In the winter-spring of 1999 I was one of the fortunate few attending the Ontario Science Center Science School; a semester long program for senior high school students who really dig science. Participants take on a normal-ish course load of science and math classes that cover all core curriculum, with added awesomeness like access to high end laboratory resources and a lot of flexibility/support when designing independent research projects. Did I mention this was all taking place inside the Ontario Science Center? Super cool.
While the freedom and toys were all very nice, the greatest value was in the incredible people. Maybe your experience was different from mine but I’ll estimate that only 15-20% of my home-school (not to be confused with home-schooled) classmates actually cared much about the learning aspect of high school. This was fine, because whatever, but then I found myself in this magical wonderland where everyone cared. And I’m not talking about marks driven, stressed out, helicopter parent pressure, ‘I’m 18 and don’t know what I’m doing with my life’, type caring; I’m talking about the-world-is-marvelous-and-holy-shit-I-get-to-live-in-it, type of caring. I really, really, liked these people.
Over 15 years have passed since my convocation from science school, yet the friendships from those formative months have persisted and grown. All of us have more letters behind our names now and we’re scattered geographically, yet we’ve always found time and opportunities to reconnect. We’ve attended one another’s weddings, held each other’s babies, and we’ve had some incredible email conversations; which finally brings me to the topic of this post, Waves and Transparency. About a month ago I visited one of these friends, Vinai, at his home in Hamilton, and our conversation meandered into electromagnetic wave theory (you know, as it does from time-to-time). Unfortunately, neither of us have any real understanding of electromagnetic waves, so we tossed around a few speculations, joked about how we could probably just ask Google on our wireless devices (wink), and then moved onto something else. Well, Vinai did actually ask Google a few days after my visit, and sent me an email to report what he’d found. He also CC’d a few of the other Science Center guys to get their feedback, some of whom have significant formal training in physics. As the email thread expanded, the communal knowledge and research potential was thus pooled, and I became sad that so few humans would have access to this really interesting information. Unless…
I like the idea of using a blog as a place for discussions; open email, for content that may have some broader interest. An experiment in public discourse by some old friends from Science School.
On Waves and Transparency
Just following up on a question that came up when you were visiting. If I remember correctly, something like, “Why can radio waves penetrate solid objects?” I thought it was something about diffracting through tiny gaps in doors, etc. That was close, but wrong.
15 minutes of Internet surfing has led me to the following explanation, which is probably somewhere close to being consistent with reality.
Why is matter sometimes transparent to waves? Essentially, matter is transparent to waves under two conditions: 1) when it does not interact with the wave; 2) when it does, but it interacts in such a way that the direction of the wave’s propagation is not changed (i.e. there is little “scatter”).
1) Electromagnetic waves can interact with electrons in matter. I don’t know all the determinants of the likelihood that a wave will interact with an electron (one will be density of the matter), but if the energy of the wave is similar to an amount of energy that can be absorbed by the electron, say to jump a shell, then there can be an interaction. If you have very high energy waves, like gamma waves, then they can pass through matter, only occasionally ionizing an electron, since it’s too high energy for a common shell-jump. (This is kind of unsatisfying: why is a shell-jump more likely than an ionization? Because high-frequency waves are “small”? Maybe this is leading down the quantum mechanics rabbit hole…) If you have a low energy wave (radio wave) then it’s less likely to be the “right” energy for an electron. The electrons of conducting materials are particularly susceptible to interaction with electromagnetism (what does that even mean, “particularly susceptible”?), which is why many conductors such as metals are opaque to a wide range of frequencies. I think that elements with large nuclei are more opaque to electromagnetism because there is more likelihood that the wave will interact with the nucleus. I think if you have a very non-dense gas, then the wave is unlikely to interact with it because there is little to interact with. But there is another way in which materials are transparent (see below) and I’m not sure which predominates in gases. But this section (1) gives a rough idea of why a wooden wall is transparent to gamma waves, but not visible light or infrared, and gives one of the reasons why wood is transparent to radio waves.
2) Apparently, if you put a stick in water which has waves passing through it, the wave will diffract around the stick and you will scatter the direction of the wave. I guess this happens with molecules and electromagnetic waves, too, since X-ray crystallography is a real thing. If you place many sticks at a recurring distance that is close to or smaller than the wavelength in the water, the diffracting waves will tend to destructively interfere, whereas this doesn’t happen in the “forward/backward” dimension, so the wave propagates through. Since molecules of fluids tend to be jostled tightly together, the size of the waves that are transmitted in this way includes visible light. Which is why lead glass is a real thing that is opaque to gamma rays (phenomenon 1) but transparent to visible light (phenomenon 2). If the material has electrons which can jump levels at energies that are in the visible spectrum, then it will appear to have a colour, although the rest of the light will pass through without scattering. This would be the case for Kool-Aid, or urine.
Since radio waves are very large, phenomenon 2) occurs with solids and they propagate through without scattering. Since they are low-energy, phenomenon 1) also occurs, I think. But, materials whose electrons can interact with low-energy waves, like conductors whose electrons are very promiscuous, will be opaque to radio waves. So you will not be able to listen to the radio in a room whose walls are made of gold (or iron, or tin, or silver). But you can listen to the radio in a room whose walls are made of solid brick or wood. Apparently, small changes in the conductivity of the walls, such as when they are wet, can make a big difference in opacity to radio waves, which may be part of the reason reception is poorer when it’s raining.
Also, phenomenon 2) causes a brick to be opaque, and phenomenon 1) causes it to be red. And mirrors work by phenomenon 2) except that the wave is propagated backwards instead of forwards. I think that is why water and glass are mirrors.
As usual, it’s all a matter of putting it in metaphors to help us remember what actually happens. The more I read what I’ve written, the less satisfying it is. Would appreciate a physicist’s input on the following:
- how does lead glass work (absorbs gamma, but transmits visible)? This may be another way of asking why are gamma waves more susceptible to interaction with nuclei than visible light waves?
- why does the sky appear blue? (and please explain what you mean by “scatter” when answering this question, and how “scatter” results in a blue appearance.)
OK. Figured out why the sky is blue. Essentially, because our brains rely on rectilinear propagation of light. Since the wavelength of blue light is shorter than that of red light, the spaces between molecules of air are more likely to be farther apart than the wavelength of blue light. Since the canceling out thing happens best when the spaces are smaller than the wavelength, there is less canceling and more scattering of blue light. Light from the sun is going in all directions, including off to the right and left of our eyes. If this blue light is scattered to our eye, our brain assumes it originated from some point in the sky to the right or left of the sun. This is true for all the points around the sun, so we see the sky as blue.
I’d be more happy if I could be shown that the distance between air molecules is right for this to work. Could probably do a napkin calculation… AND, I’m going to try the sticks in water thing. Which would be better with people in a wave pool…
For the sky being blue: it is due to Rayleigh scattering, or scattering of light off particles significantly smaller than the wavelength. This obtains in our atmosphere: visible light has a wavelength of ~500 nm and a nitrogen molecule is ~50 pm. The probability that a photon will Rayleigh scatter is proportional to the “cross-section” of the molecule, but cross-section is just a synonym for this same probability, and it is wavelength dependent—in fact, strongly wavelength dependent:
σ ∝ l / λ4
where `l` is the size of the particle and `λ` is the wavelength. So shorter wavelength scatters much more efficiently than longer wavelengths—hence, more blue light is scattered by molecules in the sky towards you. This is also why the sun is yellow-red in colour: the blue has been scattered away; and at sunset, the amount of atmosphere is great enough that the blue gets scattered away from the surrounding atmosphere making it red or orange.
So at the end of the day, it doesn’t have anything to do with the spacing of the molecules in the sky, but only with the fact that they are small compared to a wavelength of light. The rest of the effect is driven by the various wavelengths of visible light.
As for the question of how transparent stuff is to various types of waves, I think some of the basics are correct. For electromagnetic interaction, though, I believe it doesn’t have much to do with exciting transitions between atomic energy levels. It has more to do with interaction with free electrons or electrons in the outer shell that aren’t strongly localised to a particular atom. In a solid, it isn’t as though every electron belongs to a specific nucleus. And it’s the wave interacting with these free or semi-free electrons that makes the difference. Peter can probably speak to this a lot better than I can. Astrophysics is mainly about gases and plasmas and solid state physics is more subtle!
For a mirror, though, I think it’s pretty easy to get a mental cartoon of what’s going on. The light excites free electrons at the surface of the conductor and they begin oscillating at the same frequency as the light. But because accelerating charges radiate light, the oscillating electrons re-radiate the same wavelength that they absorb.
Well, I’ve been thinking and reading about this for the past few days (and asking my dad) because I don’t feel very satisfied with the answers that I have. This being said, I think that there are some problems with the metaphors you put forward, Vinai. (This is always the case – to paraphrase, all metaphors are wrong, some are useful.)
One shift in perspective for me over the past days that I think is important is that the question is the wrong way around: we shouldn’t ask why solid (or indeed any) matter is transparent, but rather why any matter is opaque. We see EM waves, which are produced by accelerations of charged particles. ‘Solid’ objects aren’t opaque by default – they are opaque because some process absorbs or scatters incident EM waves.
The second thing to say is that both the EM waves and the atoms they interact with are quantum phenomena, but their quantum nature becomes more obvious in certain limits. For some processes classical metaphors work well for the radiation, for others you need quantum ideas, and a similar divide exists for the electrons/atoms, though there are some fundamental quantum things you can’t really get away from in the latter case. So rather different metaphors are useful for Rayleigh scattering than for compton scattering of gamma rays.
The most useful classical rule of thumb is that waves interact with structures that have length scales similar to their wavelength. This is true of all waves, not just EM radiation; for instance, to think about the water waves Vinai appealed to, if the stick is much smaller than the wave, it’s not much different from just raising and lowering the level of the water around the stick. If the stick is much bigger than the wave, the wave will reflect off of it geometrically in much the same way light bounces off a mirror, or sound off of a wall. If the length scales are comparable, you get complicated patterns of constructive and destructive interference that depend a lot on the scattering direction
Ok, so if we’re talking about visible light (wavelength say about 500 nm), atoms and small molecules are way smaller, so they don’t interact very strongly. Rayleigh scattering happens because the electric field associated with the wave will tend to push electrons and protons in opposite directions, though it’s like pulling against a stiff spring. Nonetheless, you are accelerating charged particles, and you get weak emission of photons at the same frequency as the incident light, and the directional dependence of the scattering is pretty simple. It gets much stronger (as Adam says) for shorter wavelengths because the difference in length scales is getting smaller, but it also depends on the ‘stiffness’ of the spring attaching the electrons to the nucleus — this is called the index of refraction, and it depends on the details of the atoms and molecules doing the scattering.
This doesn’t really change for solids. The atoms are still way smaller; all that is different is that they’re packed closer. They’ll have a very different index of refraction because the ways electrons are bound to the nuclei are quite different, but visible light is still basically a featureless electric field on these scales. If we think about transparent materials like diamond (crystalline = ordered) or glass (amorphous, disordered), or indeed liquid water, their index of refraction is very different than air (so you get partial reflections at the surface and changes in direction etc), but once the light is in the material it doesn’t scatter much. So the idea of disorder at these scales (Vinai’s (2)) doesn’t really matter. More important is the fact that these materials are uniform at scales of a half a micron or so. This is not the case for most solids – crystal domains, defects, polymerization patterns, biological features, large suspended particles (like in milk, paint, or clouds), thin films etc. all have structure on these length scales, and so scatter visible light strongly. Indeed even in a pure diatomic gas, when you get thermal fluctuations at the same scale as the light you get strong refraction – this happens in a rather dramatic way (look up critical opalescence) close to the critical point where there are fluctuations at a huge range of length scales.
Since X-rays have wavelengths of the order of the spacing of atoms in molecules and crystals, they scatter in complicated ways off the atomic-scale structures and you can back out information about, e.g. crystal and protein structure.
All of this has been more or less classical in terms of understanding the interactions between photons and electrons, and the accelerating charges are slight shifts in the electrons and nuclei of the atoms. But of course you can do more dramatic things to atoms for which quantum mechanics really matters. For instance, if you think about light with somewhat longer wave lengths, say about 15 microns, the absorption by carbon dioxide is so strong that the atmosphere is completely opaque. This is because the frequency of the light is just right for vibrating the co2 molecules, so the photons are much more likely to be absorbed.
I don’t think there is a truly satisfying way of answering why this is much more likely than Rayleigh scattering (to address Vinai’s rabbit hole) without appealing to the full theory of quantum electrodynamics, but there is *some* relevance to the idea of a resonance – i.e. if you push a swing at the right frequency you can get it to go way higher than if you push it at the wrong frequency. In both cases you do work on the swing, but in the first case it absorbs way more energy.
In a gas molecule, there are a relatively small number of ways to push charges around (vibrations, rotations, electron shell jumps; these latter are more likely to be present in the visible part of the spectrum, the former in infrared). These give rise to isolated spectral features where light is selectively absorbed or emitted. Not many of these happen to be in the visible spectrum for the gases which make up our atmosphere (which may be why eyes evolved to be sensitive to this part of the EM spectrum).
So what’s different about solids? In this case the nuclei of atoms tend to be within a nanometer (or less really) of each other, which means the valence shell electrons don’t just ‘orbit’ one atom, but instead are distributed across the material. The quantum states for electrons are no longer isolated, but are dense across ranges of energies called ‘bands’. In insulators like glass and diamond, these bands are either completely occupied by electrons, or completely empty, and they are separated by a large gap on the energy scale of visible photons — which makes it hard to move charge around (and therefore also to scatter visible light). In a conductor, the full bands and empty bands overlap, so it’s very easy to move charges around. If the surface is well polished over many wavelengths, you get the reflection Adam described. But there are also lots of other ways that electronic transitions are modified around defects and dopants so that you can still get rather localized spectral features that are one way to give you pigment in crystals or in coloured glass. So being uniform on scales of half a micron is necessary for transparency (to visible light), but not sufficient.
What about gamma rays and leaded glass? Well, doping glass with lead doesn’t change the uniformity on the scale of visible light, and lead doesn’t have spectral features in the visible range, so as long as there’s not enough lead to turn the glass into a conductor, it’s still transparent. Gamma rays are more energetic than x-rays which means their wavelength (10-3 nm) is much smaller than the spacing between atoms. So classically you don’t get much scattering. But because the photons have so much energy, you really can’t ignore the fact that the waves themselves are strongly quantized – and in many ways they look like particles. The main processes by which they interact with matter is through a) the photoelectric effect (at lower energies) b) compton scattering (moderate) and c) pair production (higher). All of these are very quantum.
- All of the energy of a gamma ray is absorbed by an electron, which is plenty to kick it right out of the atom. Visible light can’t do this except for relatively weakly bound electrons. It’s most probable when there’s just enough energy to free the electron and rapidly becomes less likely – again why this is less likely boils down to QED (and I can’t help you here but I can imagine that the different length scales of the photons are relevant here).
- In this case the gamma ray ‘ricochets’ off of an electron, sending it off at relativistic speeds and yielding another (albeit lower energy) gamma ray.
- Here the gamma ray basically turns into an electron and a positron – so it needs to be energetic enough to produce the mass of the latter.
You’ll note that none of these directly involve the nucleus (though the latter apparently needs to happen in the large fields close to the nucleus) – you need yet more energy to interact directly with the nucleus. However, if you want to absorb gamma rays, in general you win by putting more electrons in their way. Lead has lots of electrons (and it’s probably cheaper and plays nicer with glass than other heavier atoms, not to mention less radioactive), hence leaded glass.
Radio waves are even bigger (mm to km), so atomic structure is pretty irrelevant classically, but if you have a conductor that’s big enough, that absorbs them strongly (e.g. antennae). They are also low energy photons so classical ideas work pretty well.
Ok, that was ridiculously longwinded. Have a cool gif
This is great! And thanks for the pictures! Once in a while I go on a physics binge on wikipedia to try to figure out the universe. Now it’s coming to me!
I did deal with EM waves when I was doing event-related potential (ERP) experiments. Basically, you put an EEG cap on someone’s scalp and detect tiny fluctuations in the electrical field caused by groups of firing neurons as their brains process them. EEG has very good temporal resolution for us but not much spatial resolution because the waves are scattered (field is distorted? Help?) by the brain and the skull and the scalp. So, if I present you with a word or a picture, I can see something interesting happen within about 50 milliseconds, but I can’t tell you where in the brain it’s happening with any confidence. fMRIs have the opposite properties – great (mm) spatial resolution but poor temporal resolution. In MRI, a giant magnet generates and then releases a strong magnetic field in the brain and waiting for the atoms to emit radio waves. You can tell what’s where because different types of atoms emit radio waves at different rates once the field is released. Why is this the case? I, like the Insane Clown Posse, do not know. But, thanks to this thread, I understand why the radio waves are emitted without as much scattering, making it easier to tell where they’re coming from.
Functional magnetic resonance imaging works by focusing on the iron in blood. More active parts of the brain need more oxygenated (and thus iron-rich) blood, so you can see what parts of the brain are working harder by where there’s more iron. It’s hard to tell to within more than about 1-2s of precision when the brain activity changes, though, because of how long it takes to generate the field and wait for the… electrons to go back to ground state? At any rate, you get one picture for each loud knock of the MRI machine.
This was a problem for us. Like a lot of psychological experiments where you’re looking for unconscious reactions, we were looking for a physiological response that correlates to surprise. If you’re surprised by a word for some reason, at around 400msec after it hits your retina you’ll have a slightly more negative electric field somewhere in your brain. (You can even detect different levels of surprise – if I show you “the person ate the pizza”, “the person ate the beer”, and “the person ate the rock”, “pizza”, “beer” and “rock” should generate increasing strengths of negative potential.) At any rate, an fMRI that generates a picture every two seconds would obviously have no chance of detecting this difference.
I’ve been reading and thinking about this some more, and it’s led me to question, “What do I mean when I ask, ‘Why does a phenomenon occur’?” This came up because I found that all of the “explanations” end up being “descriptions” of what is observed. This, of course, makes perfect sense, because that is what science does. I think what I mean when I ask “Why?” is: “What are the minimum requirements for this phenomenon to take place?” Or (which I think is equivalent): “What is the most general way of describing the circumstances under which this phenomenon takes place (that remains consistent with observation)?”
So, “Why is matter opaque sometimes to some electromagnetism?” is really asking “What are the bare circumstances required for matter to be opaque to electromagnetism?” This is perhaps an obvious point for some of you, but worth dwelling on. The way to get to it is to observe interactions between the individual components of matter and electromagnetism, and start putting them together in different ways, and I am sure that this is what physicists have done. I suppose it is called science.
Peter says re: Rayleigh scattering, “the directional dependence of the scattering is pretty simple.” Not simple enough for at least one of us! Can someone confirm that I’ve got this right: in glass or water, the summation of the wave goes in the same direction as the incident wave. Why doesn’t this happen in Rayleigh scattering? What is different about the interaction between the matter in Rayleigh scattering and the matter in glass? I think it is because in Rayleigh scattering the particles are not uniformly distributed on the scale of the wavelength of the light. So, you don’t have this effect of the induced lateral waves canceling out and the “forward” waves not canceling out. (From a classical perspective) Is this true? I imagine taking a transparent glass block, shattering it into uniform small glass spheres, and suspending those uniformly in space. If the suspension is perfectly uniform, would it still be transparent? Water and oil in a vinaigrette is a good example of a suspension that is not perfectly uniform. From a quantum perspective, I guess you work out the probabilities of all the possible interactions, superpose them, and find the probability of the result. How might one think of Rayleigh scattering from a quantum perspective (if possible to explain without totally leaving behind all analogy and resorting to pure descriptive maths)?
P.S. Someone ask me something about human physiology, and I will feel better about myself 🙂
When Peter said that the directional dependence of Rayleigh scattering is “simple”, I suspect he meant that its functional form is simple. The derivation is at a second- or third-year undergraduate level, so in that sense, it is simple only relatively.
The radiation pattern of a dipole goes as sin^2(\theta) (the aforesaid simple function) where \theta is the angle away from the axis of the dipole. Thus, a dipole radiates most efficiently in directions perpendicular to the axis, and not at all along the axis. However, the dipoles in the molecules in the atmosphere are randomly aligned (if I am not mistaken), so the net effect is that the scattering is isotropic.
Now, there are two ways of thinking of Rayleigh scattering that I think make sense. First, you can think of the incoming light from the sun as a plane wave. In the classical analogy used earlier, the molecules are like very slender pencils interrupting a much larger wave. So the wave will largely remain a plane wave, but there will be a weak component that is scattered in different directions. Now, the pencils are not circular, but have a shape such that the wave each one produces when the water wave hits goes as sin^2(\theta). But each is oriented differently, so the individual shapes of the scattered waves get lost and the net result is that a small component of the total wave goes off in all directions as it moves through the field of little, oddly shaped pencils.
You can also think of the incoming light as a stream of photons. Each photon has a probability of exciting the molecular dipole and being re-radiated in a different direction. The probability of that direction goes, again, as \sin^2(\theta), where \theta is the (random) alignment of the dipole in the molecule. The probability that this excitation will occur, as discussed earlier, is wavelength dependent. At all wavelengths, most of photons pass through the atmosphere without scattering. (Otherwise, you wouldn’t be able to see the sun: you’d just see an atmosphere that glowed smoothly everywhere.) But blue photons scatter far more often that red photons, and hence the colour of the sky.
I’m not sure if this answers your question or not. In solids, as Peter pointed out, the electrons are generally not localised, so a lot of the time the transparency or opacity doesn’t depend on structure of the lattice of the solid but rather on what bands of energies the electrons are able to interact with, except in cases where quantum effects are important, as in the cases he gave above.
When I first read your post, I mistakenly thought (for some reason) that you were asking about why light bends when it enters glass or water, and wrote the paragraphs below. Even though they don’t answer any of your questions, they may shed some light (pun intended) on the discussion.
<Start of paragraphs on light bending.>
Now, as for water bending in light, it’s probably best not to think of this as scattering at all. The electrical properties of water are different than that of air and so there is a different index of refraction: i.e., the speed of light is different (by about 30%, which is why the bend is so easy to see). True, the photons are interacting electromagnetically with the charged particles in the water (as they were in the air, for that matter), but it’s not helpful to think of photons scattering off of individual particles.
As for why the speed of light causes it to bend, there are a few ways of looking at it that are formally equivalent. I find an appeal to conservation of momentum most intuitive. (This might also be the most naturally “quantum” explanation Vinai was looking for because you can think of each photon as having a momentum.) I was about to write an explanation here, but I found that Wikipedia explained it pretty well, so I’ll refer you there! (Perhaps you will remember Snell’s equation from our classes together at the OSCSS. I think that was covered in class!)
By the way, both of these phenomena (Rayleigh scattering and changing index of refraction) are classical, in the sense that you don’t need quantum mechanics to derive them or to understand them.