o 377 ohms. The energy that is carried by the wave is given by the Poynting vector as EAH watts per square meter. Historical understanding of the fields from electric charges and magnets led to the prediction of the electromagnetic wave traveling through space. Two major categories of receiving antenna (rods and loops) extract from the wave voltages related to the electric and magnetic fields. Furthermore, many other features of the wave can be accu- rately formulated from the theory (some of which are given here; others can be found in textbooks with mathematical derivation). Thus, there is a tendency to attach more signifi- cance to the theory than is justified. It does not prove that the wave is composed of distinct electric and magnetic vectors. It only shows that it is very convenient for us to make the distinction. Boundary Conditions If there are discontinuities in the electrical properties of the medium, determination of the wave behavior requires a knowledge of what are called "boundary conditions." The most relevant of these is that components of both E and H tangential to a surface must be continuous. Thus, it is possible to determine how a wave behaves if it is incident on a plane surface where there is a change of impedance from N1 to n2 and of refractive index from N1 to N2. If the incident wave-normal makes an angle, A1, with the plane, as shown in Figure 7.1, Snell's law gives the angle A2 for the wave passing into medium 2. n1cosa1=N2cosa2 (7.15) To determine the reflection, r, and transmission, t, coefficients it is necessary to consider two cases, as follows. Chapter 7 Electromagnetic Waves Medium 1 N1,N1 Medium 2 n2, N2 Fig. 7.1 Reflection and refraction at a boundary with the electric vector in the plane of incidence. Case 1 The electric vector in the plane of incidence (equivalent to a vertically polarized trans- mitter), as shown in Figure 7.1, gives equations 7.16 and 7.17. missing (7.16) (7.17) At high frequencies this can be simplified because it is possible to neglect magnetic permeabil