Optipedia • SPIE Press books opened for your reference.

Internal Reflection

When light enters a medium that has a lower index of refraction, Snell's law indicates that the light refracts so that it makes a greater angle with respect to the normal.

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 90^o.

At this particular value of θ₁, the angle of refraction is ≥90^o and the light does not leave the first medium. This is total internal reflection. The critical angle θ_c at which total internal reflection will occur is given by the expression

Not only is total internal reflection important in fiber optics transmission and polarizers, but a form of spectroscopy—attenuated total reflectance (ATR) spectroscopy—is based on this phenomenon.