This treatment is missing an important thing: Sunlight is not coherent over such long distances such as window pane thicknesses. Basically the two reflections cannot even interfere in the case of sunlight because they do not have a phase relationship.
You're right, but soap bubbles in the sun also appear colorful.
You only care about those that come at a specific angle and are reflected to an observer. For most angles it doesn't matter, remember that lakes polarize their reflection (as seen by an observer).
Soap bubbles appear colourful in the sun in spite of low coherence because the soap film is thin. Soap films can be as thin as tens of nanometers meaning that light has to be only coherent for a femtosecond for interference to happen -- and this is very comparable to the cycle time of the light itself so that coherence is practically assured. But the round trip time in a 5mm window pane is 50 picoseconds, which is thousands of times larger making coherence important.
Sunlight's coherence length is on the order of 5µm. If this weren't the case, reflection holograms wouldn't work in sunlight. 5 - 10 µm is the typical thickness of the holographic layer. If you want, a reflection hologram is a somewhat sophisticated soap bubble.
In what sense does sunlight have any coherence length at all? I was under the impression that coherence length was essentially a function of how tightly controlled the wavelength is of a monochromatic source like a laser. Sunlight is completely incoherent.
I mean, the spectrum still has a width, it's just a very large width -- which is why the coherence time is very low.
In a more abstract way, you're right that we are reaching for a metaphor here: if a frequency distribution is sharply peaked around one frequency then we can roughly say that the light "is that frequency" but then modify this by saying that the bits that are off-frequency, while they are "also that frequency," become "phase-incoherent" after a characteristic time or distance. That is not actually correct; they are simply different frequencies -- but it makes the interpretation easier. That metaphor begins to break down when you've got such a wide spread of frequencies: red light can only "pretend to be" blue light for a vanishing period of time.
To put it more plainly, the phase-coherence time is the inverse of the spectral width in frequency-space; multiply it by $c$ to get a phase-coherence length. If you applied it to a truly monochromatic ideal source, you would find that the time and length are infinite -- it only makes sense for real distributions with normal spread. But that's all distributions, including blackbody distributions like sunlight -- it's just that those distributions have very large spread and therefore very low coherence lengths: but it's the same definition either way.
Coherence is defined as a correlation of the light with itself. In simpler terms "how similar it is to itself after letting it evolve for a bit". Sunlight has a lot of different wavelengths evolving in many different ways, therefore it is not too coherent compared to an ideal single wavelength laser which will be identical even after "evolving" for a while.
However, if you look at sunlight at a certain time and then look at it one femtosecond later, the second look will still be similar to the first look to some extent, therefore you would have to say that the light is somewhat coherent.
This is why sunlight is definitely NOT "completely incoherent".
In fact any thermal radiator (e.g. black body) will be coherent over short distances proportional to the temperature of the body. Effectively the light's phase doesn't (on average) change faster than the quantum of energy (h-Plank's constant) divided by the thermal energy of the body (kT) so the power of a particular wavelength averaged in your eye can still have significant interference effects for a high temperature radiator. The distance of coherence is then related to that coherence time times the speed of light (so redder-longer wavelengths are coherent for fewer wavelenghths).
That leads to an equation of L= c*h / 4kT where the Sun can be treated roughly as 6000K. This gives a coherence length measured in microns, which is conveniently several times the half wave is necessary for interference for visible light (0.4-0.7um full wave). It's pretty cool, because I think it means that if you evolved eyes to see light near the peak of your black body radiator then you will be able to see Newton Rings for internally reflective thin membranes sized close to that peak due to the coherence length (due to Wien's law).
Coherence ultimately has to do with photons interfering with themselves. Films and beamsplitters can “cut” a photon in two pieces in the sense that the photon takes both paths. Separately, the photon has an uncertainty in its energy which corresponds to a bandwidth and hence a coherence time. If the system conspires to bring the photon paths back together again, meaningful interference effects occur when the photon is destroyed (measured) provided the path difference is within the coherence time. This is relatively easy to do in a bulk optical instrument like a Michelson or Mach-Zender interferometer: just carefully adjust the two optical paths to be equal. Remarkably, if you sweep one path back and forth with respect to the other, while passing through the zero optical path difference point, and take the Fourier transform of the detected signal, an accurate depiction of the light source spectrum is produced.
A fascinating read from 1890, "Soap Bubbles and the Forces Which Mould Them", C. V. Boys. Talks about colors in a film of soap (and a primer on scientific deduction and reasoning) :
Ah I see your point. I guess a similar thing happens when you look at plastic with polarized sunglasses, then you see different colors (though there's a chemical issue with plastic as well that affects the polarization of light)
You could do a 5mm(+/-10nm) glass pane for it to reflect/absorb a specific wavelength but it would be hard.
Most plastic sheets are birefringent due to the way they are produced. In the right circumstances, that can make a very colorful appearance when viewed in polarized light. As the difference in refraction index is normally rather small this works also for thicker sheets as no long coherence length is required for the effect to work. The effect should be strongest if you hold up the sheet to the clear sky with the sun behind you (the light coming from there is polarized horizontally). Sunglasses have the polarization vertically (to block exactly this light). As the birefringence turns the polarization the patch viewed through sheet becomes brighter. If you add in dispersion, you can get colored patches.
It's the same effect mineralogists use with polarizing microscopes.
I address that point in the notebook. Thanks to Fourier you could decompose any waveform, coherent or not, into a sum (integral really) of sine waves. So the lack of coherence should not make no difference to the argument.
I would strongly disagree with "coherence should not make no difference to the argument". This is exactly what we mean when we say "a coherence length of X um" - you take all the spectral components and correlate them with their future selves and then look at something akin to average correlation.
Therefore the "coherence answer" is exactly and precisely the correct one. What you are doing is simply explaining it with different words. "The lack of coherence" of the wave as a whole is THE argument.
What your explanation is doing is applying a narrow wavelength filter and evaluating the conditions for each \Delta\lambda, which is absolutely a valid approach, but it is the same thing. Overall I like your explanation very much, but please be careful about statements like "not really the answer, at least not directly" as they only point at a misunderstanding of the coherence explanation.
> Therefore the "coherence answer" is exactly and precisely the correct one.
The correct answer to what question?
If the question is why we don't see iridiscence when "white" light (wavelength 380-740nm) is reflected on a "wide" film (several orders of magnitude larger than the wavelength), do you really need to talk about lack of coherence? The fact that for a particular width the film will supress/enhance thousands or millions of colors across the visible spectrum should be enough to make the resulting light white as far as human perception is concerned, I think.
I know this is a techy sort of place, but this article isn’t about the code. I think the original link should be replaced with this one since it is useful without additional steps.
Well, because the thickness on the soap bubble is on the order of the wavelength of visible light, which causes interference that we can see. Windowpanes are far too thick for this to occur.
OP here. Why thickness should matter is precisely the question.
If you look at the treatment of this on Wikipedia or a physics text it is the phase difference beteween the front and back reflections which matter and not the total path length.
Even for a windowpane there will be some wavelengths where the two waves are in phase and others where they are out of phase. The true explanation is that for a windowpane these two kinds of wavelenghts are clustered densely together and therefore even for tiny wavelength ranges the interference effect averages out.
For the effect the phase difference is the thing which matters. However, the wave reflected from the back and the wave reflected from the front run through different path length (twice the thickness). For the effect to work the waves need to be in phase along that distance which is a few µm for sunlight (look up coherence length).
The different wavalengths make only up for color. Some wavelength will have destructive interference and go missing. As the eye is quite sensitive to that you will see a colored surface, whichs color changes with view angle (as different wavelengths will cancel for different angles).
Actually the authors point would stand even for a perfectly smooth window pane. The point is that as the thickness increases the length scale over which light goes from constructive to destructive interference reduces, and as this happens you end up sampling more and more uniformly colours from a uniform spectrum. At some point our eye can no longer tell that we are only seeing n monochromatic wavelengths of light.
Okay not monochromatic, but very narrow bandwidth peaks
If d (width of the window) is large. Small changes in the wavelength create large differences in phase.
So if you have say light in the range 400 to 401nm coming through the window. There are peaks and troughs in that range, but overall there is no effect.
Light sources are like that in general, they’re not 450.00001nm but some Gaussian distribution around a point. And within that Gaussian there are peaks and troughs but they cancel out.
Actually as the article explains it's a little more interesting. Naively even in a thick window pane we would expect interference patterns from light reflected from the front and the back of the window pane. The article explains why we don't.
Having read QED early on, my understanding is that while treating a windowpane or mirror as a front and back surface is a useful simplification in most cases, it is not for interference.
The "sum of the histories" explanation is that light interacts with all of the molecules at every depth, and once the depth becomes larger than the "wavelength," the interactions statistically can el each other out, and the probability of an interference pattern appearing beco,es infinitesimal.
I have also heard that while "sum of the histories" was useful for explaining QED to undergrads, it wasn't an effective way to calculate results and didn't yield any predictions that more math-heavy approaches coukdn't produce, so it was discarded.
For all I know it has been shown to be wrong for some observed phenomena.
Anyhow... Is that explanation the correct "sum of the histories" explanation? And if so, is ot considered useful to think of it in these terms for laypersons who don't want to dive into the math?
It sounds like you're thinking of Feynman's popular book QED (which I'd agree ought to be great for people who want an actual idea of what's going on without taking a college course) -- but in chapter 3 he shows how "we can get the correct answer for the probability of partial reflection by imagining (falsely) that all reflection comes from only the front and back surfaces... what is really going on: partial reflection is the scattering of light by electrons inside the glass." This comes from adding up the coherent effects of that scattering -- he wasn't saying the interference goes away (becomes incoherent).
It's not my field, but my impression was that path integrals (sum over histories) did initially figure mainly in discovering the Feynman rules for QED, without getting used much directly by others, but later did find more applications.
You can still get interference if the medium is thicker than a wavelength, but it needs to be close. This effect is quite often seen in CCD detectors used in infrared spectroscopy, as well as certain detectors used for visible spectroscopy. It's called etaloning. But as you suggest, in thicker media there's much less chance of it happening.
It’s great to read an explanation for this. Glassblowers can see iridescence when we blow ‘bubble trash’, which happens when you blow glass so thin it can float away in the air. If one could get it on thicker bubbles without using chemicals such as tetraisopropyl titanite, that would be fantastic.
IIRC, this is also exactly the reason that anodized metals create a rainbow effect. In that case, the thin oxide layer creates the necessary interference.
I think there are some big misunderstandings here unfortunately, and it's likely because coherence is rarely defined well.
yomritoyj claims that the lack of coherence shouldn't impact whether or not destructive or constructive interference occurs. That is, if a monochromatic light source is impinging on a layer of material, one will ultimately still get that the returning electromagnetic wave is the sum of the wave that hit the front surface and reflected, and the wave that hit the back surface and reflected some time earlier. For white light, one could simply say that you could decompose it into many separate wavelengths that behave this way (a continuum of wavelengths).
The missing point here is the following: imagine the above is true, and you can absolutely draw plots as is given by the notebook above. Now, let's make the analysis a little more general: assume that in the time that the light hit the back surface of the layer of material, something happened to the incoming light and it shifted in phase. That is, your final sum-of-two-fields (as described above)
where phi is some extra nasty angle. It should be clear this happens, for example, from this first result for "incoherent light" on google [1].
Now, we haven't proven yomritoyj's conclusions to be wrong --- there is still interference. Now, however, let's add two details:
1) phi depends on wavelength. if phi depends on the wavelength, then the plots he drew could have a random extra phase added at each wavelength. This would destroy any interesting features in the plots, and you'd get some basically random reflection from each wavelength.
2) phi changes over time. if phi changed in time, you now not only get a random reflection, but the amount of light reflected at a certain wavelength will change to something else sometime later. This time is usually very quick for incoherent light like the sun, and your eye is constantly averaging over many different intensity reflections over time for each wavelength.
Lastly, given the above, why the hell does this work at all for soap bubbles then? Well, for soap bubbles, the light is not so terrible (so incoherent) that it gets a chance to have that extra "phi" phase to include in the interference --- that's because the wave reflecting from the back surface comes back so quickly! (soap bubbles are so thin!)
I encourage people to plug in the speed of light to get a feel for these timescales --- this is the sort of thing physics phd's get used to =).
Thanks, great. Slight addition: visible light spectra is between 400-700nm; sure you can still see 390nm and 730nm, but the sensitivity is rapidly decreased there.
