Relation between diffraction and wavelength

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Discussion Overview

The discussion revolves around the relationship between diffraction and wavelength, exploring both classical and quantum mechanical perspectives. Participants examine the conditions under which diffraction occurs, the role of apertures, and the implications for various types of waves, including electromagnetic, water, and sound waves.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants suggest that diffraction occurs when the slit width is comparable to the wavelength, while others argue that diffraction can happen regardless of this condition.
  • One participant mentions that the extent of diffraction depends on the ratio of wavelength to aperture width, particularly in the case of an infinite plane wave.
  • There is a discussion about whether a laser beam will diffract when passing through a doorway, with some asserting that diffraction occurs only if the beam is wider than the aperture.
  • Participants explore the concept of truncation of wavefronts and how it relates to diffraction, noting that a laser beam may diffract even without an aperture due to its inherent properties.
  • Some participants draw parallels between classical wave diffraction and quantum mechanical effects, suggesting that the uncertainty principle plays a role in the behavior of particles like electrons when passing through slits.
  • Concerns are raised about the adequacy of explanations found in elementary physics texts, with some participants finding them overly simplistic or lacking rigorous derivation.

Areas of Agreement / Disagreement

Participants express differing views on the conditions necessary for diffraction to occur, the role of wavelength, and the adequacy of existing explanations in educational materials. The discussion remains unresolved regarding the best way to conceptualize these phenomena across different contexts.

Contextual Notes

Some claims rely on specific assumptions about wave behavior and the definitions of terms like "truncation." The discussion also highlights the complexity of relating classical and quantum perspectives without reaching a consensus on the interpretations.

eep
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In order for diffraction to occur, the slit width must be on the order of the wavelength, correct? I'm puzzled because if the wave is measured along the x-axis while the slit is along the y-axis, I don't see the connection. Is this best described as a quantum mechanical effect? By passing through the slit the position of the wave is well known, resulting in a great uncertainty in the momentum which leads to the "spreading out" of the wave. What's the classical analong? Hyugens' principle?
 
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Diffraction occurs regardless, there is no prior requirement that must be met. In the (theoretical) case of an infinite plane wave incident on a rectangular aperture, the extent of the diffraction (i.e. the far-field angle) depends on (wavelength)/(aperture width), that is, the size of the wavelength compared to the size of the aperture.

Diffraction is usually regarded as a classical effect since diffraction is 'built-in' to Maxwell's equations.

Claude.
 
So say I shine a laser pointer though a doorway, there's still going to be some (albeit slight) diffraction?
 
If the beam is narrower than the doorway, you're not going to get any diffraction from the doorway.

If you shine the beam so it grazes one side of the doorway, then ideally you get "knife-edge diffraction" which is a well-studied situation. The thickness of a real wall will mess things up in practice, though.
 
So the beam has to be wider than the doorway for diffraction to occur. Does the wavelength play a role if it is not an infinite plane wave hitting the slit, but instead some other sort of wave (spherical, for example)?
 
A laser beam diffracts even in the absence of any apertures.

Why does an aperture cause an infinite plane wave to diffract? Because it TRUNCATES the wavefront. It is this truncation (or 'cutting-off') that results in the diffraction predicted by Maxwell's equations. A laser pointer emits wavefronts that are ALREADY truncated, thus it will diffract. Shining a laser through a doorway will not have an effect because the doorway does not truncate the wavefront any further.

Any aperture that DOES truncate the beam further, will cause the laser beam to diffract more than normal.

Claude.
 
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So forget about laser beams or electromagnetic waves. What about water waves or sound waves? Obviously these will also diffract if the wavefront is truncated because they are described by similar (wave) equations. What about my quantum-mechanical viewpoint. Is that another way of viewing the same phenomena for, say, an electron through a slit?
 
Yes, you truncate the possible locations where the electron could be.
 
Which I say is equivalent to knowing the position of the electron better, therefore greater uncertainity in the momentum which "spreads out" the wavefunction.
 
  • #10
I have seen such arguments made in elementary physics texts, though I find it a little too hand-wavey for my liking.

Claude.
 
  • #11
Really? What's hand-wavey about it? I guess one would have to do some calculations to make it more concrete. Do you know if this has been done?
 
  • #12
eep said:
Which I say is equivalent to knowing the position of the electron better, therefore greater uncertainity in the momentum which "spreads out" the wavefunction.

I have written about this quite a while back, so if you care to read about it...

https://www.physicsforums.com/journal.php?do=showentry&e=79&enum=24

Zz.
 
Last edited by a moderator:
  • #13
eep said:
Really? What's hand-wavey about it? I guess one would have to do some calculations to make it more concrete. Do you know if this has been done?

Most of these types of 'derivations' assume that the particles diffract without explaining why, many quote a circular proof such as citing the HUP as being responsible for diffraction, when the HUP is the result being pulled out of the analysis.

These textbooks are written for an audience who are just being introduced to QM, and is more to illustrate the idea of the HUP. So I can see why they would skip that part or just gloss over it, a rigorous analysis would be far more intimidating for the reader. I'm sure such rigorous derivations exist, but they belong in advanced texts and journal papers.

Claude.
 

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