Does the Bragg equation hold for arbitrary diffractions?

[Coffee_]

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:

 

[mfb]

Scattering is coherent, you scatter at the whole plane either way. Looking at specific atoms in the plane just makes the analysis easier.

 

[Coffee_]

Is my 'proof' correct?

 

[mfb]

If the result is right, I guess so, I'm just saying it is more complicated than necessary.