
Why soap bubbles are colourful and windowpanes are not - yomritoyj
https://gist.github.com/jmoy/4dda9b8b8e2b3eb27666bd6ebe208ea3
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razimantv
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.

~~~
raverbashing
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).

~~~
razimantv
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.

~~~
raverbashing
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.

~~~
chopin
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.

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osrec
Not sure why, but I see the raw markup rather than a formatted article.
Interesting content nonetheless, but difficult to read on mobile.

~~~
uranusjr
Formatted from the gist, served on nbviewer.jupyter.org:

[https://nbviewer.jupyter.org/gist/jmoy/4dda9b8b8e2b3eb27666b...](https://nbviewer.jupyter.org/gist/jmoy/4dda9b8b8e2b3eb27666bd6ebe208ea3)

~~~
jtbayly
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.

~~~
ehsankia
It seems like an issue with Gist on mobile. On desktop, Gist properly renders
the notebook exactly as that other link.

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kgwgk
Feynman's explanation for iridiscence:
[https://books.google.ch/books?id=2o2JfTDiA40C&pg=PA33](https://books.google.ch/books?id=2o2JfTDiA40C&pg=PA33)

See also: [https://en.wikipedia.org/wiki/Thin-
film_interference](https://en.wikipedia.org/wiki/Thin-film_interference)

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knolan
The colours of a soap bubble can be understood with a Michel-Levy chart and
thin film interference of a birefringent medium.

[https://www.itp.uni-
hannover.de/fileadmin/arbeitsgruppen/zaw...](https://www.itp.uni-
hannover.de/fileadmin/arbeitsgruppen/zawischa/static_html/twobeams.html)

You can observe the same colours in thick plastics under crossed polarisers.

~~~
greeneggs
Yes, there is also a simple derivation in Boys's classic book, "Soap Bubbles:
Their Colors and Forces Which Mold Them", p. 136. [1, 2]

[1] pdf link (it is out of copyright):
[http://www.arvindguptatoys.com/arvindgupta/soap-bubbles-
boys...](http://www.arvindguptatoys.com/arvindgupta/soap-bubbles-boys.pdf)

[2] google books link (free preview), go to the very last page for the color
plate

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saagarjha
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.

~~~
y04nn
I would have explained it by the irregularities at the surface of windowpanes.
Huh, is it what is said in a more mathematical way in the link?

~~~
moopling
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

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braythwayt
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?

~~~
abecedarius
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.

~~~
braythwayt
I am most definately speaking of the book.

~~~
abecedarius
Sorry that wasn't friendlier -- I was writing on too little sleep.

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code_duck
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.

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mistercow
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.

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asafira
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)

E_returning = E_incoming (2 * thickness/lambda) + E_incoming(0)

is NOT that simple, but instead written as

E_returning = E_incoming (2 * thickness/n) + E_incoming(phi)

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 =).

[1]
[http://www.schoolphysics.co.uk/age16-19/Wave%20properties/Wa...](http://www.schoolphysics.co.uk/age16-19/Wave%20properties/Wave%20properties/text/Coherent%20and%20incoherent/index.html)

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zsellera
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.

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olliej
Um, thin film interference. It even has a nice succinct name.

It’s a simple byproduct of basic optics :-/

