Assume a row of scatterers separated by constant repeat, a. Radiation of wavelength l is incident on this row at an angle a_{o}. Examine the the scatter from this row at an angle a_{n}.
The path difference of rays scattering at points A and D is just ABCD. If the incoming rays are in phase, the path difference must be some integral multiple of the wavelength for constructive interference to occur. This leads to the first Laue equation:

This result is valid for any scattered ray that makes an angle a_{n} with the unit cell axis. Thus the Laue condition is consistent with a cone of scattered rays centered about the a axis. This equation can be restated in vector terms. The repeat distance a, becomes a unit cell vector a. Call a unit vector parallel to the incoming rays, S_{0}, and one parallel to the scattered rays, S. There are then some simple vector dot products:

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