Total internal reflection (TIR) is the optical phenomenon in which (for example) the surface of the water in a fish-tank, viewed from below the water level, reflects the underwater scene like a mirror with no loss of brightness (Fig.1). In general, TIR occurs when waves in one medium strike sufficiently obliquely against the boundary with a second ("external") medium, in which the waves travel faster than in the first ("internal") medium; the second medium must also be perfectly transparent to the waves. TIR occurs not only with electromagnetic waves such as light and microwaves, but also with other types of waves, including sound and water waves. In the case of a narrow train of waves, such as a laser beam (Fig.2), we tend to describe the reflection in terms of "rays" rather than waves; in a medium whose properties are independent of direction, such as air, water, or glass, the "rays" are perpendicular to the associated wavefronts.