cients it is necessary to consider two cases, as follows. (6.19) 6.1.3.1 Case 1 (6.20) Electric vector in the plane of incidence (equivalent to a vertically polarised transmitter), as shown in Figure 6.1, gives Equations 6.16 and 6.17. These results allowed for a relative magnetic permeability of non-unity, but conductivity was zero. For propagation over the (6.16) Earth's surface, it is more appropriate to approximate magnetic permeability to unity, but allow for the finite conductivity of the medium. It is also reasonable to assume unity for the refractive (6.17) index of air, to obtain formulas for reflections off the Earth's surface. Then, for a wave of angular frequency w Equation 6.21 may be obtained. At high frequencies this may be simplified because it is possible (6.21) to neglect magnetic permeability, giving Equation 6.18. cot (a, - a2) (6.18) Then the reflection coefficient modulus and phase are given by Equations 6.22 and 6.23. Principles 6/5 (6.22) (6.23) sin a1 - sina,+(n'-con'a,)" Examples of the use of these formulas are given by Figures 6.3 and 6.4 for the land, and by Figures 6.5 and 6.6 for the sea. Horizontal polarisation Vertical polarisation Grazing angle a 1 (degrees) Figure 6.3 Magnitude of reflection coefficient over the ground (frequencies above 100MHz) Horizontal polarisation Vertical polarisation Grazing angle a 1 (degrees) Figure 6.4 Phase of reflection coefficient over the ground (frequencies above 100MHz) 6/6 Electromagnetic waves 100MHz Horizontal polarisation 3GHz 100MHz Vertical polarisation Grazing angle a1 (degrees) Figure 6.5 Magnitude of reflection coefficient over the sea Horizontal polarisation all frequencies Vertical polarisation 100MHz Grazing angle a1 (degrees) Figure 6.6 Phase of reflection coefficient over the sea 6.1.4 Huygen's principle and Fresnel diffraction screen is assumed to exist between transmitter and receiver, as shown in Figure 6.7. Then, Fresnel's integral states that the attenu- ation is related to free-space, in amplitude and phase, by the com- An ear