DIFFRACTION OF RADIO WAVES BY A PARABOLIC CYLINDER 437 



-2024 



Fig. 2.9 — Behavior oi \ E \ and \ H \ on tiie shadow boundary far hchiiid I ho 

 half-phme or parabolic cylinder. This is a magnified view of the region around 

 /, = 0, ! exp i-ix) + <S, I = Vi in Fig. 2.2. 



tends to cancel the direct wave when i/' is very small. On the other hand, 

 the reflection coefficient for H (vp) is + 1 and the reflected wave tends 

 to add to the direct wave. 



The distances 1.71/i^'^ and —lA^li'^ appearing in Fig. 2.9 are the 

 amounts, measured in units for which the wavelength is 27r, l)y which 

 I E I and | H \ are shifted by the curvature of the parabolic cylinder. 

 If ij' — h' is the shift in meters for | E \ and if the radius of curvature 

 of the crest is a = 2/i' meters, Fig. 2.9 gives fi{ij' - h') = 1.71 (0h'f'^ = 

 1.71 (/3a/2)''' where ^ = 27r/X. Thus >/ - h' = 0.399X (a/A)"' meters. 

 The corresponding shift for \ H \ is — 0.34GX(a/X)' '^ meters. Artmann 

 gives the values 0.39 and —0.20 for the respective coefficients. The 

 discrepancy between —0.346 and —0.20 is cause for worry because it 

 seems to indicate either a mistake in our work, which I have been un- 

 able to locate, or a shortcoming in the approximations made by Artm.ann 

 for the case of vertical polarization. 



As h approaches zero the paral)olic cylindei- becomes a half-plane 

 and the curves d and e should approach curves b and c, respectively. 

 According to Fig. 2.9 both d and e approach curve a. Tiiis failure is an 



