54 



FACTORS INFLUENCING TRANSMISSION 



4.2.4 



Fresnel's Formulas 



For finite conductivity, the reflection coefficient 

 may assume a variety of values. The general formu- 

 las, as derived from electromagnetic theory, are 

 given in equations (19) and (20). For horizontal 

 polarization 



sin i/* — V fij, — cos-\p 



R 



sin i/' + V e^ — cos-i/' ' 

 and for vertical polarization 



„ ^ i^sm^p — ^ e^ — cos- xp 



(19) 



(20) 



ization the phase change is 180° from \p = up 

 to an angle \po determined by tan i/'o=l/Ver. 

 Here, the coefficient is zero. For larger angles the 

 phase change is zero. As t, increases indefinitely, 

 i/'o approaches zero and for infinite e^ the phase shift 

 is zero everywhere, except for i/ = where it is 

 indeterminate. The angle lAo is called the Brewster 

 angle. For i/' = the amplitude is unity, and for 

 ■A = 90° 



P = -;=r 



Ve,+ 1 



(22) 



e^ sin i/- + V e^ — cos-i/' 



where e,. is the complex relative dielectric constant of 

 the reflecting ground which is gi^•en by 



(c = ir-jii. (21) 



A material that acts like a good conductor for 



.140 



for both cases of polarization. Allien e; is no longer 

 zero, the amplitude p will show a deep minimum 

 for a certain value of i/* instead of the zero found for 

 €; = 0. The angle corresponding to the minimum is 

 called the pseudo-Brewster angle. These various 

 points are illustrated by examples in Figure 16. 



Figure 11. 



low-frequency waves may act as an approximately 

 pure dielectric for microwaves. The case e,- = is 

 therefore of considerable practical importance. When 

 «i = 0, and R consequently is real, the phase lag is 

 180° for horizontal polarization. For vertical polar- 



Dielectric constant of sea water at 17 C 



4.2.5 'pjig Complex Dielectric Constant 

 of Water 



As much of the available radar and communica- 

 tion equipment is either shipborne or erected along 

 the coast, reflection from sea water is one of the 



