REFLECTION COEFFICIENTS 261 
sults of the 10-cm waves obtained under less well- 
defined conditions.’ The latter results are given al- 
ways in graphical form. 
The grazing angle interval (0° to about 30°) ex- 
plored with the 10-cm waves was quite large, and a 
graphical representation of the results is well justi- 
fied. At 9 cm only three or at most four angles of in- 
cidence were investigated. 
The schematic representation of the experimental 
setup is given in Figure 3. If p denotes the ratio of 
TRANSMITTER RECEIVER 
h, h 2 
[ (NZ) 
e EARTH 
“N 
. SS 
N he 
Ficure 3. Idealized geometry of the experiment.® 
the amplitude of the reflected wave to that of the 
incident wave in the vicinity of the reflecting sur- 
face, then at the position of the receiver the total field 
received in case of reinforcement is 
Enax = E + kp. 
E is the field strength of the direct wave and & is a 
correction factor taking into account the directivity 
of the transmittér and receiver as well as the increased 
path length of the reflected ray as compared to that 
of the direct ray. In case of phase opposition 
Enin = E — kok. 
REFLECTION COEFFICIENT p! 
These lead to 
eS kp = (Emax / Emin) — 1 
(Emax / E xin) ar 1 
Throughout the work at 10 cm this corrected reflec- 
tion coefficient (kp) or p’ has been investigated. Pre- 
sumably & is nearly unity so that p’ = p. 
Very Dry Sandy Ground. Table 1, for 9 cm, refers 
to very dry ground. In order to obtain a precise value 
of the complex dielectric constant of this very dry 
sandy ground its absorption coefficient was measured 
directly. The measurement was made by interposing 
a filled container between transmitter and receiver. 
TaBLeE 1. Reflection coefficients of very dry sandy ground 
for \ = 9 cm.12 
Grazing 
angle _- Vertical polarization 
degrees Calculated Observed 
Horizontal polarization 
Calculated Observed 
22 0.18 0.20 0.48 0.47 
36.5 0.015 0:03 0.33 0.33 
46.5 0.08 0.09 0.26 0.27 
The container, a wooden trough, had % in. plate 
glass ends, 18 in. square, one of which was movable, 
thus allowing a test of the absorber up to a thickness 
of 12 in. The most suitable values of «, (real part 
of the complex dielectric constant «,) and conductivity 
co or « = 60 oA (imaginary part of the complex 
dielectric constant) which fit the reflection and ab- 
sorption coefficient data were found to be « = 2, o 
= 0.033 mho per meter, «, = 0.18. 
It should be mentioned here that the calculated 
reflection coefficients were obtained by using the gen- 
eralized Fresnel formulas for reflection of electro- 
magnetic waves by plane dielectric surfaces. The in- 
cident waves travel in vacuum (or air) and fall on 
the plane surface of a dielectric at the grazing angle y. 
PLACE-OAK BEACH 
EARTH ~SMALL DRY SAND HILLOCKS 
SOME VEGETATION 
«24 oO 
© VERTICAL POLARIZATION 
x HORIZONTAL POLARIZATION 
H- APPROXIMATE THEORETICAL p! 
V- APPROXIMATE THEORETICAL p! 
GRAZING ANGLE IN DEGREES 
Ficure 4. Reflection coefficient p’ versus y. A=10 cm. d=225, 100, 75 ft. 
