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Total external reflection is the situation where the light starts in air and vacuum (refractive index 1), and bounces off a material with index of refraction less than 1. For example, in X-rays, the refractive index is frequently slightly less than 1, and therefore total external reflection can happen at a glancing angle. It is called ''external'' because the light bounces off the exterior of the material.<ref>{{cite book|last=Attwood|first=D|title=Soft X-Rays and Extreme Ultraviolet Radiation|year=1999|publisher=Cambridge University Press}}</ref> This makes it possible to focus X-rays.<ref>See, for example, NASA {{webarchive|url=https://web.archive.org/web/20161213145838/http://imagine.gsfc.nasa.gov/science/toolbox/xray_telescopes1.html|date=12-13-2016|title=X-ray Telescopes}}</ref>
The critical angle of total external reflection can be calculated as:<ref>Y. Chen, "General law of refraction" https://assets-eu.researchsquare.com/files/rs-4783430/v1_covered_eebd8628-fdf9-4366-bfaa-bef42f6128d5.pdf</ref>
:<math display="block">\theta_\mathrm{c} =\arcsin\!\left(\frac{|\underline{n_2}|}{|\underline{n_1}|}\right)\!= \arcsin\!\left(\frac{\sqrt{n_2^2+\kappa_2^2}}{\sqrt{n_1^2+\kappa_1^2}}\right)\!.</math>
where <math>\underline{n}</math> is the complex refractive index, and <math>\kappa</math> is the extinction coefficient.
==References==
{{reflist}}
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