text: If  with , ,  as integers represents the reciprocal lattice for a crystal lattice  (defined by ) in real space, we know that  with an integer  due to the known orthogonality between primitive vectors for the reciprocal lattice and those for the crystal lattice. (We use the physical, not crystallographers, definition for reciprocal lattice vectors which gives the factor of .) But notice that this is nothing but the Laue equations. Hence we identify , means that allowed scattering vectors  are those equal to reciprocal lattice vectors  for a crystal in diffraction, and this is the meaning of the Laue equations. This fact is sometimes called the Laue condition. In this sense, diffraction patterns are a way to experimentally measure the reciprocal lattice for a crystal lattice.'
  The Laue condition can be rewritten as the following.
  Applying the elastic scattering condition  (In other words, the incoming and diffracted waves are at the same (temporal) frequency. We can also say that the energy per photon does not change.) 
  To the above equation, we obtain
  The second equation is obtained from the first equation by using .
  The result  (also ) is an equation for a plane (as the set of all points indicated by  satisfying this equation) as its equivalent equation  is a plane equation in geometry. Another equivalent equation, that may be easier to understand, is  (also ). This indicates the plane that is perpendicular to the straight line between the reciprocal lattice origin  and  and located at the middle of the line. Such a plane is called Bragg plane. This plane can be understood since  for scattering to occur. (It is the Laue condition, equivalent to the Laue equations.) And, the elastic scattering  has been assumed so , , and  form a rhombus. Each  is by definition the wavevector of a plane wave in the Fourier series of a spatial function which periodicity follows the crystal lattice (e.g., the function representing the electronic density of the crystal), wavefronts of each plane wave in the Fourier series is perpendicular to the plane waves wavevector , and these wavefronts are coincident with parallel crystal lattice planes. This means that X-rays are seemingly "reflected" off parallel crystal lattice planes perpendicular  at the same angle as their angle of approach to the crystal  with respect to the lattice planes; in the elastic light (typically X-ray)-crystal scattering, parallel crystal lattice planes perpendicular to a reciprocal lattice vector  for the crystal lattice play as parallel mirrors for light which, together with , incoming (to the crystal) and outgoing (from the crystal by scattering) wavevectors forms a rhombus.' 
  Since the angle between  and  is , (Due to the mirror-like scattering, the angle between  and  is also .) . Recall,  with  as the light (typically X-ray) wavelength, and  with  as the distance between adjacent parallel crystal lattice planes and  as an integer. With these, we now derive Bragg's law that is equivalent to the Laue equations (also called the Laue condition):