Total internal reflection

When light travels from a denser to a rarer medium, the refracted ray bends away from the normal; at the critical angle i_c the refracted ray grazes the surface (r = 90°).

For incidence greater than i_c there is no refracted ray and all the light is reflected back into the denser medium: total internal reflection.

Two conditions are needed: light must go from denser to rarer, and the angle of incidence must exceed the critical angle.

For a denser medium of refractive index n relative to the rarer one, sin i_c = 1/n. For glass of n = 1.5 in air, i_c is about 42°.

Since n = c/v, the critical angle can also be found from sin i_c = v_denser / v_rarer.

Optical fibres use total internal reflection: a core is surrounded by cladding of lower refractive index, so light entering the core is reflected again and again along its length with very little loss.

Bundles of optical fibres (light pipes) are used to transmit and receive signals in telecommunication and to look inside the body in medical examinations.