What happens when an EM wave impinges from a dielectric medium on a planar interface with air? The EM wave bends its propagation direction. The angle forms between the surface normal and the propagation direction is bigger in the air than in the dielectric medium (Snell’s Law). Increasing the incidence angle in the dielectric, it be achieved an angle of propagation in the air equal to 90º. In this case, the incidence angle is called “critical angle”. For incidence angles bigger than the critical angle, total reflection can be achieve, that is, no energy flows from the dielectric to the air. That can be seen clearly in these experiment, where the light (a EM wave, of course) goes from water to air, forming different incidence angles.
This total reflection is a key element to understand optical fibers: the light can be “catched” because the angle of incidence from the dielectic medium is bigger than the critical angle.