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Excerpt from Field Guide to Spectroscopy
As the incoming ray increases its angle with respect to the normal, the outgoing ray in the second medium increases its angle also, and at some point reaches 90o.
At this particular value of θ1, the angle of refraction is ≥90o and the light does not leave the first medium. This is total internal reflection. The critical angle θc at which total internal reflection will occur is given by the expression