When a ray of light encounters an interface between two media of different refractive indices, some of it is reflected and some is transmitted. This chapter will concern itself with how much is reflected and how much is transmitted. (Unless the media are completely transparent, some of the light will also be absorbed - and presumably degraded as heat - but this chapter will concern itself only with what happens at the interface, and not in its passage through either medium.) We shall do this at three levels: Normal incidence; incidence at the Brewster angle (we’ll explain what is meant by this); incidence at an arbitrary angle.
The result for the transmitted and reflected amplitudes is an inevitable consequence of the continuity of displacement and gradient of a wave at a boundary, and is not particularly restricted to waves in a rope. It should be equally applicable to electromagnetic waves moving from one medium to another at normal incidence, and indeed it is verified by measurement.
If a ray of light is incident at an interface between two media in such a manner that the reflected and transmitted rays are at right angles to each other, the angle of incidence is called the Brewster angle. If a ray of unpolarized light is incident at the Brewster angle, the reflected ray is totally plane-polarized. The is no component of the oscillating electric field that is in the plane
We need to remind ourselves of one other thing from electromagnetic theory before we can proceed, namely the meaning of impedance in the context of electromagnetic wave propagation.
