Posted by Steve Simon on March 8, 2015, 4:49 pm, in reply to "Scattering Experiments"
Remember that Bragg's law 2 d sin theta = n lambda was our derived condition for constructive interference assuming a given spacing between lattice planes d. Suppose there is some family of lattice planes {hkl} with spacing d=2 pi/G(hkl) and (hkl) the shortest recip latt vector in the given direction. Suppose this satisfies 2 d sin theta = lambda. Now note that there is also a set of planes corresponding to {2h,2k,2l} which will have half the lattice plane spacing, or equivalently in the Bragg formula you can use the same value of d, but n=2. So if you consider all possible {hkl} you have already considered all possible n. Does that make sense? 
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