# On why in transparent media light speed is altered by elastic scattering of photons and their path lengths

https://en.wikipedia.org/wiki/Higgs_boson Where it says:

"Symmetry breaking in optics In a vacuum, the light of all colours (or photons of all wavelengths) travels at the same velocity, a symmetrical situation. In some substances such as glass, water or air, this symmetry is broken (See: Photons in matter). The result is that light of different wavelengths appears to have different velocities (as seen from outside)."

and this:

https://en.wikipedia.org/wiki/Variable_speed_of_light

where it says:

" the situation in a medium, where a shorter wavelength $${\displaystyle \lambda}$$ , by means of $${\displaystyle c=\nu \lambda } c = \nu \lambda$$, leads to a lower speed of light"

and this:

https://en.wikipedia.org/wiki/Photon#Photons_in_matter where it says:

"In a classical wave picture, the slowing can be explained by the light inducing electric polarization in the matter, the polarized matter radiating new light, and that new light interfering with the original light wave to form a delayed wave. In a particle picture, the slowing can instead be described as a blending of the photon with quantum excitations of the matter to produce quasi-particles known as polariton (other quasi-particles are phonons and excitons); this polariton has a nonzero effective mass, which means that it cannot travel at c. Light of different frequencies may travel through matter at different speeds; this is called dispersion (not to be confused with scattering). In some cases, it can result in extremely slow speeds of light in matter. The effects of photon interactions with other quasi-particles may be observed directly in Raman scattering and Brillouin scattering."

and this:

https://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field

where it says:

"Photon energy Apparently, the single-photon state is an eigenstate of $$H$$ and $$ω = hν$$ is the corresponding energy."

and this:

"Particle model and quantum theory. As a photon is absorbed by an atom, it excites the atom, elevating an electron to a higher energy level (one that is on average farther from the nucleus). When an electron in an excited molecule or atom descends to a lower energy level, it emits a photon of light at a frequency corresponding to the energy difference. Since the energy levels of electrons in atoms are discrete, each element and each molecule emits and absorbs its own characteristic frequencies. Immediate photon emission is called fluorescence, a type of photoluminescence. An example is a visible light emitted from fluorescent paints, in response to ultraviolet (blacklight). Many other fluorescent emissions are known in spectral bands other than visible light. Delayed emission is called phosphorescence."

As soon as I am trying to explain the slower speed of light in transparent media, and try to switch to photon level, I get into a problem. There can be two different ways that it is explained on the photon level, either by

1. absorption-reemissions, and so the time (excited state) needed for these slows down the wave.
2. or by elastic scattering of the photons, and thus creating lengthened paths' for the individual photons and so slowing down the wave. "In transparent media, it is elastic scattering of photons, which has the effect of lengthening the path of the individual photons, therefore a longer time is taken by the group velocity of the wavefront "

"Elastic scattering of the individual photons has an angular distribution, whereas the light front built up goes in a straight line. The photon at an angle goes at velocity c, but the path is longer than if it went straight. "

Now in one of my questions, I got some help and got the answer that it is #2, the elastic scattering. But I do not have information on how this elastic scattering exactly on the photon level will cause the photon's paths' to be lengthened(and so slowing down the wave). What I mean is I do not have information on how this elastic scattering is exactly happening on the photon level, if they don't get absorbed-reemitted then what exactly happens to the photons?

Questions:

1. Can somebody please help me explain how the elastic scattering of photons in transparent media lengthens the path of the photons (and thus the wave gets slowed down)? I understand this "Elastic scattering of the individual photons has an angular distribution, whereas the light front built up goes in a straight line. The photon at an angle goes at velocity c, but the path is longer than if it went straight. "

2. But I still don't understand how elastic scattering is different in this case from absorption-reemission. Absorption-reemission has an angular distribution too. How is elastic scattering different from absorption-reemission on the photon level?

3. How does elastic scattering of the photons in transparent media in this case exactly work/happen on the photon level? What happens to the photon, is it absorbed-reemitted or is it just bumping off from particles, or does it get into interaction with other particles?

4. And mostly, I understand that the photon after elastic scattering goes in an angle, but the wavefront goes straight, but what brings the photons back to the straight path? They bump back from the edge of the media or how?

• +1 Hi Árpád , nice question, I highlighted the excerpts and put in some mathjax and two more tags. Would you please check they are what you intended, thanks. Look forward to seeing an answer. – user108787 Nov 29 '16 at 2:21
• – user108787 Nov 29 '16 at 2:31
• Not really 'different' mechanisms; elastic scattering means energy conserved, and for a photon and ONE massive particle, that requires FORWARD scattering, i.e. a phase shift. – Whit3rd Mar 30 at 7:57