Double-Slit Questions

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I am trying to force myself in this direction. Thank you for the collaboration.
 
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ZapperZ said:
So I was curious as to how "branches of trees" is of the same "situation" as double slits.
They are the same in that narrow, elongated apertures are created through which light can shine. Obviously they are different in some important way, though, because you don't see interference patterns in shadows from tree branches or tall grass. This lead me to wonder about the minimum requirements for this effect to be seen.

Interference in water waves is visible with the crudest of set-ups: any old puddle, a breeze, a rock and a beer can will do. Or three rocks and two beer cans and a chunk of wood: you still can see the interference.

It struck me as funny that at least once in a while you don't run into naturally occuring interference lines with light. I decided that must be because the requirements for it to be visible must be more stringent than it sounds from the descriptions I read.
I was also curious to know if anyone knew details about this "pin tip" set up I read that G. I. Taylor
had used.
 

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zoobyshoe said:
They are the same in that narrow, elongated apertures are created through which light can shine. Obviously they are different in some important way, though, because you don't see interference patterns in shadows from tree branches or tall grass. This lead me to wonder about the minimum requirements for this effect to be seen.

Interference in water waves is visible with the crudest of set-ups: any old puddle, a breeze, a rock and a beer can will do. Or three rocks and two beer cans and a chunk of wood: you still can see the interference.

It struck me as funny that at least once in a while you don't run into naturally occuring interference lines with light. I decided that must be because the requirements for it to be visible must be more stringent than it sounds from the descriptions I read.
Ah, now I understand.

There are, however, two very important reasons why you don't see such things:

1. The "slit size" when compared to the wavelength of the waves involved. Visible light has wavelength of the order of hundreds of nanometers. I doubt that you could notice that kind of spacings in between branches leaves. I believe this point has been mentioned already in this thread.

2. You are also dealing with a whole spectrum of wavelenghts, not just a monochromatic source. So even if interference occurs, this will occur in a particular location for a particular wavelength, and most likely it will be wiped out by the non-interfering effects from other wavelengths within the visible spectrum.

Zz.
 

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Zapper, consider zooby's example of the oil film in the street, which I believe can be close to monomolecular, I think one could work up a simple demonstration in the spirit of QED (sum over paths) where the interference between the reflections from the top of the layer and that from its bottom produces the spectral colors we see.
 
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A couple of comments about terminology. All the above ideas are essentially
right.

Diffraction is not an interference penomenon. It is a consequence of wave
action interacting with a geometrical discontniuity. Only if you generalize
your thinking all the way back to Huygens would this interpretation be correct.
That is, if you treat the motion of a plane wave as Huygens did
by assuming that each point of the front is a spherical source for the next
infinitesimal front then yes, even the motion of a plane wave through space
is an interference pheomenon. But while this is mathematically true, it is
not helpful for understanding what diffraction is. It is certainly not what
an engineer today working on an electromagnetic propagation problem would
consider to be diffraction.

The term diffraction is most properly applied the case of describing
the propogation of waves around obstacles with features of the order of a
wavelength or less.

This description relies on interferece in the larger sense that a "diffracted
wave" is mathematically added to say the "incident wave" and the correct
results are obtained through interference.

Finally,

Oily films get their color from interference (of the reflected [not diffracted])
waves between the oil-water-air interfaces. Window panes refract and
reflect. They aren't considered to diffract except perhaps at the edges
or at blemishes which are on the order of a wavelength or less in size.

Feathers get their color by a grating effect which is diffraction because
the geomtrical features of interest are smaller than a wavelength. The
multiple diffracted wavefronts do interefere mathematically, but the term
interference when referring to large-scale wavefronts like plane or
spherical waves implies something different from diffraction.
 
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ZapperZ said:
Visible light has wavelength of the order of hundreds of nanometers.
This suggests another, probably equally naive, question: do photons have anything that corresponds to width? Are shorter wavelength photons narrower than those with longer wavelengths?
2. You are also dealing with a whole spectrum of wavelenghts, not just a monochromatic source. So even if interference occurs, this will occur in a particular location for a particular wavelength, and most likely it will be wiped out by the non-interfering effects from other wavelengths within the visible spectrum.
This makes perfect sense to me. Just to be certain, let me ask: a given photon can only be interfered with by another photon of the same frequency, and it has to be exactly 180º of of phase, correct?
 
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Antiphon said:
Oily films get their color from interference (of the reflected [not diffracted])
waves between the oil-water-air interfaces.
Does this mean that the colors which you don't see have been cancelled by interference?
 

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zoobyshoe said:
This suggests another, probably equally naive, question: do photons have anything that corresponds to width? Are shorter wavelength photons narrower than those with longer wavelengths?
I don't know. Photons are not defined by its physical size. The wavelength are typically used as a characteris length. However, it would be wrong of me to say that yes, that's the size of a photon.

This makes perfect sense to me. Just to be certain, let me ask: a given photon can only be interfered with by another photon of the same frequency, and it has to be exactly 180º of of phase, correct?
Since you have started to use the "photon language", here is something you have to make sure you understand.

The interference pattern that you are familar with is the result of the interference of SINGLE photons. In a 2-slit experiment, ONE photon has a superposition of 2 different paths. In classical language, it means that it "interferes" with itself! This is what will result in the beloved interference pattern. 2-photon interference almost never happen. It is a higher order effect, and it also produces a remarkably different type of interference pattern.[1,2]

Thus, you can understand why your question above would sound a bit "strange" within the QM/photon picture.

Zz.

[1] T.B. Pittman et al., PRL v.77, p.1917 (1996).
[2] L. Mandel, Rev. Mod. Phys. v.71, p.274 (1999).
 
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ZapperZ said:
The interference pattern that you are familar with is the result of the interference of SINGLE photons. In a 2-slit experiment, ONE photon has a superposition of 2 different paths. In classical language, it means that it "interferes" with itself! This is what will result in the beloved interference pattern. 2-photon interference almost never happen. It is a higher order effect, and it also produces a remarkably different type of interference pattern.[1,2]
I was going to ask how, with white light, all the different frequency photons would happen to end up with another of the same frequency to cancel out. Your explanation, however, neatly takes care of that problem.

However, your exlanation raises at least two more questions 1.) Do some of the photons somehow reinforce themselves by self interference? And, 2.) What happens to the the ones that cancel themselves out? Where does the energy end up?

Thus, you can understand why your question above would sound a bit "strange" within the QM/photon picture.
Same old problem: people who know enough to ask non-strange question usually don't need to ask at all.

[1] T.B. Pittman et al., PRL v.77, p.1917 (1996).
[2] L. Mandel, Rev. Mod. Phys. v.71, p.274 (1999).
If these are on line in a form I don't have to subscribe to something to read them, I'd be very interested to have a look at them.
 
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zoobyshoe said:
Does this mean that the colors which you don't see have been cancelled by interference?
No, it is likely that either the "color" (wavelength) is outside the range of
your vision or is a balence of red green and blue that appears as a shade
of grey.
 
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Antiphon said:
Feathers get their color by a grating effect which is diffraction because
the geomtrical features of interest are smaller than a wavelength.
Iridescence on Butterfly Wings
Address:http://newton.ex.ac.uk/research/emag/butterflies/iridesc-text.htm [Broken]
Yes?
 
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