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In single slit experiments with sodium light whose wavelength is of order micrometer and slit width of order of hundreds of micron, we still observe the diffraction pattern. How do we explain this?

user102493
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  • I don't understand the problem...would you mind explaining? – auden Jul 28 '16 at 16:34
  • Homework: predict the angle between the central maximum and the first-order minimum. – rob Jul 28 '16 at 16:34
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    This is explained by the standard treatment of diffraction. You'll have to tell us what you don't understand about that. – garyp Jul 28 '16 at 16:39
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    Remember, you get diffraction from one edge - that is, no 'slit' required. All ok under normal diffraction theory. – Jon Custer Jul 28 '16 at 16:49
  • @JonCuster Sure, but there is also a standard claim that diffraction happens only when light interacts with objects of the order of the wavelength. Obviously that standard claim is ultimately not completely right, but the OP has a valid question in terms of why that is (or in which sense the standard claim is true). – Emilio Pisanty Jul 28 '16 at 17:13
  • @EmilioPisanty: The "standard claim" is completely nonsensical and whoever teaches that is guilty of a mind-crime... messing with the minds of young students. :-) I can make beautiful diffraction in sixty seconds at home with slits with 0.5mm feature size, hundred times the size of the wavelength. I think that's how we need to teach this, by hands on showing students that it's not just the ratio between wavelength and slit feature size that matters, the remainder of the geometry also plays a role. That's implicitly in the formula which calculates diffraction angles. – CuriousOne Jul 28 '16 at 18:10
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    @CuriousOne Sure. But railing against it won't make it go away, and it's definitely repeated pretty often. Instead, a clear explanation of when it holds and why it doesn't where it doesn't, like dmckee's, goes a much longer way. – Emilio Pisanty Jul 28 '16 at 18:15
  • @EmilioPisanty: I find that saying it loud when they teach nonsense goes a very long way. I also said that a hands on experiment goes a much longer way. We can explain it all day long here, but it won't necessarily enter the minds. If we do it with the kids practically even once, it will, and that's true for all kinds of things that can be demonstrated experimentally. – CuriousOne Jul 28 '16 at 18:18

2 Answers2

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The often heard claim that

"diffraction only happens when the slit size is comparable to the wavelength"

(or variations thereon) is mis-stated in a overly broad way for ease of rattling it off.

A more complete understanding comes from examining how the results of the diffraction experiments vary as a function of the feature size. The angles involved (angular location of the $n$th maxima or the $m$th minima) go by the ratio $$\frac{\text{wavelength}}{\text{linear feature scale}} \,,$$ for many diffractive experiments and demos. When this ratio gets small the fringes are very close together (unless you project over very long distances).

As a result, the visible fringes are easily washed out when the feature scale is too big. For instance, use a broad band source and too large a slit size or spacing and the overlapping of different order maxima of various wavelengths can end up looking like a slight ripple of color that is not easily pulled apart into distinct bits, unless you project them a long way, indeed. The effects are still there, but limitation of the human visual system are getting in the way of your seeing them.

If the angular scale of the features ever drops below the angular dispersion of the beam from your source the pattern will be washed out at all projection distances.

Then there is the matter of intensity. Projecting a long way to increase the linear size of the projected pattern means that you pay the usual cost in intensity. If you start with a relatively dim source, you won't be able to see the pattern with the naked eye.

But a carefully constructed experiment can still demonstrate diffractive physics with large features. See, for instance, my answer to a question about making diffraction grating with a laser printer. The scale of my slits is much larger than the wavelength, but by using a narrow-band source (a laser in this case, but the sodium D lines from your lamp are almost as good) and projecting over eight meters I get a distinguishable pattern. The pattern is quite lost if projected over less than one meter because the size of dots is larger than their spacing.

So, it might be a more accurate to say something like

"The results of diffraction are easily observed when the size of the slit is comparable to the wavelength."

But those words also carry the possibility of misinterpretation when given to a beginner.

SchrodingersCat
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dmckee --- ex-moderator kitten
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You always get a diffraction pattern, no matter the slit or object size. The issue becomes: "Is it focused well enough to be observable?"

You get a nicely viewable diffraction pattern under finely tuned circumstances where the slit is small with respect to the wavelength, but even a baseball creates a diffraction pattern interfering with itself, however at that scale any observable features are washed out and you would have to go to the math to do your "observing."

C. Kent
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