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

[studiot]

9 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

Yes I too like least action but by itself that does not provide the mechanism. +1

Your 'lattice field energy' appears in a simpler guise which I explore below.

 

2 hours ago, exchemist said:

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,

I rarely try to explain the videos of others, and like joigus I didn't watch this one.

But I try to relate  your idea of forced oscillation to Seth's lattice field below.
This too is a good one, so long as you are not trying to imply that there are two waves transmitted in the medium travelling at different speeds. +1 also

 

11 hours ago, joigus said:

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.

Yes I agree it is difficult to provide a simple intuitive explanation but I think I can now offer one using my sound analogy as below.

You can also classically make this as complicated as you wish.
 

Joos (Theoretical Physics) takes four chapters to develop it from simple vector calculus to tensor calculus for the anisotropic case where ε is a tensor complete with components and principal direction, dependent upon position in the non-homogenous case.

My first pages above were from

The 1966 MIT series  "The Structure and Properties of Material - volume IV -  Electronic Properties"  byRose, Shepard and Wulff

The second pages were from

Vibrations and Waves in Physics  by Iain G Main

Cambridge University Press.    (My copy 1979)
 

[exchemist]

1 hour ago, studiot said:

 

I rarely try to explain the videos of others, and like joigus I didn't watch this one.

But I try to relate  your idea of forced oscillation to Seth's lattice field below.
This too is a good one, so long as you are not trying to imply that there are two waves transmitted in the medium travelling at different speeds. +1 also

 

 

Indeed, I am not saying that. As I said in earlier posts, Lincoln's portrayal of it is that there are two component waves, that due to the light itself and that due to the secondary forced oscillation of the medium's electrons, and what actually takes place is the resultant, from the superposition of the two components. This is unavoidable as the two components will willy-nilly interfere to produce a single combined waveform.  

[studiot]

1 hour ago, exchemist said:

Indeed, I am not saying that. As I said in earlier posts, Lincoln's portrayal of it is that there are two component waves, that due to the light itself and that due to the secondary forced oscillation of the medium's electrons, and what actually takes place is the resultant, from the superposition of the two components. This is unavoidable as the two components will willy-nilly interfere to produce a single combined waveform.  

If Lincoln genuinely said that then the video is best forgotten.

 

Now to horse to horse.     @Boltzmannbrain    

I am going to offer you a wave explanation, though the principles that come out of it apply to any level, including quantum.

So first what is a travelling wave ?
A wave is described by an equation connecting time and space.
In order to make this equation dimensionally corrrect (all terms in the same units) it must include a factor we call the velocity or speed.

The basic equation is a differential equation which is satisfied by an infinity of ordinary equations , also called wave equations.

All these equations must include the units factor I mentioned.

These waves have certain charracteristics or requirements.

1. Before a wave can travel it must be generated. Seems obvious, but the equations themselves do not tell us how this is achieved.
    
2. The velocity of a wave is characteristic of the medium, not the wave.
    
3. If a wave has material moving elements or particles the speed of these is not the same as the speed of the wave.
    
4. In the light of 2 it is not suprising that a wave travels at different speed in different media.

 

So let us consider a sound travelling through several media, air then a solid partition  (say a pane of glass or sheet of wood), then back to air again.

Very simple but it will do the job.

In the air the sound wave is made by the particles alternately bunching together (thus increasing the pressure and density locally) and spreading apart (thus decreasing the pressure and density locally).
Note that these air particles are free to move about. They are not linked to other particles directly by forces.

When the wave arrives at the left hand partition surface this alternating pressure increase and decrease causes alternating displacements of the surface particles.
Note these partition particles are connected to neighbouring particles by springlike forces as in my original diagrams.
This pattern of alternating displacements is thus transmitted onwards through the partition to its right hand surface, where the reverse occurs and the motion is returned to the air the other side.

 

Now these two modes of tranmission are fundamentally different by virtues of their different mechanisms.

But there is only ever one sound wave in either medium.

 

This process can be likened to handing on the baton in a relay, each runner operating in a manner appropriate to him or her.
The baton is the wave energy.

A travelling wave transmits energy and the mechanism of travel will, unsuprisingly, vary from medium to medium.

 

So sound is not light, but they are both waves.
The mechanisms are different but the above applies.
That brings us to the level of mechanism you wish to study the phenomenon for light ?

[Lorentz Jr]

2 hours ago, exchemist said:

As I said in earlier posts, Lincoln's portrayal of it is that there are two component waves, that due to the light itself and that due to the secondary forced oscillation of the medium's electrons, and what actually takes place is the resultant, from the superposition of the two components. This is unavoidable as the two components will willy-nilly interfere to produce a single combined waveform.

Exactly. +1 for that, and any comments to the contrary are best forgotten.

[joigus]

6 hours ago, exchemist said:

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. 

Studiot's post already summarised at least part of the approach. At this point I think my explanation has lost interest TBH, because it's not so much one about 'mechanisms' as it is one about quickly and efficiently plugging in what we know, and simplifying the maths.  I don't think there's any fundamental disagreement between one and the other, in spite of some sentiments expressed to the contrary. When you consider matter is made up of atoms, it's sometimes more convenient to package properties together in different densities, that's the essence of it.

The main idea is that every time you have a material, it will react according to its properties, and those are --in the case at hand-- conductivity, polarisability, and magnetic properties. I'm busy trying to wrap up a quick explanation while simplifying the maths as much as possible, but it's turning out to be harder than it looked.  

Here's part of the reason: 

Quote

A word of warning is needed regarding terms and units for magnetic fields. I grew up with B called the magnetic field and H the magnetic intensity, and I’m too old to change. However, the venerable Jackson (1962), the standard graduate-level text on electromagnetic theory for over 60 years, calls H the magnetic field and B the magnetic induction. The equally competent and respected Griffiths (1981) calls B the magnetic field and H the auxillary field. Griffiths (page 232) says calling B the magnetic induction is “an absurd choice” because it leads to confusion with electromagnetic induction, which is something totally different. He also says, “H has no sensible name; just call it ’H’ ”. The great Arnold Sommerfeld, doctoral or postdoctoral adviser to seven students who later won Nobel prizes, says that (in Electrodynamics, 1952, page 45) “The unhappy term ’magnetic field’ for H should be avoided as far as possible.” The thing to keep in mind is that E and B are the fundamental quantities; D and H arise from rewriting the fundamental equations (Eqs. 1 to 4 of the previous page) in forms convenient for material media. To make matters even worse, the units of B and H, whatever you call them, depend on the system of fundamental units chosen. Here I have used SI units (previously called “rationalized mks” units). B and H then have different units, as we have seen. [...] This whole business is a confusing mess; see the discussion in Feynman et al. (1964) §36-2.

(from https://www.oceanopticsbook.info/view/theory-electromagnetism/level-2/maxwells-equations-matter#:~:text=ρ b %3D − ∇ ⋅ P,ρ f − ∇ ⋅ P .)

I think I can do it, but please keep in mind,

(1) I realise now that my explanation is not all that interesting --especially considering you're a chemist, and are probably more interested in the molecular mechanism. Also, I've finally watched the video, and it's more than good enough for me.

(2) It's going to take some more time. I have to clarify notation, review the maths, and trim the whole thing down to what's of interest to us.

[studiot]

7 minutes ago, joigus said:

I've finally watched the video, and it's more than good enough for me.

Did you notice any faults ?

Perhaps the one at 5:34 where the Dr Lincoln says that "Photons absorb atoms"

[joigus]

Just now, studiot said:

Did you notice any faults ?

Perhaps the one at 5:34 where the Dr Lincoln says that "Photons absorb atoms"

Oh, I missed that part. Sorry. I've started at about 7.05, as Lorentz Jr & exchemist said that was the juicy bit.

Maybe it's worth a thorough look. I'll do that ASAP.

This link @Lorentz Jr posted,

On 2/9/2023 at 12:23 PM, 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 (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.

https://en.wikipedia.org/wiki/Ewald–Oseen_extinction_theorem

is worth a look or two. It's pretty much what I was fumbling towards.

[exchemist]

1 hour ago, joigus said:

Studiot's post already summarised at least part of the approach. At this point I think my explanation has lost interest TBH, because it's not so much one about 'mechanisms' as it is one about quickly and efficiently plugging in what we know, and simplifying the maths.  I don't think there's any fundamental disagreement between one and the other, in spite of some sentiments expressed to the contrary. When you consider matter is made up of atoms, it's sometimes more convenient to package properties together in different densities, that's the essence of it.

The main idea is that every time you have a material, it will react according to its properties, and those are --in the case at hand-- conductivity, polarisability, and magnetic properties. I'm busy trying to wrap up a quick explanation while simplifying the maths as much as possible, but it's turning out to be harder than it looked.  

Here's part of the reason: 

(from https://www.oceanopticsbook.info/view/theory-electromagnetism/level-2/maxwells-equations-matter#:~:text=ρ b %3D − ∇ ⋅ P,ρ f − ∇ ⋅ P .)

I think I can do it, but please keep in mind,

(1) I realise now that my explanation is not all that interesting --especially considering you're a chemist, and are probably more interested in the molecular mechanism. Also, I've finally watched the video, and it's more than good enough for me.

(2) It's going to take some more time. I have to clarify notation, review the maths, and trim the whole thing down to what's of interest to us.

You understand me well! Indeed, as a chemist what interests me is what happens at the level of molecules, or the electron orbitals in a giant structure such as glass. Also the link with spectroscopic properties, which I found so eye-opening.  

From the discussion so far I would hazard a guess that what we have may be a bit similar to what happens in bonding, when the spherical potential of an isolated atom is replaced by, say, the tetrahedral potential of something like methane. You can then get mixing of the atomic orbitals of the spherical case to form new combinations, appropriate to the new symmetry - the so-called orbital hybridisation: s + 3x p ->  4 x sp₃ in the methane case. With light passing through a medium, the electric field is antisymmetric, so the temporary induced polarisation could maybe be expressed as a transitory mixing of (spherical) states of different symmetry. This looks very much like the  "transition dipole moment" involved in an absorption event.     

 

[studiot]

2 hours ago, joigus said:

Maybe it's worth a thorough look. I'll do that ASAP.

Take a pen and paper and note them down as you go through.

I noted several: we can compare notes when you have done.

[Boltzmannbrain]

8 hours ago, studiot said:

If Lincoln genuinely said that then the video is best forgotten.

 

Now to horse to horse.     @Boltzmannbrain    

I am going to offer you a wave explanation, though the principles that come out of it apply to any level, including quantum.

So first what is a travelling wave ?
A wave is described by an equation connecting time and space.
In order to make this equation dimensionally corrrect (all terms in the same units) it must include a factor we call the velocity or speed.

The basic equation is a differential equation which is satisfied by an infinity of ordinary equations , also called wave equations.

All these equations must include the units factor I mentioned.

These waves have certain charracteristics or requirements.

1. Before a wave can travel it must be generated. Seems obvious, but the equations themselves do not tell us how this is achieved.
    
2. The velocity of a wave is characteristic of the medium, not the wave.
    
3. If a wave has material moving elements or particles the speed of these is not the same as the speed of the wave.
    
4. In the light of 2 it is not suprising that a wave travels at different speed in different media.

 

So let us consider a sound travelling through several media, air then a solid partition  (say a pane of glass or sheet of wood), then back to air again.

Very simple but it will do the job.

In the air the sound wave is made by the particles alternately bunching together (thus increasing the pressure and density locally) and spreading apart (thus decreasing the pressure and density locally).
Note that these air particles are free to move about. They are not linked to other particles directly by forces.

When the wave arrives at the left hand partition surface this alternating pressure increase and decrease causes alternating displacements of the surface particles.
Note these partition particles are connected to neighbouring particles by springlike forces as in my original diagrams.
This pattern of alternating displacements is thus transmitted onwards through the partition to its right hand surface, where the reverse occurs and the motion is returned to the air the other side.

 

Now these two modes of tranmission are fundamentally different by virtues of their different mechanisms.

But there is only ever one sound wave in either medium.

 

This process can be likened to handing on the baton in a relay, each runner operating in a manner appropriate to him or her.
The baton is the wave energy.

A travelling wave transmits energy and the mechanism of travel will, unsuprisingly, vary from medium to medium.

 

So sound is not light, but they are both waves.
The mechanisms are different but the above applies.
That brings us to the level of mechanism you wish to study the phenomenon for light ?

Yes, thanks, but my math stops after first year university calculus and linear algebra.  I was hoping just to get a basic visual/mechanical understanding of how this worked, and I think I got it by visualizing the two waves combining.       

 

I appreciate your help!

[joigus]

2 hours ago, studiot said:

Take a pen and paper and note them down as you go through.

I noted several: we can compare notes when you have done.

Excellent idea. Thank you.

 

[joigus]

OK. So what I see here is:

(1) Indeed Dr Lincoln says 'the photon absorbs the atom' at about 5.34. But I think that's just a slip of the tongue.

(2) He doesn't mention the amplitudes, nor does he mention the frequencies involved.

A forced oscillator responds with an amplitude that depends on the forcing oscillation frequency, the friction coefficient, and the natural frequency of the oscillator. But the frequency that survives, after the transient has died out, is the same as the frequency of the driving force.

He omits those aspects, I think, for the sake of simplifying the explanation. He's mainly concerned with what he perceives as ongoing confusion due to flawed arguments on YT and the like. If you treated every single atom in the crystal as dipole, you could in principle calculate, by solving Newton's equation, how much it accelerates. You would need a formula to calculate the additional radiation, which is not easy at all. Of course, none of these details are dealt with in the explanation. And I understand why they aren't.

[studiot]

3 minutes ago, joigus said:

OK. So what I see here is:

(1) Indeed Dr Lincoln says 'the photon absorbs the atom' at about 5.34. But I think that's just a slip of the tongue.

(2) He doesn't mention the amplitudes, nor does he mention the frequencies involved.

A forced oscillator responds with an amplitude that depends on the forcing oscillation frequency, the friction coefficient, and the natural frequency of the oscillator. But the frequency that survives, after the transient has died out, is the same as the frequency of the driving force.

He omits those aspects, I think, for the sake of simplifying the explanation. He's mainly concerned with what he perceives as ongoing confusion due to flawed arguments on YT and the like. If you treated every single atom in the crystal as dipole, you could in principle calculate, by solving Newton's equation, how much it accelerates. You would need a formula to calculate the additional radiation, which is not easy at all. Of course, none of these details are dealt with in the explanation. And I understand why they aren't.

Thanks for your input. +1. 

I thought he has stated that twice, but even once is not good when you are dissing other people, especially as the video was not properly checked (ie hurried).

 

I will come back with my full list but,

He seems to imply that photon scattering only happens off the nucleus.

In fact

Quote

https://www.sciencedirect.com/topics/physics-and-astronomy/photonuclear-reactions

3.2.6 Photonuclear reactions

Although photons usually interact with atomic electrons or are affected by the nuclear field without penetrating it, highly energetic photons can penetrate the nucleus and result in the emission of nucleons, α particles, or other particles. Noticeable at a relatively low photon energy are the photoneutron reactions: ²H(γ,n)¹H and ⁹Be(γ,n)⁸Be; with threshold energies of 2.226 and 1.666 MeV, respectively, since these two nuclides have the lowest neutron separation energy among all nuclides.

My highlighting.

[joigus]

16 hours ago, studiot said:

He seems to imply that photon scattering only happens off the nucleus.

The video certainly makes it looks as if it's the nuclei that are working as forced oscillators. Looking forward to your comments.

[exchemist]

17 hours ago, studiot said:

Thanks for your input. +1. 

I thought he has stated that twice, but even once is not good when you are dissing other people, especially as the video was not properly checked (ie hurried).

 

I will come back with my full list but,

He seems to imply that photon scattering only happens off the nucleus.

In fact

My highlighting.

He obviously can't mean that and he does not say that. It will be just a defect of the animation in the video, which certainly does seem to be suboptimal. But @joigus's point about forced oscillations having the same frequency as the forcing is a far more serious objection to his explanation, it seems to me.

[studiot]

Just now, exchemist said:

He obviously can't mean that and he does not say that. It will be just a defect of the animation in the video, which certainly does seem to be suboptimal. But @joigus's point about forced oscillations having the same frequency as the forcing is a far more serious objection to his explanation, it seems to me.

He does indeed say exactly that  and I gave you the time stamp.

Although I was wrong in saying I thought he said it twice.

Hes also says

Glass is made of atoms surrounded by electrons, around about 7.58

 

But as G & S say "I've got a little list"

 

38 minutes ago, joigus said:

The video certainly makes it looks as if it's the nuclei that are working as forced oscillators. Looking forward to your comments.

It's coming, but I'm trying to reply to our newbie's question about wind forces first so it will be later today.

[exchemist]

1 hour ago, studiot said:

He does indeed say exactly that  and I gave you the time stamp.

Although I was wrong in saying I thought he said it twice.

Hes also says

Glass is made of atoms surrounded by electrons, around about 7.58

 

But as G & S say "I've got a little list"

 

It's coming, but I'm trying to reply to our newbie's question about wind forces first so it will be later today.

OK fair enough, what I meant was photon scattering off the nucleus bit. The video uses the Bohr atom of course to visualise atoms, which is misleading and no doubt part of the problem with the animation. If it had shown blobs it would have been better.

The guy's been a lecturer at Notre Dame and does research at Fermilab, so he will no doubt understand it properly himself. But this just shows how hard it is to give an explanation without walls of Greek and bracket notation etc. 

Edited February 12, 2023 by exchemist

[studiot]

OK so here is my critique of the video.

Firstly this question is not a high shool question it is university level.

But at whom is the video aimed ?
Well at the end he talks about the "Physics coolkids club", implying an intended school level audience.
 

2 hours ago, exchemist said:

The guy's been a lecturer at Notre Dame and does research at Fermilab, so he will no doubt understand it properly himself. But this just shows how hard it is to give an explanation without walls of Greek and bracket notation etc. 

Yes I'm sure he knows and many of my comments would be quickly picked up by un undergraduate physics class.

 

So he starts by introducing the index of refraction, as a measurement of the observerved slowdown, but then only uses that index for a flashy optical illusion that I rather like, though I question its worth in the explanation. He states, without support that the index is a measure of the slowdown.

Then at 3 minutes in he says there are two completely wrong explanations going the rounds but does not say that both effects are actually observed fact, although, as he rightly says, they do not contribute to the slowdown.
A junior audience might be forgiven for believing that neither scattering nor absorbtion actually occur.

In dismissing both these explanations he  uses both good animations with spreading or fuzzy light rays, and poor ones looking like 1950s atromic representations.
In particular he shows both scattering and absorption by the nucleus only an fails to distinguish between the nucleus (red dots) and the whole atom. What makes it worse is that he lated describes glass as made of atoms surrounded by electrons.

How's that for confusing the coolkids club ?

Then he correctly introduces his explanation as a wave explanation and again correctly shows how two waves of different velocities can be combined to form a new wave of slower velocity than either of them.
 

But in his explanation both his waves are going in the same direction. He ignores the fact that the electrons (which actually produce the random scattering not the nucleus) will be travelling every which way but loose ands so any wave their interaction produces will be just as randomly oriented.

He also says that light is just oscillating electric fields, again suggesting to less experienced minds that there is no magnetism involved.

At around 8.00 he correctly says that electrons experience a force from an oscillating electric field and move under the influence of this force, in turn generating their own electric field its their own new wave. 
But he does not say why this new wave has a different velocity from the driving field, which was his condition for the resultant being slower.

At 6.37 he introduces superposition, but does not mention Huygens principle.

So all in all I do not feel that this video provides a satisfactory explanation, although it does satisfactorily rules out a couple of others.
Since he does say that a new wave is generated, he is marginally better than the others, but also hides missing pieces of his own explanation whiils overcomplicating parts of it.

 

 

[Tutoroot]

When light propagates through a material, it travels slower than the vacuum speed, c. This is a change in the phase velocity of the light and is manifested in physical effects such as refraction. This reduction in speed is quantified by the ratio between c and the phase velocity.