Does the Bragg equation hold for arbitrary diffractions?

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In summary, the conversation discusses the Bragg law and its various simplified cases. The first case involves both rays reflecting on points that are perfectly on a vertical line, while the second case assumes that the rays perfectly combine at the same spot. The conversation also mentions a general case where the only assumption is that the waves fall and go out parallel and diffract on two planes. The speaker questions the need for these simplified cases and shares their own proof for the general case. They also mention that scattering is coherent and looking at specific atoms in the plane makes the analysis easier. They ask for confirmation on the correctness of their proof and suggest that the Bragg law is more complicated than necessary.
  • #1
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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  • #2
Scattering is coherent, you scatter at the whole plane either way. Looking at specific atoms in the plane just makes the analysis easier.
 
  • #3
Is my 'proof' correct?
 
  • #4
If the result is right, I guess so, I'm just saying it is more complicated than necessary.
 

FAQ: Does the Bragg equation hold for arbitrary diffractions?

1. What is the Bragg equation and how does it relate to diffraction?

The Bragg equation is a mathematical relationship that describes the diffraction of X-rays or other electromagnetic radiation by a crystal. It states that the angle of incidence of the radiation, the angle of diffraction, and the wavelength of the radiation are related by the equation: nλ = 2d sinθ, where n is an integer, λ is the wavelength, d is the distance between crystal planes, and θ is the angle of diffraction.

2. Does the Bragg equation only apply to crystals?

No, the Bragg equation can also be applied to other periodic structures, such as diffraction gratings or interference filters. However, it is most commonly used to describe the diffraction of X-rays by crystals.

3. Is the Bragg equation applicable to all types of diffraction?

No, the Bragg equation is specifically used for describing the diffraction of X-rays or other electromagnetic radiation by a periodic structure. It is not applicable to other types of diffraction, such as acoustic or electron diffraction.

4. Is the Bragg equation valid for all angles of diffraction?

No, the Bragg equation is only valid for certain angles of diffraction, known as Bragg angles. These angles satisfy the condition λ = 2d sinθ, where d is the distance between crystal planes and θ is the angle of diffraction. Other angles of diffraction may not follow this relationship.

5. Can the Bragg equation be used for any wavelength of radiation?

No, the Bragg equation is only applicable for a specific range of wavelengths. This range is determined by the crystal structure and the distance between crystal planes. For example, the Bragg equation for X-ray diffraction will not be valid for visible light, as the distances between crystal planes in a crystal lattice are much larger than the wavelength of visible light.

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