Scattering by a Stack of Planes Bragg Diffraction

Let an electromagnetic wave is incident on the system of two parallel planes at an angle 0 with respect to the planes. Then, as seen in Fig. 5.5, the scattering vector is again described by Eq. 5.9. Now, let us introduce a new vector, a wavevector of the structure with period d qo = 2nld. Then, at a certain resonance angle Gq the wavevectors of scattering and structure coincide  

The same condition can easily be found by comparison of the wave path difference 2 /sim9 with wavelength X. 

For a stack of layers we will have m multiple reflections and equation 

This interlayer distance can be found as V2sim o from the X-ray experiment measuring the angle of the first-order diffraction spot (m = 1) or from higher order reflections. It is convenient to plot the diffracted beam intensity as a function of q then different diffraction orders are located at equidistant positions, as shown in Fig. 5.6  

Note that Eqs. 5.9-5.11 tell us nothing about the amplitude of waves and the intensity of scattering because we used only the momentum conservation law. 

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