Traveling wave multiple reflection

In the diagram opposite, an ordered array of atoms is represented simply by black dots. Consider the two waves of incident radiation (angle of incidence = 0) to be in-phase. Let one wave be reflected from an atom in the first lattice plane and the second wave be reflected by an atom in the second lattice plane as shown in the diagram. The two scattered waves will only be in-phase if the additional distance travelled by the second wave is equal to a multiple of the wavelength, i.e. n. If the lattice spacing (i.e. the distance between the planes of atoms in the crystal) is d, then by simple trigonometry, we can see from the diagram opposite that ... 

W L Bragg [7] observed that if a crystal was composed of copies of identical unit cells, it could then be divided in many ways into slabs with parallel, plane faces whose distributions of scattering matter were identical and that if the pathlengths travelled by waves reflected from successive, parallel planes differed by integral multiples of the... 

To understand how a diffraction pattern may be generated, consider the scattering of X rays by atoms in two parallel planes (Figure 11.24). Initially, the two incident rays are in phase with each other (their maxima and minima occur at the same positions). The upper wave is scattered, or reflected, by an atom in the first layer, while the lower wave is scattered by an atom in the second layer. In order for these two scattered waves to be in phase again, the extra distance traveled by the lower wave must be an integral multiple of the wavelength (A) of the X ray that is,... 

---