In many areas of science, Bragg's law — also known as Wulff–Bragg's condition or Laue–Bragg interference — is a special case of Laue diffraction that gives the angles for coherent scattering of waves from a large crystal lattice. It describes how the superposition of wave fronts scattered by lattice planes leads to a strict relation between the wavelength and scattering angle. This law was initially formulated for X-rays, but it also applies to all types of matter waves including neutron and electron waves if there are a large number of atoms, as well as to visible light with artificial periodic microscale lattices.

Bragg diffraction (also referred to as the Bragg formulation of X-ray diffraction) was first proposed by Lawrence Bragg and his father, William Henry Bragg, in 1913 after their discovery that crystalline solids produced surprising patterns of reflected X-rays (in contrast to those produced with, for instance, a liquid). They found that these crystals, at certain specific wavelengths and incident angles, produced intense peaks of reflected radiation.

Lawrence Bragg explained this result by modeling the crystal as a set of discrete parallel planes separated by a constant parameter d. He proposed that the incident X-ray radiation would produce a Bragg peak if reflections off the various planes interfered constructively. The interference is constructive when the phase difference between the wave reflected off different atomic planes is a multiple of 2π; this condition (see Bragg condition section below) was first presented by Lawrence Bragg on 11 November 1912 to the Cambridge Philosophical Society. Due to its simplicity, Bragg's law provided a powerful new tool for determining crystal lattices from X-ray diffraction data. Lawrence Bragg and his father, William Henry Bragg, were awarded the Nobel Prize in physics in 1915 for their work in solving crystal structures beginning with NaCl, ZnS, and diamond. They are the only father-son team to jointly win.

The concept of Bragg diffraction applies equally to neutron diffraction and approximately to electron diffraction. In both cases the wavelengths are comparable with inter-atomic distances (~ 150 pm). Many other types of matter waves have also been shown to diffract, and also light from objects with a larger ordered structure such as opals.

Bragg diffraction occurs when radiation of a wavelength λ comparable to atomic spacings is scattered in a specular fashion (mirror-like reflection) by planes of atoms in a crystalline material, and undergoes constructive interference. When the scattered waves are incident at a specific angle, they remain in phase and constructively interfere. The glancing angle θ (see figure on the right, and note that this differs from the convention in Snell's law where θ is measured from the surface normal), the wavelength λ, and the "grating constant" d of the crystal are connected by the relation:$${\displaystyle n\lambda =2d\sin \theta }$$where ${\displaystyle n}$ is the diffraction order (${\displaystyle n=1}$ is first order, ${\displaystyle n=2}$ is second order, ${\displaystyle n=3}$ is third order). This equation, Bragg's law, describes the condition on θ for constructive interference.

A map of the intensities of the scattered waves as a function of their angle is called a diffraction pattern. Strong intensities known as Bragg peaks are obtained in the diffraction pattern when the scattering angles satisfy Bragg condition. This is a special case of the more general Laue equations, and the Laue equations can be shown to reduce to the Bragg condition with additional assumptions.

In Bragg's original paper he describes his approach as a Huygens' construction for a reflected wave. Suppose that a plane wave (of any type) is incident on planes of lattice points, with separation ${\displaystyle d}$, at an angle ${\displaystyle \theta }$ as shown in the Figure. Points A and C are on one plane, and B is on the plane below. Points ABCC' form a quadrilateral.

There will be a path difference between the ray that gets reflected along AC' and the ray that gets transmitted along AB, then reflected along BC. This path difference is $${\displaystyle (AB+BC)-\left(AC'\right)\,.}$$