“…It has been shown by many workers (Kiessig, 1931;Wainfan & Parratt, 1960;Parratt, 1954) that X-rays incident upon the surface of a material at small glancing angles are specularly reflected, the reflection coefficient being in excellent agreement with the re-* Supported by National Aeronautics and Space Administration grant t The work reported here is taken, in part, from a dissertation presented to the faculty of the Polytechnic Institute of Brooklyn in partial fulfilment of the requirements for the degree of Doctor of Philosophy (Physics), 1969, flectivity predicted by the Fresnel equations (Born & Wolf, 1964). Since the index of refraction for most materials is less than unity at X-ray frequencies, the X-ray beam will be totally reflected if the angle of incidence (as measured from the surface) is less than a 'critical angle' 0c, and if absorption is negligible.…”