Total external reflection is an optical phenomenon where electromagnetic radiation (e.g. visible light) can, at certain angles, be totally reflected from an interface between two media of different indices of refraction (see Snell's law). Total internal reflection occurs when the first medium has a larger refractive index than the second medium, for example, light that emerges from under water. The optically denser material (water in this case) is the "internal" medium. For visible light, water has an index of refraction of 1.33 and for air it is very close to 1. For vacuum the index of refraction is exactly 1 for all wavelengths.
For X-rays, however, all materials have indices of refraction slightly below 1. This entails that total reflection of X-rays only can occur when they travel through vacuum and impinge on a surface (at a small glancing angle). Since this kind of total reflection takes place outside of the material it is termed total external reflection. This makes it possible to focus X-rays (see, for example, NASA http://imagine.gsfc.nasa.gov/docs/science/how_l1/xray_telescopes.html)
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