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Total internal reflection can happen only when a beam of light travelling through a dense medium crosses the interface with a rarer medium.

For example, through a glass piece to air.

When such a beam reaches an interface it makes an angle (called the angle of incidence) with the perpendicular at that point. When the beam exits the interface into the rarer medium. it makes a larger angle(called the angle of refraction) with the same perpendicular.

As the angle of incidence increases, so does the angle of refraction. There is one value of the angle of incidence for which the angle of refraction is 90 degrees and the emerging ray is tangential to the interface. This is called the critical angle.

For all angles of incidence greater than the critical angle the incident ray will not emerge into the rarer medium at all. In stead it gets reflected back into the denser medium itself.

This phenomenon is called total internal reflection.

Rainbows are a result of this phenomenon.

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