hey, you're right! The first wave moves so slowly at 7:05, I thought it was supposed to be stationary.

Dr. Lincoln also repeats the "combined wave" idea at 8:30.

Edited February 9, 2023 by Lorentz Jr

[joigus]

1 hour ago, Lorentz Jr said:

I suggested that, but I tried not to be too factual or authoritative about it.

Dr. Lincoln said there's a light wave moving at c and a standing electron wave (i.e. not moving at all).

My apologies. The original sentence I was answering to was --I'd say-- ambiguous,

2 hours ago, Boltzmannbrain said:

From what the seems to be saying,

I understood it referred to @exchemist and/or @studiot. In any case, it's wrong to say that the light wave and the 'electron wave' --which I understood as meaning 'the electron wave function'-- combine into another wave, never mind who says that. 

I didn't watch the video and wasn't offered a clear explanation of its contents. If that's what it says, I think the explanation can be made a wee bit simpler, but never mind.

Edited February 9, 2023 by joigus
Added 'or'

[Lorentz Jr]

9 minutes ago, joigus said:

In any case, it's wrong to say that the light wave and the 'electron wave' --which I understood as meaning 'the electron wave function'-- combine into another wave, never mind who says that.

Lincoln mentions adding the field generated by the electrons (i.e. by atomic polarization with quasi-stationary nuclei) to the incident wave.

Edited February 9, 2023 by Lorentz Jr

[joigus]

14 minutes ago, Lorentz Jr said:

Lincoln mentions adding the field generated by the electrons (i.e. by atomic polarization with quasi-stationary nuclei) to the incident wave.

I see. Thank you.

@Boltzmannbrain. Sorry for the misunderstanding. You may find this YT function useful,

Peace out. 🖐️ 

[studiot]

Here is a more mathematical classical treatment.

Things to take away.

Coherence/incoherence v superposition

scattering

dispersion

Real and displacement currents

 

[joigus]

13 minutes ago, studiot said:

Here is a more mathematical classical treatment.

Things to take away.

Coherence/incoherence v superposition

scattering

dispersion

Real and displacement currents

 

Exactly. That's how I would explain it anyway. When the medium is linear and homogeneous, the wave equation has to be modified by including the electric displacement \( \boldsymbol{D}=\boldsymbol{E}+\boldsymbol{P}=\left(1+\epsilon_{0}\chi\right)\boldsymbol{E} \). It's only natural to assume that polarisation varies with the frequency, as how much it responds naturally depends on how fast I shake the atoms of the material. Which book is this?

I don't know if Lincoln mentions that the material has to be a dielectric. If the material is a conductor, the wave will be damped, which can also be incorporated in the formalism with a complex refraction index --the imaginary part accounting for absorption. As usual, what's hard is trying to find an intuitive explanation with no maths.

[sethoflagos]

1 hour ago, joigus said:

As usual, what's hard is trying to find an intuitive explanation with no maths.

One picture that I found comfortable is to firstly accept that the paths taken are simply governed by a form of least action (via Fermat's Principle of least time) - which I think is one way of saying that any potential deviation from Snell's law would be corrected by wave interference. 

Then taking a first law view, the total energy of the incoming light is transformed at the interface into a composite package of equal energy that now includes some level of induced motion in the local lattice electrons. This package, if viewed as a particle in its own right, now has some albeit small mass and therefore must adopt a sublight speed appropriate to the amount of 'baggage' it's now carrying. 

 When leaving the medium the lattice field reclaims its baggage and returns its borrowed energy back to the reconstituted photon which continues on its way.

I'm sure there's some phrasing here that I've got wrong but at least it's a process I can picture.   

 

[joigus]

10 minutes ago, sethoflagos said:

Then taking a first law view, the total energy of the incoming light is transformed at the interface into a composite package of equal energy that now includes some level of induced motion in the local lattice electrons. This package, if viewed as a particle in its own right, now has some albeit small mass and therefore must adopt a sublight speed appropriate to the amount of 'baggage' it's now carrying. 

Like some kind of drag? Yes, that could do the work. I liked exchemist's analogy of the person trying to run on a trampolin too. I have to confess I've become sort of simplistic. And I'm far too fond of the formalism too. I think I understand polarisation well. I plug in the electric displacement, and that modifies the velocity constant. If the medium happened to be inhomogeneous, with regions of higher refraction index and regions of lower one, the explanation based on superposition of waves would be a mess. But you could still depart from the principle of least action and proceed from there. If one is happy with an intuitive explanation, the "drag" argument that you suggest sounds perfect. How natural that is in the mind of a person who wants to understand it crudely, I don't know.

[exchemist]

11 hours ago, joigus said:

My apologies. The original sentence I was answering to was --I'd say-- ambiguous,

I understood it referred to @exchemist and/or @studiot. In any case, it's wrong to say that the light wave and the 'electron wave' --which I understood as meaning 'the electron wave function'-- combine into another wave, never mind who says that. 

I didn't watch the video and wasn't offered a clear explanation of its contents. If that's what it says, I think the explanation can be made a wee bit simpler, but never mind.

No, I'm sure Lincoln is not referring to an electron wave function. He is speaking in terms of a semi-classical model, in which the collective forced oscillation of the electrons in the medium sets up a secondary electric field wave, moving with the electric vector of the light but  more slowly, and the superposition of the two leads to a reduction in phase velocity. The important part of the video comes in the final 3 minutes. The rest is background explanation of what refractive index is, why some of the popular explanations are wrong, and so forth.  

By the way, I'd like very much to hear your simpler explanation, if you care to summarise it. I find this an interesting topic and I feel I'm on slightly shaky ground relying just on what I recall from Peter Atkins at Oxford in 1974!   But maybe I can get the gist of it from your posts up to this point. I'll read them carefully. 

7 hours ago, sethoflagos said:

One picture that I found comfortable is to firstly accept that the paths taken are simply governed by a form of least action (via Fermat's Principle of least time) - which I think is one way of saying that any potential deviation from Snell's law would be corrected by wave interference. 

Then taking a first law view, the total energy of the incoming light is transformed at the interface into a composite package of equal energy that now includes some level of induced motion in the local lattice electrons. This package, if viewed as a particle in its own right, now has some albeit small mass and therefore must adopt a sublight speed appropriate to the amount of 'baggage' it's now carrying. 

 When leaving the medium the lattice field reclaims its baggage and returns its borrowed energy back to the reconstituted photon which continues on its way.

I'm sure there's some phrasing here that I've got wrong but at least it's a process I can picture.   

 

I like this a lot. It contains the idea that energy is borrowed from the light by the lattice electrons, which quantum mechanically can - I think - be thought of as mixing in a bit of, mainly, the nearest excited state (in transition frequency). This is the exciting piece, to me, as it explains the link between the magnitude of refractive index and the proximity in frequency of absorption bands in the spectrum of the medium.   

Edited February 10, 2023 by exchemist