Reflection and Refraction of X-Rays

In the previous sections, we had assumed that the scattering of X-rays could be fully described by kinematical theory. Since the scattering from a surface is very 

Because n 1, there is a finite angle i below which total reflection occurs. This critical angle Uc is found from cos i = n. Ignoring absorption (and using the fact that o c is small), we find 

The intensity of the reflected and transmitted beams is given by the Fresnel equations 

The real part, or amplitude, of at is then found from 

This has a very different form than the dynamical result in Eq. (3.4.2.52). In order to show that the two approaches are the same for large values of the incoming angles, we need to simplify the dynamical result For large values of ai, it is straightforward to derive the following expression from Eq. (3.4.2.52) 

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Reflection and refraction of X-rays follow the laws of optics (Fig. 4.2) The glancing angles of incidence (i) and reflection ( ) are equal. The respective refraction angles follow Snell s law for different phase velocities v in mediums 1 and 2 ... 

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