Laue equations and Braggs law

The geometry of diffraction from a lattice, or in other words the relationships between the directions of the incident and diffracted beams, was first given by Laue (see the footnote on page 31) in a form of three simultaneous equations, which are commonly known as Laue equations  

Laue equations once again indicate that a periodic lattice produces diffraction maxima at specific angles, which are defined by both the lattice repeat distances (a, b, c) and the wavelength (A,). Laue equations give the most general representation of a three-dimensional diffraction pattern and they may be used in the form of Eq. 2.20 to describe the geometry of diffraction from a single crystal. 

According to the Braggs, diffraction from a crystalline sample can be explained and visualized by using a simple notion of mirror reflection of the incident x-ray beam from a series of crystallographic planes. As established earlier (see Chapter 1, section 1.14.1), all planes with identical triplets of Miller indices are parallel to one another and they are equally spaced. Thus, each plane in a set hkJ) may be considered as a separate scattering object. The set is periodic in the direction perpendicular to the planes and the repeat distance in this direction is equal to the interplanar distance dhki- Diffraction from a set of equally spaced objects is only possible at specific angle(s) as 

The integer n is known as the order of reflection. Its value is taken as 1 in all calculations, since orders higher than one ( 1) can always be represented by first order reflections ( = 1) from a set of different crystallographic planes with indices that are multiples of n because 

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