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Total internal reflection

Under circumstances where the incident medium has a refractive index which is larger than the second medium, as is the case for the rear surface boundary of an uncoated substrate, and if the incident angle (θ) is large, then Snell's law, as defined in equation 2-33 gives values that become meaningless as sinθt has values greater than 1. The refracted wave under these circumstances then propagates parallel to the rear surface. The critical angle of incidence defining this condition being given by

θc = sin-1(n2/n1), where n2<n1. For Ge, Si, CdTe, ZnSe and ZnS the values of this critical angle are 14.5°, 17.1°, 22.0°, 24.6° and 27.0°. At incident angles greater than these values there can be no energy flow across the boundary and the wave becomes totally internally reflected. The amplitude of the reflected wave differs from the incident amplitude by a change of phase to the s and p polarizations given by:



Substrate optical theory