ULTRA-SHORT WAVE PROPAGATION 



137 



to the requirement for regular reflections: h, the height of the hill, 

 should be small compared with \D/8H, which equals X/40, where 

 7r/2 — 6 is the angle of incidence. This relation expresses the fact 

 that the regularity of reflection from a given rough surface can be 

 improved either by increasing the wave-length or by decreasing the 

 angle 6. 



While these considerations show the reasonableness of regularity of 

 reflection, they do not enable us to calculate the value of the coefficient. 

 In the over-land tests which we have described, the amplitude of the 

 coefficient of reflection would have been very near to unity and its 

 phase angle would have been very near to 180° if the ground had been 

 smooth. In the absence of data on the reflection from rough surfaces, 

 we have used these same values although it is apparent that the 

 coefficient will be less than unity due to scattering and increased 

 penetration. The fact that a fairly good quantitative check has been 

 obtained experimentally indicates that this assumption is reasonable. 

 The check is somewhat better when the magnitude of the reflection 

 coefficient is somewhat reduced (Fig. 16). 



Diffraction 



In ultra-short wave propagation, the effect of an obstacle, such as a 

 hill, can be visualized best by considering it from the point of view^ of 

 this same principle of Huyghens. Fig. 10-^ represents this. A wave 



A 



Fig. 10 



B 



originates at T and travels unobstructed to R, passing through the 

 plane P. It is, of course, incorrect to say that the eft'ect travels 

 exclusively along the line TOR. Consideration must be given to 

 other paths such as TER, and the effect of the latter can be neglected 

 only in case the path length TER exceeds TOR by many w^ave- 

 lengths; or more properly, a region about E can be neglected only in 

 case the phases of the components transmitted through the elements 

 within it {e.g., along TER) are such as to cause destructive inter- 

 ference among themselves. 



