Bragg's Law refers to the simple equation:

Derived (by the English physicists Sir W.H. Bragg) to explain why the cleavage faces of crystals appear to reflect X-ray beams at certain angles of incidence (θ, q). The variable   is the distance between atomic layers in a crystal, and the variable  is the wavelength of the incident X-ray beam n is an integer

• This observation is an example of X-ray wave interference commonly known as X-ray diffraction (XRD), and is a direct evidence for the periodic atomic structure of crystals postulated for several centuries. Although Bragg's law was used to explain the interference pattern of X-rays scattered by crystals, diffraction has been developed to study the structure of all states of matter with any beam, e.g., ions, electrons, neutrons, and protons, with a wavelength similar to the distance between the atomic or molecular structures of interest.
• Bragg's Law can easily be derived by considering the conditions necessary to make the phases of the beams coincide when the incident angle equals and reflecting angle.
• The rays of the incident beam are always in phase and parallel up to the point at which the top beam strikes the top layer at atom z (in figure).
• The second beam continues to the next layer where it is scattered by atom B. The second beam must travel the extra distance AB+BC if the two beams are to continue traveling adjacent and parallel.
• This extra distance must be an integral (n) multiple of the wavelength (λ) for the phases of the two beams to be the same

• Recognizing d as the hypotenuse of the right triangle ABz, we can use trigonometry to relate to the distance (AB+BC). The distance AB is opposite q so,

Because AB = BC equation 2 becomes,

Substituting equation 3 in equation 4 we have,

Hence, Bragg's Law has been derived.

Bragg’s Spectrometer