REFLECTION THEORY — PROPAGATION BEYOND THE HORIZON 



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provided 1 » A" » (If. This reflection coefficient for an incremental 

 change in dielectric constant can be used to calculate the reflection from 

 discontinuities in the gradient of the dielectric constant of the atmos- 

 phere such as those shown for a sti-atified medium at .// = and /y = h 

 in Fig. o(b). 



Such variations of dielectric constant are assumed to be representatix'e 

 of discontinuities in gradient as they exist in the physical atmosphere. 

 The variations form the reflecting layers. 



The method of calculating the reflection coefficient of such a stratified 

 medium is due to S. A. Schelkunofl" and is illustrated schematically in 

 Fig. 3 in which the medium has been subdi\'ided into incremental steps. 

 Consider the reflected wave from a typical incremental layer, dy, situated 

 a distance ij above the lower boundary of the la^^er, 0. From Fig. 3(a) 

 it is clear that the phase of this wave is -iiTij/X sin A relative to that of a 

 wave reflected from the lower boundary. The incremental reflection co- 

 efficient is c?f/4A^ = —K dy/4:A', where K is the change in gradient of 

 the dielectric constant at the boundaries of the layer. The field reflected 

 by layer dy is therefore, 



dEn = -Ei 



K _, 



j{iiryl\) sin A 



4A2 



dy 



One now obtains the complete reflected field by summing the reflec- 

 tions from all increments within the layer of thickness h. 



E.. 



f 



dEr = jE, 



K\ 



[1 



e 



-j(iirhl\) sin Ai 



JO 16xA- sin A 



This relation shows that the layer is equi\'alent to two boundaries at 



*-e 



Fig. .3 — Plane-wave reflection at an incremental layer di/ within a stratified 

 medium extending from y = to y = h. 



