# How Does Light Travel Through Glass?

I've mentioned before that I'm answering the occasional question over at the Physics Stack Exchange site, a crowd-sourced physics Q&A. When I'm particularly pleased with a question and answer, I'll be promoting them over here like, well, now. Yesterday, somebody posted this question:

Consider a single photon (Î»=532 nm) traveling through a plate of perfect glass with a refractive index n=1.5. We know that it does not change its direction or other characteristics in any particular way and propagating 1 cm through such glass is equivalent to 1.5 cm of vacuum. Apparently, the photon interacts with glass, but what is the physical nature of this interaction?

I didn't have a ready answer for this one, but I'm pretty happy with what I came up with on the spot, so I'll expand on it a little bit here. I think it's an interesting question not only because the issues are a little bit subtle, but because it also shows the importance of understanding classical models as well as quantum ones. The key to understanding what's going on here in the quantum scenario is to recognize that the end result is the same as in the classical case, and adapt the classical method accordingly.

So, how do you explain this classically, that is, in a model where light is strictly a wave, and does not have particle character? The answer is, basically, Huygens's Principle.

To understand the propagation of a wave through a medium, you can think of each component of the medium-- atoms, in the case of a glass block-- as being set into motion by the incoming wave, and then acting as a point source of its own waves. In the picture above, you can see that each of the the little yellow spots in the gap in the barrier is at the center of its own set of concentric rings, representing the emitted waves.

When you work this out, either by drawing pictures like the above, or by doing out the math, you find that these waves interfere constructively with one another (that is, all the peaks line up) in the forward direction, but that the waves headed out sideways to the original motion will interfere destructively (the peaks of one wave fall in the valleys of another), and cancel out. This means that the light continues to move in the same direction it was originally headed.

When you work out the details, you also find that the wave produced by the individual point sources lags behind the incoming wave by a small amount. When you add that in, you find that the wave propagating through the medium looks like it's moving slightly slower than the wave had been moving outside the material. Which is what we see as the effect of the index of refraction.

This model of light propagation through a medium is fantastically successful, so our quantum picture should reproduce the same features as long as you're at a frequency where quantum effects don't play a role. So, how do we carry this over to the quantum case, thinking about light in terms of photons?

This is a tricky question to answer, because in many ways it doesn't make sense to talk about a definite path followed by a single photon. Quantum mechanics is inherently probabilistic, so all we can really talk about are the probabilities of various outcomes over many repeated experiments with identically prepared initial states. All we can measure is something like the average travel time for a large number of single photons passing through a block of glass one after the other. We can come up with a sort of mental picture of the microscopic processes involved in the transmission of a single photon through a solid material, though, that uses what we know from the classical picture.

To make the classical picture quantum, we say that a single photon entering the material will potentially be absorbed and re-emitted by each of the atoms making up the first layer of the material. Since we cannot directly measure which atom did the absorbing, though, we treat the situation mathematically as a superposition of all the possible outcomes, namely, each of the atoms absorbing then re-emitting the photon. Then, when we come to the next layer of the material, we first need to add up all the wavefunctions corresponding to all the possible absorptions and re-emissions.

Thus, we more or less reproduce the Huygens's Principle case, and we find that just as in the classical case, the pieces of the photon wavefunction corresponding to each of the different emissions will interfere with one another. This interference will be constructive in the forward direction, and destructive in all the other directions. So, the photon will effectively continue on in the direction it was originally headed. Then we repeat the process for the next layer of atoms in the medium, and so forth.

It's important to note that when this picture is valid the probability of being absorbed then re-emitted by any individual atom is pretty tiny-- when the light frequency is close to a resonance in the material, you would need to do something very different. (But then, if the light was close to a resonant frequency of the material, it wouldn't be a transparent material...) while the probability of absorption and re-emission is tiny for any individual atom, though, there are vast numbers of atoms in a typical solid, so the odds are that the photon will be absorbed and re-emitted at some point during the passage through the glass are very good. Thus, on average, the photon will be delayed relative to one that passes through an equal length of vacuum, and that gives us the slowing effect that we see for light moving through glass.

Of course, it's not possible to observe the exact path taken by any photon-- that is, which specific atoms it scattered from-- and if we attempted to make such a measurement, it would change the path of the photon to such a degree as to be completely useless. Thus, when we talk about the transmission of a single photon through a refractive material, we assign the photon a velocity that is the average velocity determined from many realizations of the single photon thought experiment, and go from there.

The important and interesting thing here is that the effect that we see as a slowing of a particle-- a photon taking a longer time to pass through glass than air-- is actually a collective effect due to the wave nature of the photon. The path of the light is ultimately determined by an interference between parts of the photon wavefunction corresponding to absorption and re-emission by all of the atoms in the material at once. And since we know the photon has wave characteristics as well as particle characteristics, we can use what we know from classical optics to understand the quantum processes involved.

This is, as I said, an explanation invented on the spot yesterday, when I started thinking about the question, but I think it's fairly solid. As always, if you see a major hole in it, point it out in the comments.

And if you have physics questions, I encourage you to take them to the Stack Exchange site. I've got dozens of other things I'm supposed to be doing, so I won't necessarily have time to address specific questions, but that's the beauty of the crowd-sourced option-- there's bound to be somebody out there who isn't too busy to answer...

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So is the idea here that if you had a particular atom and photon, absorption and re-emission would be a stochastic process (and we wouldn't know which direction it'd emit).

But when you have a whole bunch of atoms and the photon can't really be said to be absorbed by any one in particular, then the interference effects of all the possible paths it can take would add up to the classical description of refraction? Because all the paths include being absorbed and emitted by all the atoms, and in all directions, and the sum of those is back to the classical deterministic path?

I had been avoiding absorption-emission in my own conceptualization of optical transmission but I see now I didn't have to...

It's been a while since I read it, but didn't Feynman use the passage of light through a transparant refractive medium as an example in his book QED?

Actually, I think he also tied in why there is partial reflection when light passes through a junction of materials with two different indices of refraction as well. My recollection is that when the photon interacts with an atom, it stands a chance of being scattered forward or backward (so a transmission through, say, 3 layers of atoms could be forward-forward-forward (and go through) or backward (and be reflected, or forward-backward-forward-forward-forward (and go through seemingly a bit slowly) or any number of other combinations). Since, under QED, the overall amplitude is the sum over all possible paths, the end result is delayed from what it would be without the media.

By Blaise Pascal (not verified) on 15 Dec 2010 #permalink

Wow -- what an over-explanation.

You could just put up Maxwell's equations in dielectrics -- that's the answer. Hundreds and thousands of words to "explain" 4 equations that still aren't fully covered by all the words.

If you want to derive them from quantum mechanics -- then do it, instead of talking about it.

Frog -- you miss the point that, yeah, sure, Chad could just put up Maxwell's equation including material terms, and derive a wave equation that has a speed lower than c in in it. Which might be illuminating for somebody who knows vector calculus and partial differential equations. What he did write, however, might be illuminating for others as well... and might also help those who *do* know vector calculus and PDEs understand how to interpret the equations that they've seen.

Frog - that's all very well if you a) know that particular formation of Maxwell's equations and b) understand it. Those of us without that level of physics education but who are interested in this sort of thing find a textual and graphical explanation much more useful, thank you very much.

Over explanation? That depends very strongly on your audience.

The question reminded me for some reason of Bob Shaw's "Light of Other Days" which tells a story of a place that sells slow glass. Slow glass panes are placed facing beautiful scenes. The glass captures the light over a period of years and eventually the light starts coming out the other side. That's when people buy the panes. It eventually occurred to me that light means energy, and that fairly thin pane has to contain all the energy of the light that falls on it over many years. It must get pretty hot.

"When you work out the details, you also find that the wave produced by the individual point sources lags behind the incoming wave by a small amount." So what you are saying is that there is a time lag between when the "point source" ie atom, receives the incoming wave and when it re-emits a wave? These time lags add up. Is my interpretation correct?

Owen: "Those of us without that level of physics education but who are interested in this sort of thing find a textual and graphical explanation much more useful, thank you very much."

I think you're misleading yourself. I understand your point -- you feel as if you understand it, but I think that all there is to understand is Maxwell's equations. If you can't do that -- you don't actually understand it. You can't actually predict experimental results with the graphics and the verbalization.

It's like arguments over what QM "means". Huge amounts of hot air go on -- when the only real explanation are the equations for the wave functions. The words at best are just a way to make the equations palatable.

As a bonus, Maxwell's equations are particularly simple. You don't have to try to bend your head in 20 ways to understand them -- if you know what a vector is and a few measurements, you've got all of electrodynamics in your head.

As a bonus, Maxwell's equations are particularly simple. You don't have to try to bend your head in 20 ways to understand them -- if you know what a vector is and a few measurements, you've got all of electrodynamics in your head.

All of classical electrodynamics. Maxwell's equations aren't the complete story of electrodynamics, because if they were, we wouldn't need quantum electrodynamics (QED).

Now, it's true that you don't need QED to describe the propagation of light through a dielectric medium well off resonance. However, we know that QED is a more complete theory of reality (because Maxwell's equations aren't sufficient to describe non-classical states of light such as single-photon states), so it is perfectly reasonable to ask how you would explain propagation through a medium in quantum terms. While the results you get won't differ appreciably from what you'd get using Maxwell's equations, it can be illuminating (heh) to think about how those results arise from the deeper quantum theory.

If I were interested in predicting the results of a photon propagation experiment, then I'd be a quantum physicist. But I'm not. So I'll settle for Chad's very interesting (and well written) explanation, while you, frog, can go hide in a hole with the other eletists and calculate numbers.

Chad's post is not an over explanation. Ok, it does not explain how to model this situation. An explanation of how to model the situation using Maxwell's equations might be shorter than Chad's post. But that totally misses the point; Chad's post (and blog in general) is about the ideas behind the quantum model, and how they relate to ideas about the classical model.

You might call this type of writing scholarly writing (in this case aimed at a general audience), rather than technical writing. Scholarly writing tends to be under-appreciated, and also under-identified, in the math and physics world. At least, that's my experience as a mathematician.

This reminds me of something I heard many years ago that I found bothersome at the time--the breathless reports of experiments that measured interference effects in a small loop of superconducting wire, proclaiming that while the currents involved were minuscule, they were a first-time demonstration of quantum effects operating at the macroscopic level because every atom in the (barely) macroscopic wire was "participating" in conducting the currents.

But how is that really any different than conducting, say, a two-slit experiment submerged in water, or inside a solid block of glass? A substantial fraction of the atoms in the medium "participate" in the propagation of a single photon, and so they all "participate" in generating the interference pattern on the photodetecting surface. So why was doing essentially the same thing with electricity considered to be some sort of breakthrough?

You may have a hard time with this, but the common language of description and explanation, as with mathematics are really a structured analytical analogy, with mathematics closer to reality.

There is no such thing as a perfect analogy.

Such is the world...experience rules.

To convey a process to the masses both can be used in conjunction, though it is rarely done successfully and accurately, as it can be difficult.

Much better understanding can be achieved with a higher language and mathematics but then you leave out a whole slew of people.

By Sphere Coupler (not verified) on 15 Dec 2010 #permalink

so is them glass transparent due to the way the atoms are arranged i did not now that.
Forgive me im hoping to become a physicist but in the south our education is lacking
im only now getting to the university physics courses.

The behavior of photons is all probabilistic then can this characteristic be expressed on the large scale ie the wave functions are interfering constructively on the large scale and can this behavior be induced in an observable way

@Sphere: You may have a hard time with this, but the common language of description and explanation, as with mathematics are really a structured analytical analogy, with mathematics closer to reality.

The question is what is the cut-off -- at what point are words simply insufficient. The historical progress has been from verbal to mathematical descriptions. You can still do some physics primarily using words and drawings -- at least a first cut of ballistics can be done that way.

But at some points words simply mislead. It's too easy to make a mistake (see my eliding of "classical" from the entire classical electrodynamics phrase). At a certain level, no matter how clear your verbiage it, it creates more noise than signal simply because the necessary number of words to explain the phenomenon to any amount of accuracy are more words than a person can understand.

Then you get folks who "think" they understand it, when they simply don't. See almost any popular discussion of quantum mechanics, which is almost much more wrong than it is right. How much effort is wasted in "understanding" wave/particle duality or uncertainty? Words simply don't suffice.

Some things just simply require a certain "elite" understanding -- the essence is in the numbers and not in the words. Making that clear to people is important, I think. There's no short-cut to carpentry or physics. You either can build a bookshelf or you can't (but you can always practice and try to learn). But a sculpture of building bookshelves just isn't terribly useful -- if that's elitism or a "misunderstanding", then I guess I stand guilty.

And I wonder how "elitist" it is to say -- well, you can't understand the real physics, so here's something that'll make you feel involved and happy, even if you can never predict a single experiment with what I give you.

I guess it's the old question from Feynman's intro -- are you doing any one any good by putting physics in terms that anyone thinks they can understand, but no one can actually do any physics with? And where do you draw the line. For me, this passed the threshold of being way complicated for what is mathematically simple -- that's a sign that you're simply trying to do the impossible and non-useful. We're not talking here actually nasty mathematics where you can really argue that you capture a good chunk in the words and the math only adds a few decimal points.

I'm not sure I buy your explanation of the change in propagation speed, at least in the classical case. You say "when you work out the details" you see this but I think the details require more than Huygen's principle. The wave crest from a particular "Huygens" point moves out from that point at the same speed as it arrived, so the front of the wave in medium shouldn't be any slower. This might change of course if there is a delay between absorption and emission of photons from atoms, but that isn't Huygen's principle by itself. Put another way, there needs to be some reference to the (probably dialectric) properties of the different media. The picture by itself provides no intuitive explanation since you could flip the incoming/outgoing wavelets around the horizontal axis and come to the same conclusions as before. The picture shows refraction from a gap but that's about it at the classical level.

I was under the impression that in classical optics we simply take for granted that the speed of light is reduced in many materials, by a factor of the material's refractive index. Of course in the quantum mechanical picture each photon is (possibly) absorbed and re-emitted continually, and the speed of light in the material is simply the sum of all possible outcomes as you said.

The Huygens principle is a fantastic way of explaining diffraction or refraction, but does it have anything to do with the speed of light changing in the material? Take refraction: It's easy to directly "see" the wavefront changing direction when you draw all of the circular wavefronts being emitted from rays striking the surface. However you have to decrease the radial spacing of the circles for the wavefront to change direction (in a rather ad hoc manner). As far as I know, the Huygens principle doesn't say anything about what this new radial spacing is (proportional to 1 / the refractive index). Can you clarify?

What I would like to know is how an atom absorbs and then re-emits the photon.

What exactly happens? At one point in time we have a photon and an atom, at another point in time we have only an excited atom - what exactly happens in between? How the photons energy get's absorbed by atom's electron? It cannot be absorbed instantly as that would mean spacetime is discontinuous.

Why? Even if you assume both the photon and the electron are point particles (which is absurd IMHO, but that is beside the point here) the curvature their mass-energy induces (however small it is) is extended in spacetime. An instant absorption of the photon would mean that it's curvature vanishes "instantly and simultaneously in an extended region of space" but that makes no sense from relativity POV, first simultaneity is observer dependent, but even worse it would make spacetime curvature discontinuous.

So because of general relativity the process of absorption has to be gradual and the mass-energy configuration of the photon+atom state has to continuously transform into mass-energy configuration of the excited atom state.

But how exactly does that happen?

Frog;

Much agreed,and I personally don't think of someone who has these abilities to be an elitist. I myself utilised (big words) when communicating with others in a normal everyday setting and of course no-one could understand a word I said and since most of the people (even though I have been at Uni. for over two decades)speak in a common tongue, speaking with only higher language came natural to me and took effort to retrain myself at a great personal lose. I have been forced to conform to this reality, and have lost this vocabulary due to lack of use.The only reasurence that I have is when I am amongst those (so called elite), it all comes back!

THAT is not elitist, it is skill and talent.
;?)

It takes so many unrefined words to explain a situation that it becomes tedious and as you say, the background noise can be overwhelming and the original concept lost.

I have thought about this for many years and have come to the conclusion that any and all papers that I should write would take four forms or levels, Mathematical,A higher language, the common tongue, the metaphysical. In this way one could start from the level most comfortable and progress. I think that each of these communication forms, operating in their own parameter, overlap, and in such a way a higher standing can be achieved to anyone with the desire to pursue.

Analogies are great, yet nothing beats experiment, and since experiment is not always available to the masses, a difficult situation is before the communicators of our time.

The math should be spoon fed at every possible opportunity along with, side by side, at every step, common and/or high. In this way, overtime, understanding could come to fruition.It is redundant, tedius and ugly for those already trained.

Could you imagine if everyone spoke as the so called elitist, there would be very little verbalised yet a whole lot said.

By Sphere Coupler (not verified) on 15 Dec 2010 #permalink

I'm not sure I buy your explanation of the change in propagation speed, at least in the classical case. You say "when you work out the details" you see this but I think the details require more than Huygen's principle.

Yes, they do.
Specifically, they require a model of the sources of the waves as little dipoles driven off-resonance. This is a reasonable approximation of an atom-- negative electrons outside a positive nucleus-- and works to get you what you need.

The crucial factor is that when you drive the dipoles by applying an oscillating electric field that pulls the electrons back and forth (by a tiny amount-- we're not talking big distortions, here, so it's not going to upset the binding of atoms into a solid) their response is very slightly out of phase with the driving field. This is a basic result for any driven harmonic oscillator, that you can derive from classical mechanics, but I have a hard time thinking of a good conceptual explanation for (which is why I didn't put it into the post).

That slight phase lag in the oscillation means that the waves emitted by the little dipoles are slightly out of phase with the incoming field doing the driving. When you add those two waves together, you get a wave of the same frequency that lags a little behind the incoming wave, and thus moves more slowly than the incoming wave.

If you want to see this all worked out in detail, the bible for classical optics stuff like this is the textbook by Hecht. I was supposed to teach an upper-level elective on classical optics next term, so I was mentally reviewing some of it recently, hence this response.

(Alas, the class had to be cancelled due to low enrollment. Sigh.)

Two comments (which I may steal for my own posts!): The technically inclined may be interested to know that photon wavefunctions are tricky things. In some important senses, photons don't have one at all. Among other things, Schrodinger's equation doesn't work with m = 0. You can construct correlation functions that work more or less like a photon wavefunction, but this isn't quite the same thing. You know this of course, and conceptually it makes no difference for the intuitive explanation, but it's a neat thing to think about.

Second, "When you add those two waves together, you get a wave of the same frequency that lags a little behind the incoming wave, and thus moves more slowly than the incoming wave." Usually! But it's also possible to have a refractive index of less than 1, which means a phase velocity greater than c. This doesn't violate relativity, but the reason (elucidated by Sommerfeld and Brillouin a century ago) is by no means trivial, and my first first-author paper is tangentially related to this (or it will be when the referee gets around to sending in his report!).

Sounds reasonable. I wonder how believers in the Bohmian pilot wave concept explain basic things like linear propagation through glass. And what do they think a "photon" is, anyway? I can intuitively get the idea of "an electron" (tiny locus of electric field) being "a true classical object" that is guided into apparent interference etc., but "a photon": imagined in flight and not just as a receiving-end quantum of energy, is ... what?

BTW transparent things are of course a way to detect passage of a photon without "affecting the target" in any significant way (and I *don't* mean the E-V bomb scheme.) Just send the photon through a piece of glass, and if normal incidence there is no residual momentum transfer etc. You could either count for delay in photon reception, or better: use interference to show it's there.

But all these examples of interaction-free or interaction-irrelevant measurements cause a problem for QM: the early arguments about the HUP etc. relied on the idea that a photon use to e.g. measure position would have to impact momentum in a straightforward way (scatter-type process) as if a piece of flat glass couldn't be found in a position, but with negligible momentum transfer. What gives?

I have to agree that Huygens principle is a better explanation than Maxwell's equations in dielectric media. The latter are (very important and amazingly effective) approximate equations, but they gloss over all of the atomic processes involved (e.g. is the dielectric constant really constant?). There is of, course, a middle ground, by mathematically expressing the total electromagnetic wave as a sum of the incident wave with all of the (absorbed and re-emitted) waves from the medium; this has the added advantange of highlighting the beauty of linearity and the principle of superposition.

A nice exposition along these lines can be found in a paper by Mary James and David J. Griffiths, "Why the speed of light is reduced in a transparent medium": http://ajp.aapt.org/resource/1/ajpias/v60/i4/p309_s1. From the abstract: "This paper offers some elucidation of the ââmiracleââ by which the radiation from many induced molecular dipoles conspires to produce a single wave propagating at the reduced speed."

Frog, about use of words: we need to words to explain what the math is doing, otherwise "f = ma" is the same as "a = fm" etc, they are just labels for the same function.

I have to quibble with Chad saying this: "All we can measure is something like the average travel time for a large number of single photons passing through a block of glass one after the other." Although it is hard to time a single photon, it can be done within the limits imposed by coherence time. With a thick piece of glass, you should be able to observe (as I noted above) that a single photon was delayed before reaching a detector.

To extend my example about observation that does not affect momentum: we could use rotation of polarization too, to find that something was there. I hate to say it, but it seems even thinkers like Heisenberg working out the "Heisenberg microscope" are looking for the example that seems to prove their point. They aren't saying, as we must do to be candid: "what if there's another case where my wonderful illustration does not work?"

According to a more complete theory, if a process deals with a low number of action, then the Proper Time Tau have to be substituted by the Action S, and that is not a invariant nor a continuous but a discrete dimension:

0 â 1/hÂ² dSÂ² - 1/tplÂ² ( dtÂ² - 1/cÂ² {dq1Â² + G0Â²/GÂ² [ dq2,3Â² - ...]}) with G0 = tplÂ²câµ/h â G

With this, we have to expect a delay on each pass near an atom which will be an 'interaction' with it (which happens or not happens - discretely). The amount of the delay is question of the 'metric coefficient' omitted in above formula, but it is potentially either one frequence of the photon, or one planck time.

In its own sistem, the photon feels only the events of absorbtion and emission; its own sistem consists of these two events, separated by one planck quantum or almost-zero. It depends now entirely on the sistem of the world of any observer, if this almost-zero is splitted into an appearent light-speedy motion (observed in a world whose two relevant coordinates have a quotient c in the metrics), or if it is considered in smaller scales where implicitely becomes relevant the dimension of the action, resulting then in quantum effects.

Thus, in the curvature formula above, on each passagem near an atom which in the world and dimension of us (observer) is an discrete 'interaction', that must be an event or action together with the production of a new fact (f.ex. the exact amount of the scattering or miss vector), which needs going together with a small delay of the coordinate time, so that their sum dS^2 - E dt^2 is zero, because as explained in the proper sistem of the photon the two effects together also results in zero or unperceived by the photon.

Thus, the relative delay, directly calculable from the diffraction index, means that in the average, in Glass, after all 2 or 3 waves way occurs one event of an interaction and a corresponding delay by 1 full wave.

At this opportunity, it should be noted, that in an absorbtion-reemission model, the photon would not be the same, but on any of this occurence change its identity, so that the 'light speed' in media would be the delay of the absorption and reemission. Obviously, such an explanation isnt possible because we would expect the speed depending on the intensity too - because as a stimulated, asynchron emission it would need a next photon, and on the other hand the reemission should occur faster before many next photons arrive.

This is a great post, but I think the most enlightening part was your comment #21. That answered the real question in my opinion. I may not be your average reader though, so maybe I'm wrong about what most people would need explained to them.

By the way, Hecht is great, but if you're talking specifically about Huygens principle, and the scalar diffraction theory which follows, the one true reference is Goodman.

In my post above, dS^2 - E dt^2 should be dSÂ² - E dtÂ² , that's zero in the photon's system, thus also for the observer (any Action or Event happening, produces a forward skip in the coordinate Time and thus also a contribution to the global time, new Facts produce time flow)

Feynmann treats the problem as an oscillator. What however resists against all theories, is, that the diffraction (and lower speed in matter) occurs also with single photons, which inclusive during all of this continue as a wave package - as f.ex. in astronomy we observe single photons with refractors.

Purity and clarity of concept is a reward for the initiated. First we understand in part, then we refine our understanding.

The arguments against analogy discount the importance of recruiting the uninitiated in producing future experts. Those who refuse to modify their language for their audience earn their reputation as a bad communicator, and teacher. They also set the standard by which certain fields are judged hopelessly rarefied. Criticizing others for lacking strict adherence to technical language also reveals academic vanity. Either you enjoy lording over those on the path, or you forget nobody can be an expert in everything.

I'm not trying to be aggressive, but consider the opportunity that is a person enthusiastic about your subject who may not share your expertise. Like students, friends, or taxpayers.

Purity and clarity of concept is a reward for the initiated. First we understand in part, then we refine our understanding.

The arguments against analogy discount the importance of recruiting the uninitiated in producing future experts. Those who refuse to modify their language for their audience earn their reputation as a bad communicator, and teacher. They also set the standard by which certain fields are judged hopelessly rarefied. Criticizing others for lacking strict adherence to technical language also reveals academic vanity. Either you enjoy lording over those on the path, or you forget nobody can be an expert in everything.

I'm not trying to be aggressive, but consider the opportunity that is a person enthusiastic about your subject who may not share your expertise. Like students, friends, or taxpayers.

For the purposes of explanation, I think it makes more sense to talk about the waves interacting with the atoms as oscillators. One would expect the resonance to preserve the wavelength, but there to be phase effects that could slow the transmission of the wave. If you use Huygen's principle, you have to assert that the mathematics works out, but there is no physical intuition. As a bonus, you can think of the light wave as having an electrical component (up and down) and a magnetic component (left and right) and having two sets of resonances with the atoms. When they reinforce, the material is transparent. When they interfere, the material is opaque. If the resonances are both 180 degrees out of phase, you get a negative refractive index. There is still plenty of handwaving, but you can explain more stuff.

It also makes it easier to move into the quantum explanation, because you can just change the "wave" to the "photon" which also has electrical and magnetic components when it interacts with the atoms. Here, the sum of all the possible interactions, weighted by their probabilities work out to give just about the same results as the classic case. Of course, in QM, the wavelength is preserved because the same energy is absorbed and emitted.

P.S. I'll apologize for my quantum approach to commenting. I'm probably about 70% correct here, but I've preserved the wavelength.

Hey everybody! I love you guys! all this stuff is way way over my head. I love it! but I have a couple questions for all you brainiacs (that's a compliment). 1) I heard or read somewhere that light travels in three diferent forms, wave, particle, & one other. is this true and what is it (obviously)? and a brief explanation of each would be nice. And 2) that there have been some experiments or studies that show the possibility that the speed of light is slowing down. albeit very very slowly, but still slowing. what has anybody heard about this?

and keep up all your freakin' studying! I wish I could understand half this stuff! oh, and please put yer anser en laymens turmz pleez. :0)

Maybe Iâm wrong; I think there may be a simpler view or hypothesis. Light or for that matter, any energy is in waves, correct? Like light, sound, heat, invisible light, inaudible sound, smell, etc. just like a human canât detect maybe what a dog or animal can. If we look at energy and really all matter, at the atomic level itâs all the same thing. Whether it atoms, electrons, neutrons, photons etc. It seems to me that light is just a massive string of phonons or energy traveling in a wave depending on its frequency it may or may not be visible depending on its medium and destination.