RADIO PROPAGATION 



S3 



where K is the ratio of the amplitude of the reflected wave to that 

 of the direct wave and 7 + tt is their phase difference. 



7 = 'A - A, (22) 



where A is 2ir times the path difference in wave-lengths and 



<p = \p ±T (23) 



is the phase advance at reflection. The geometry is shown in Fig. 4. 

 A may be calculated from the geometry by means of equation (47) 

 of Appendix II (page 72). 



Fig. 4 



The magnitude and phase of the reflection coefficient, R = — Ke"f', 

 for both polarizations are plotted in Figs. 5-12 for e = 4, 10, 30 and 80 

 and a series of values of e/Q = 2a// differing by factors that are 

 multiples of 10. The coordinate system has been chosen so that the 

 quantities 1 — K and \{/ that enter into the equation for the resultant field 

 strength may be read with the same degree of accuracy for the entire 

 range of the curves. To obtain values oi I — K and \l/ for smaller values 

 of ^2 than shown on Figs. 5-12 use is made of the fact that both of these 

 quantities are proportional to ^2 for small values of ^2- This linear 

 relationship holds for the lowest cycle * of the curves so that the parts 



* An exception to this occurs for large Q in the ^-curves for vertical polarization. 

 Under these conditions the difference between ^ and zero for values not shown on the 

 chart is relatively unimportant. When Q is large and K is different from zero i/- is 

 substantially 0° or 180°. For horizontal polarization \p may be taken equal to zero 

 for most practical purposes. 



