Total reflection doubles up

As we were all taught in high school, a ray of light that is travelling through a piece of glass changes direction when it strikes the interface between the glass and the air, in accordance with Snell's law. If the angle of incidence is less than a critical angle, which is determined by the refractive indices of the glass and the air, the ray is refracted and leaves the glass. However, if the angle of incidence is greater than this critical angle, the ray undergoes total internal reflection and remains in the glass. This mechanism allows light to be transmitted over long distances inside optical fibres, but it is not quite as straightforward as our teachers might have led us to believe.