372 PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
DIELECTRIC CONSTANT 
RRS 
Weratanne 
a 
= 
Figure 11. Dielectric constant of sea water at 17 C. 
and for vertical polarization 
e,siny — Vv €, — cos’ y (20) 
R= ae 
e,siny + Ve, — cos?’ 
where «, is the complex relative dielectric constant of 
the reflecting ground which is given by 
& = & — jG. (21) 
A material that acts like a good conductor for 
low-frequency waves may act as an approximately 
pure dielectric for microwaves. The case ¢; = 0 is 
therefore of considerable practical importance. When 
e; = 0, and R consequently is real, the phase lag is 
180° for horizontal polarization. For vertical polar- 
ization the phase change is 180° from ¥y = 0 up 
to an angle yo determined by tan yo =1/Vé,. 
Here, the coefficient is zero. For larger angles the 
phase change is zero. As e¢, increases indefinitely, 
Wo approaches zero and for infinite ¢, the phase shift 
is zero everywhere, except for y = 0 where it is 
indeterminate. The angle Y is called the Brewster 
angle. For y = 0 the amplitude is unity, and for 
y = 90° 
_vVe-—1 
Ve +1 
for both cases of polarization. When «¢; is no longer 
zero, the amplitude p will show a deep minimum 
for a certain value of y instead of the zero found for 
e; = 0. The angle corresponding to the minimum is 
(22) 
called the pseudo-Brewster angle. These various 
points are illustrated by examples in Figure 16. 
The 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 
principal problems to be discussed here. For micro- 
waves the salt content in sea water makes little 
difference, so that it may be assumed that the dielec- 
tric constant and conductivity are the same over all 
oceans at the same temperature. With increasing 
temperature, the real part of the dielectric constant 
diminishes roughly by one unit per 5° C. Figure 11 
gives the dielectric constant ¢, of ordinary sea 
water at 17 C asa function of frequency. 
The dielectric constant also diminishes with in- 
creasing salinity, but in the UHF-SHF region, normal 
variations of salinity have much smaller influence 
than changes in temperature and frequency. The 
imaginary part e¢; of the dielectric constant is, for 
frequencies less than say 1,000 mc, related to the 
conductivity o as follows: 
€; = + 60cr (23) 
(co in mhos per meter and ) in meters). At 25 C the 
average conductivity of sea water is usually given as 
4.3 mhos per meter. The temperature dependence is 
given by 
o = o25[1 + 0.02(t — 25)], 
