Critical angle of reflection formula1/26/2024 ![]() This approximation results in an error below 0.021% for θ critical<1°. With n 2 = 1- δ and with the Taylor expansion of the cosine Consequently normally the reflection angles are measured as angles θ between the incoming ray and the mirrors surface. So the reflection angles α are always close to 90°. For X-rays total external reflection occurs only under grazing incidence. So the critical angle α critical isĪs n 2 is only slightly below one (for example for gold for photon energies of 12.4 keV, n 2 = 1-1.88♱0 -5), the maximum angle for TER to occur is close to 90° (for gold at 12.4 keV α critical = 89.65° = 90°-0.351°). Assuming the ray comes from vacuum, n 1=1. Total external reflection occurs for angles α 1, when the angle α 2 reaches 90°. With the angle α 1 of the incoming ray and α 2 of the outgoing ray and the indices of refraction n 2 in matter and n 1 in the medium the ray comes from. From the refraction of X-rays we know that Snell's law is The critical angle can be calculated as follows (see fig. To calculate the critical angle of total external reflection 1: Sketch showing the angles and indices of refraction used When X-rays enter matter under grazing incidence, they will be reflected by Total External Reflection (TER) when the angle of incidence is below the critical angle α critical.įig. Mostly three reflection types are distinguished: Total external reflection X-rays can be reflected under certain conditions when hitting matter.
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