Does the Bragg equation hold for arbitrary diffractions?

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Discussion Overview

The discussion centers around the applicability of the Bragg equation in various diffraction scenarios, particularly questioning whether it holds for arbitrary diffractions beyond simplified cases commonly presented in proofs. Participants explore the assumptions and conditions under which the Bragg law is derived and its implications for general cases of diffraction.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that existing proofs of the Bragg law often simplify the situation, focusing on specific cases where rays reflect in a straightforward manner.
  • Another participant argues that scattering is coherent and that analyzing specific atoms simplifies the analysis, suggesting that a broader view may complicate understanding.
  • A participant questions the correctness of their own proof regarding the general case of the Bragg law, indicating uncertainty about its validity.
  • Another participant implies that if the result of the proof is correct, it may still be more complex than necessary, hinting at a potential overcomplication in the approach taken.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and complexity of the proofs related to the Bragg law. There is no consensus on the correctness of the proposed general case or the simplifications typically used in existing proofs.

Contextual Notes

The discussion highlights limitations in the assumptions made in standard proofs of the Bragg law and the potential for differing interpretations of coherence in scattering. The scope of the discussion remains focused on theoretical considerations without resolving the mathematical intricacies involved.

Coffee_
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Any proof I look up of the Bragg law proves a simplified case of the situation.

The most common one is where both rays reflect on points that are perfectly on a vertical line like this:

http://pms.iitk.ernet.in/wiki/images/thumb/Jk2_1.png/400px-Jk2_1.png

The second most popular case is to assume that after diffraction the rays perfectly combine at the same spot like this:

http://chemwiki.ucdavis.edu/@api/de...?size=bestfit&width=444&height=236&revision=1

I don't see the point of all these simplified cases since the proof for a general case where the only assumption you make is that the waves fall in parallel and go out parallel and difract on respectively plane 1 and plane 2. The proof of the general is really not that much more difficult. At least I think I proved it. I'd like to confirm if it's correct fo the general case as I showed here:
 

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Scattering is coherent, you scatter at the whole plane either way. Looking at specific atoms in the plane just makes the analysis easier.
 
Is my 'proof' correct?
 
If the result is right, I guess so, I'm just saying it is more complicated than necessary.
 

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