Total internal reflection:
When a light wave travels from a dense substance such as glass into a less dense substance such as air, the angle of refraction will be bigger than the angle of incidence.
If the angle of incidence is big enough (i.e. bigger than the critical angle), the angle of refraction will get bigger than 90 degrees.
When the angle of incidence is less than the critical angle, most of the light passes out, but a little is internally reflected.
When the angle of incidence is equal to the Critical angle, the emerging ray comes out along the surface, and there's also quite a lot of internal relection.
When the angle of incidence is greater than the Critical angle, no light will come out, and it will all be internally reflected, known as total internal reflection.
Different materials have different densities, and so they will have different critical angles. The critical angle for light at a glass/air boundary is around 42 degrees.
Optical fibres work by total internal reflection, where the waves bounce off the sides of a thin inner core of glass or plastic using the relfection.