the Laue condition
/ Laue -> LOW-uh /
Max von Laue described diffraction without ever mentioning reflecting planes. Instead of Bragg's canyon of mirrors, picture every atom in the crystal scattering a wavelet, and ask: in which directions do the wavelets from all the atoms arrive in step? Laue's answer is a clean condition stated in reciprocal space, and it is completely equivalent to Bragg's law — the same physics wearing different clothes, preferred whenever you think in terms of the reciprocal lattice.
Here is the compact modern statement. Describe the incoming wave by a wavevector k (an arrow pointing along the beam, length 1/lambda) and the outgoing wave by k'. Their difference, k' - k, is the scattering vector. The Laue condition says a diffracted beam appears exactly when the scattering vector equals a reciprocal lattice vector: k' - k = g_hkl. In words, the crystal can only deflect the beam by amounts that land you on a reciprocal lattice point. Equivalently, von Laue's original three equations demand that the path difference between waves scattered by atoms one lattice-vector apart be a whole number of wavelengths along each of the three cell edges at once.
The Ewald sphere makes the condition visual: draw a sphere of radius 1/lambda through the origin of the reciprocal lattice, and a reflection flashes out only when a reciprocal lattice point happens to sit on the sphere's surface — the geometric picture of k' - k = g. And it collapses straight back to Bragg: because |g_hkl| = 1/d_hkl and the scattering geometry gives |k' - k| = 2 sin theta / lambda, setting them equal yields 2 d sin theta = lambda. Two languages, one law.
For a reflection with |g_hkl| = 0.5 angstrom^-1 (so d = 2 angstrom) and copper radiation (1/lambda = 0.649 angstrom^-1), the scattering vector must reach 0.5 angstrom^-1. That happens at 2 sin theta / lambda = 0.5, i.e. sin theta = 0.5 x 1.54 / 2 = 0.385, theta = 22.6 degrees — the very same angle Bragg's law gives.
Laue (k' - k = g) and Bragg (2 d sin theta = lambda) always predict identical angles; they are one law in two notations.
Laue and Bragg are equivalent, not rival, descriptions. Laue's virtue is that it works directly in the reciprocal lattice and needs no 'reflecting planes' — a fiction that becomes awkward for complex structures and electron diffraction.