When light passes from one medium to another that is optically less dense, eg. from glass to air, the ray is bent away from the normal. If the incident ray meets the surface at such an angle that the refracted ray must be bent away at an angle of more than 90 degrees, the light cannot emerge at all, and is totally internally reflected.

For glass, the angle is 42^o. For diamond, it is 24^o. This is what makes diamond so nice and pretty and sparkly.

There is an equation which will link the differences in optical density to the critical angle (the name of the angle at which total internal reflection will occur)...

Convert Critical Angle into Index of Refraction
1/(sin angle)

Convert Index of Refraction to Critical angle
sin^-1 i^-1

The first ^-1 is the inverse of sine (which converts the ratio of two sides to the angle) and the second ^-1 is the reciprocal of the index of refraction.