Total internal reflection

When light travels from a denser medium into a rarer one, the angle of refraction is always larger than the angle of incidence. As the angle of incidence in the denser medium is steadily increased, the angle of refraction increases correspondingly, until at one particular angle of incidence, $i_C$ -- the CRITICAL ANGLE -- the refracted ray just grazes along the interface itself, at exactly $90^\circ$. For any angle of incidence GREATER than $i_C$, the light cannot cross into the rarer medium at all: the entire beam reflects back into the denser medium instead. This phenomenon is TOTAL INTERNAL REFLECTION (TIR). Unlike the ordinary PARTIAL reflection and refraction that occurs at most interfaces, TIR is total reflection with ZERO refraction -- no light at all crosses over.

The critical angle for a given pair of media is formally defined as that angle of incidence in the denser medium for which the angle of refraction in the rarer medium is exactly $90^\circ$. Applying Snell's law at this specific angle, with $\mu$ denoting the refractive index of the denser medium relative to the rarer one, gives $\mu\sin(i_C) = (1)\sin90^\circ$, i.e. $\sin(i_C)=\dfrac{1}{\mu}$. For commonly used glass, $\mu=1.5$ gives $i_C\approx41^\circ49'\approx42^\circ$; for water, $\mu=4/3$ gives $i_C\approx48^\circ35'$ (both quoted with respect to air). …