There are two ways to proof Bragg's law, one of them is in wikipedia on this link
http://en.wikipedia.org/wiki/Bragg's_law
while the other one which is much easier can be written like that
AB = 2BC = nλ
sin θ = BC/d
BC = d sin θ
2BC = 2d sin θ = nλ
Hmm, I think you mean 2AB = 2BC here but I see what you mean. It's a nice and simple proof.
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