Speed of light after exiting a transparent medium

[isotherm]

TL;DR Summary

After a light wave is slowed in a medium, when exiting, in vacuum, it would regain the speed c? How?

The current explanation in Wikipedia for the slowing of the light wave phase velocity in a transparent medium considers:

At the atomic scale, an electromagnetic wave's phase velocity is slowed in a material because the electric field creates a disturbance in the charges of each atom (primarily the electrons) proportional to the electric susceptibility of the medium. (Similarly, the magnetic field creates a disturbance proportional to the magnetic susceptibility.) As the electromagnetic fields oscillate in the wave, the charges in the material will be "shaken" back and forth at the same frequency.[1]: 67  The charges thus radiate their own electromagnetic wave that is at the same frequency, but usually with a phase delay, as the charges may move out of phase with the force driving them (see sinusoidally driven harmonic oscillator). The light wave traveling in the medium is the macroscopic superposition (sum) of all such contributions in the material: the original wave plus the waves radiated by all the moving charges. This wave is typically a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity.

From another discussion I learned that the waves radiated by the "shaken" charges are real waves (not virtual), so they would also leave the medium, as the original wave. In this case, the wave traveling in vacuum would also be a superposition of the original wave and the waves radiated from the "shaken" charges. My question is: what speed this wave would have (in vacuum) and why?

 

[Orodruin]

The speed of light in vacuum.

The how part is not really anything else than ”that’s how light behaves” in accordance with Maxwell’s equations. Light in vacuum travels at c, the state of the observer or emitter does not affect this.

 

[isotherm]

The speed of light in vacuum.

The how part is not really anything else than ”that’s how light behaves” in accordance with Maxwell’s equations. Light in vacuum travels at c, the state of the observer or emitter does nog affect this.

So, the superposition of the waves in the material is slowing the original wave, but the same superposition after exiting the material, in vacuum, somehow does not have the same effect. Why?

 

[phinds]

Why?

”that’s how light behaves”

 

[Orodruin]

Why would it not? If you just look at Maxwell’s equations in vacuum there really is no other possibility.

 

[PeterDonis]

the superposition of the waves in the material is slowing the original wave

No. In the heuristic model you are trying to use, the original wave is partially absorbed by the material and re-radiated as the "wave from shaken charges". The part of the original wave that is not absorbed continues to travel at $c$.

Note that this scenario illustrates why it is not a good idea to think of phase velocity as "the speed of the wave".

 

[Dale]

The speed of light in vacuum.

The how part is not really anything else than ”that’s how light behaves” in accordance with Maxwell’s equations. Light in vacuum travels at c, the state of the observer or emitter does not affect this.

And realistically that is how any wave works, not just light.

So, the superposition of the waves in the material is slowing the original wave, but the same superposition after exiting the material, in vacuum, somehow does not have the same effect. Why?

A wave isn't a little ball that needs to be pushed to go a certain speed. Waves go their characteristic speed in a given medium. This applies to all sorts of waves: sound waves, gravity waves, gravitational waves, and light.

 

[Lord Jestocost]

TL;DR Summary: After a light wave is slowed in a medium, when exiting, in vacuum, it would regain the speed c? How?

The current explanation in Wikipedia for the slowing of the light wave phase velocity in a transparent medium considers:

From another discussion I learned that the waves radiated by the "shaken" charges are real waves (not virtual), so they would also leave the medium, as the original wave. In this case, the wave traveling in vacuum would also be a superposition of the original wave and the waves radiated from the "shaken" charges. My question is: what speed this wave would have (in vacuum) and why?

When light travels through media like water or glass or air, it merely appears to slow down.

The apparent slower speed is the result of the superposition of two radiative electric fields: (1) the incoming light, traveling at speed c, and (2) the light re-radiated by the atoms in the medium in the forward direction, traveling at speed c, too. The re-radiated light stems from the oscillating charges driven by the incoming light. The superposition of (1) and (2) shifts the phase of the resulting radiation in a way that would occur if light - so to speak - were to go slower in media.

To understand how the apparent or effective speed of light in media comes about, I recommend to read chapter 31 “The Origin of the Refractive Index” in “The Feynman Lectures on Physics, Volume I". On Bruce Sherwood’s homepage (https://brucesherwood.net/) you find an article “Refraction and the speed of light” dealing with this question, too.

 

[Orodruin]

a given medium. This applies to all sorts of waves: sound waves, gravity waves, gravitational waves, and light.

Except there is no medium in the case of light.

 

[A.T.]

So, the superposition of the waves in the material is slowing the original wave, but the same superposition after exiting the material, in vacuum, somehow does not have the same effect. Why?

You could ask the same question about the superposition before entering the material.

I don't think the superpositions outside the material are the same as inside the material, because the 2nd order waves propagating from a material layer are propagating in opposite directions, so it's not a continuous wave, but there is a kink at the emitting layer. I guess this also creates a discontinuity in the superposition of all the 2nd order waves at the material boundary.

Here is good animation related to this, but unfortunately it doesn't go into the superposition outside the material. But you might propose this as follow up video to the author. It already is a series based viewer questions.

 

[Mister T]

TL;DR Summary: After a light wave is slowed in a medium, when exiting, in vacuum, it would regain the speed c? How?

It's the way electric and magnetic fields interact. The stuff that slowed it down is no longer present, thus it resumes its normal speed.

 

[Dale]

Except there is no medium in the case of light.

Well, in this question there is. There is a medium and the question is what happens when the wave goes from the medium to vacuum. And what happens is the same as when any wave of any type transitions from one medium to another with a faster propagation speed.

 

[isotherm]

Here is good animation related to this ...

Thank you very much! The video is great. If I understood correctly, the wave is slowed by being "shifted back" (due to superposition) repeatedly. There is no only one superposition. Each layer of the material is emitting a secondary wave, and the shift due to superposition is repeated as long as there are "layers" to emit a secondary wave. Outside the material/medium, in vacuum, the wave is not shifted/slowed anymore, so its speed is c, as we know. By the way, the angle of refraction (when the wave is not exiting perpendicular to the surface) tells us that the speed outside the material, in vacuum, is c, as it should be.

Thank you all for your replies.

 

[A.T.]

Thank you very much! The video is great.

Make sure to watch the follow-up video on negative index of refraction and phase vs. group velocity:

If I understood correctly, the wave is slowed by being "shifted back" (due to superposition) repeatedly. There is no only one superposition. Each layer of the material is emitting a secondary wave, and the shift due to superposition is repeated as long as there are "layers" to emit a secondary wave. Outside the material/medium, in vacuum, the wave is not shifted/slowed anymore, so its speed is c, as we know.

Yes, the location dependent phase shift (at each layer) is key here. Outside the material you still have a superposition with the secondary wave emitted by the material, but that is a single phase shift of the entrie wave, that otherwise propagates normally at c.

By the way, the angle of refraction (when the wave is not exiting perpendicular to the surface) tells us that the speed outside the material, in vacuum, is c, as it should be.

For angle of refraction the phase velocity is relevant, but for transmitting information you have to move away from steady state, and then the group velocity matters.

Here is the other video recommended and partially used in the one above:

 

[wnvl2]

I understand that in steady state you have a superposition of waves what makes that the radiation goes slower inside the medium. But if you have a light pulse, how can you explain that the front of the pulse is slowed down? It is difficult to understand that the front of the puls can be influenced by the lagging radiation (see end of the second part of the youtube movie).

 

[PeroK]

I understand that in steady state you have a superposition of waves what makes that the radiation goes slower inside the medium. But if you have a light pulse, how can you explain that the front of the pulse is slowed down? It is difficult to understand that the front of the puls can be influenced by the lagging radiation (see end of the second part of the youtube movie).

We had this question recently. It's not a great thread, IMO, but it might be worth reading. The idea that the "front of a light pulse" gets through a medium before the medium has a chance to slow it down relies too much on an imprecise model.

https://www.physicsforums.com/threads/speed-of-information-in-a-medium.1058208/

 

[Lluis Olle]

No. In the heuristic model you are trying to use, the original wave is partially absorbed by the material and re-radiated as the "wave from shaken charges". The part of the original wave that is not absorbed continues to travel at $c$.

I agree with that. There's an extended misconception about the change in speed being somehow due to the continually absorption and re-emission of the photons... and as such process "takes a finite time", that's the reason for the slowdown.

Absorption and re-emission of photons is a random process, in the sense that the re-emitted photon will have a random direction and a random phase. It happens to some photons, and that's why we can "see" the light beam if we watch transversally to the beam direction.

 

[A.T.]

I understand that in steady state you have a superposition of waves what makes that the radiation goes slower inside the medium. But if you have a light pulse, how can you explain that the front of the pulse is slowed down?

I have made a video request to 3Blue1Brown about this. Maybe it helps if more people like it: