3

What I (think I) understand: When light is refracted in a medium (say glass), the light interacts with the electrons in the medium and the electrons create new waves. Summing the waves with the original wave gives a group velocity slower than c because of phase lags.

What I'm confused about: How is light interacting with these electrons? It's not being absorbed. Here it is described as being "virtually absorbed". I understand that you can view a photon as taking every possible path and sum them, but they're if they don't have the energy to excite an electron, then why would summing a bunch of paths where it can't excite an electron result in "virtual absorption"? What does "virtually absorbed" mean? Sixty Symbols describes it: "In an indirect way they're able to make the electrons wiggle." What is this "indirect way"? Also is dispersion a continuous or discrete phenomenon and why?

Knight98
  • 105
  • 1
    Feynman has a really thorough explanation of this: http://www.feynmanlectures.caltech.edu/I_31.html . It's a quantum (discrete) phenomenon on its smallest levels (like all mechanisms of energy transfer), with the continuum fields just representing Poisson rates of these tiny processes. – Ryan Thorngren Aug 16 '18 at 16:16

1 Answers1

4

When a photon interacts with an atom three things can happen:

  1. elastic scattering, the photon keeps its energy and changes direction

  2. inelastic scattering, the photon gives part of its energy to the atom and changes direction

  3. absorption, the photon give all its energy to the atom, and the absorbing electron moves to a higher enrgy level as per QM

In your case, when light gets refracted inside glass, it is elastic scattering, it is called Rayleigh scattering, specular reflection. This is the only way that a mirror image is kept, and the photon keeps their energies and phases. And all the photons get coherently scattered.

As photons make their way through glass, the lattice acts like in the double slit experiment. In the double slit experiment, even if you shoot one photon at a time, it will travel as a wave, and parts of the wave will interact with each other. This will create interference. The only constructive interference will be the path that the wavefront will take (bright parts of the screen). All the other directions will not be used because of destructive interference (dark parts of the screen).

Same thing happens in glass with the lattice. The waves go through the lattice's spaces, and the photons' waves will interfere. The destructive interference will cancel out every direction other then the wavefront's direction. Constructive interference will make the wavefront move in one certain direction.

Now virtual absorption means the scattering process. The photons interact with the atoms, but the electrons (around the nuclei) in this case will not absorb them physically, and the electrons will not move to higher energy levels as per QM. In the case of glass this is elastic scattering and because of that, the photons keep their energy and phase, and the electrons (around the nuclei will not gain kinetic energy).

Now you are asking basically about why and how light passing through glass can still make glass hotter. Wiggle the electrons is not correct to say. What is correct to say, is that in the case of glass, all three things happen with the photons, elastic scattering (this makes the image move in the glass), inelastic scattering, and absorption. It is the ratio of these three interactions that is different then in other material. In glass, the ratio of elastic scattering is the highest.

The ratio of inelastic scattering, that makes as you said wiggle, is smaller in glass, but it still works. Now in the case of inelastic scattering, the photons give part of their energy to the atoms and molecules. We have to clarify, that what you are talking about, the wiggle, is called vibration of the molecules. That is what we call temperature of the glass. When photons give part of their energies to the atoms and molecules of the glass, the vibrational energy of the molecules rises, temperature rises.

The ratio of real absorption in glass is smaller too. Some of the photons get really absorbed by the atoms' electrons, and then those electrons get relaxed, and re-emit photons.

You are asking about dispersion, a continuous spectrum contains many different colors or wavelengths, with no gaps. Perfectly white light shined through a prism creates dispersion. This is a continuous spectrum.

The reason you get a speed less then c, is because the way you calculate speed for the wavefront. You are using a straight path as distance, and divide it by the time the wavefront needs to pass through the glass. The individual photons always travel with speed c (when measured locally), because they always travel between the atoms in vacuum. But as the photons get scattered by the atoms of the glass, they change path, because the waves interfere, and the only constructive interference will be the path the photon will go from atom to atom. But that path will not be the same path through the glass as the straight path you calculate speed with.

enter image description here

Here is a picture of a photon making its way out if the Sun. It might take 100000 years for a photon to get through the dense gas. Is the speed of the EM wave that slow? No. The photon travels with speed c (when measured locally) between the atoms. But since it interacts with so many atoms, and as it travels as a wave, parts of the wave interfere with each other, and that changes the path of the photon.

It is a little bit similar in glass, and that is why the wavefront slows down. individual photons still travel at speed c between the atoms.

Árpád Szendrei
  • 28,452
  • szendrei I invite you to back up your answer with scientific references proving that refraction is caused by Rayleigh scattering. – my2cts Aug 16 '18 at 18:51
  • @my2cts Don't hold your breath - it is incorrect to attribute refraction in a bulk material to Rayleigh scattering, period. The term Rayleigh scattering is intrinsically tied to the requirement that the scatterer be much smaller than the wavelength of light, which is the polar opposite of the situation in a bulk material. – Emilio Pisanty Aug 16 '18 at 21:12
  • @EmilioPisanty in Rayleigh scattering, the material, like glass, the atoms are much smaller then the wavelength! This is exactly Rayleigh scattering, why are you saying not? – Árpád Szendrei Aug 16 '18 at 21:22
  • @EmilioPisanty it is elastic scattering (Rayleigh), and this is the only way to keep the energy and phases of the photons. Any other type of scattering, or absorption reemission will cause the image not to be an image and the photons would change energies and phases, and that is not an image or an image being transferred through the glass. – Árpád Szendrei Aug 16 '18 at 21:25
  • @EmilioPisanty it is called specular reflection/refraction, that is the only way to do coherent refraction. The problem I see here, is that people think that the difference between the glass creating a mirror image (reflection) or transferring an image (refraction) is more then the angle. Basically both are Rayleigh scattering. In reflection, the angle is almost opposite, and in refraction, it is almost the same as the original. – Árpád Szendrei Aug 16 '18 at 21:30
  • @EmilioPisanty Otherwise, the photons get scattered elastically in both cases. That is why we can see mirror images in glasses from certain angles, and we can see an image from the other side of the glass too. That is why glass can do both, and both are the same elastic scattering. – Árpád Szendrei Aug 16 '18 at 21:32
  • @EmilioPisanty I have read your answer to that question of duplicate, and I do not think this is a duplicate, because that is not a QM description. I gave here a QM description. But you are writing too "However, here is the important thing: the glass can do this induced-oscillations-then-emission game without absorbing any energy at all. " I believe that the solution to this at the QM level is what I am writing, but of course at the classical EM wave level what you wrote seems correct. – Árpád Szendrei Aug 16 '18 at 21:38
  • 1
    It is a mistake to equate elastic scattering with Rayleigh scattering. The latter is a strict subset of the former, with e.g. Mie scattering forming part of the difference between the two sets. Rayleigh scattering entails a very specific set of characteristics on the dependence on the scattering angle and the wavelength, but those characteristics no longer hold true when you have multiple scatterers and their scattered radiation begins to interfere (as in Mie scattering and in bulk). Once that happens, the term Rayleigh scattering no longer applies. – Emilio Pisanty Aug 17 '18 at 00:55
  • As for whether this is a duplicate or not - the OP actively closed the question by clicking the "That solved my problem!" button (and in fact I could easily have unilaterally closed the question but I actively chose not to, despite direct discouragement of that choice from the official recommendation). But you can keep debating if you want to. – Emilio Pisanty Aug 17 '18 at 01:03
  • @EmilioPisanty I really apologize, I understand that you have a better knowledge on this. i would like to learn, can you please tell me what your opinion is, what kind of scattering it is inside glass, is it elastic scattering at all? I always believed it must be either elastic, inelastic scattering or absorption. Which one would you say it should be? – Árpád Szendrei Aug 17 '18 at 02:57
  • Of course it is elastic scattering. But, as I said, that does not imply that it is Rayleigh scattering. Re-read my comments above. – Emilio Pisanty Aug 17 '18 at 09:33
  • "... because they always travel between the atoms in vacuum ... " This seems to make sense, however, never heard before, what is the reference. Doesn't it make superflous Feynman's concept of "any" path? Feynman surely doesn't mean to say that a photon must search a path in between atoms, in a vacuum, using elastic scattering, or does he imply this? I guess the Feynman's diagrams are about Heisenberg uncertainty, and that in my opinion would not be in contradiction with "vacuum in between". If "vacuum/elastic scattering" is your own personal theory I'd be impressed. – Peter Bernhard Nov 16 '22 at 21:46
  • Refering to the "lengthy discussion: it should be made clear to the reader that with "Rayleigh scattering" counterintuitively there is no change of frequencies, only change of direction. Maybe that somehow relates to the discussion in the comments. Is the term restricted to reflections in the atmosphere? If not, it might be the only way - different angles by differing directions that a photon makes it through a thicket of electrons. Refering to the answer I miss additional information if with Rayleigh electrons first absorb then emit electrons. - This is an amazing answer which I recommend. – Peter Bernhard Nov 17 '22 at 08:42
  • Refering to an error in answer: ".... called Rayleigh scattering, specular reflection. This is the only way that a mirror image is kept, ... " This, indeed, cannot be. A mirror image would not be preserved as rays of light were distorted in direction of colour-frequencies. Rayleigh reflection angles depend (4th potency) on their frequency. This amazing answer, however, shows that Raleigh may be a mode to make it through some medium, whereas at it's boundary Newton perpendicularity applies (the mirror, angle in is angle "out"). First pages of Opticks, Newton says there is slight deviation. – Peter Bernhard Nov 17 '22 at 17:25