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| Total reflection is a process that occurs when Snell's law for refraction can no longer be solved for real angles. As shown in the figure below, light from one medium, when entering a different medium is both reflected and refracted, with the refracted angle being given by Snell's law. For typical wavelengths (visible, infrared, ultraviolet), a vacuum has the lowest index of refraction (n=1) while other media have indices that are greater than 1. Thus, it is possible to achieve total internal reflection when the refracted angle becomes complex. For x-rays, a solid medium is optically less dense than a vacuum, and thus total external reflection occurs.
When the condition of total external reflection holds, the penetration depth of the incident x-ray beam is only a few tens of angstroms, and the reflectivity is near unity as shown in the figure below. Naturally, as the angle is increased past the critical angle, the reflectivity decrease rapidly, while the penetration depth increases.
Our experiment are done at a condition of total external reflection to provide for a surface sensitive beam that will only excite surface level atoms and to generate x-ray standing waves that increase the fluorescence intensity from excited atoms. |
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