464. - PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
with M), » = F(v) = 0 and E = £)/2. Clearly, the 
effects of diffraction are not confined to the shadow 
region but extend considerably into the illuminated 
zone. If the receiver is sufficiently deep in the 
shadow, about » > —1, the following approximate 
formula holds: 
0.225 
v 
a 
Ep 
2=> 
ABOVE LINE OF SIGHT V——> 
0.8 
MAGNITUDE OF RELATIVE 
FIELD STRENGTH E/Eo 
0.1 = 
Seu 
ai ales 
(e) 
(o] -{ -2 3 
Figure 4. Magnitude of relative field strength E/E 
versus 0. 
Polarization. Large Angles 
It may be noticed that in the preceding equations 
no reference is made to the state of polarization of 
the diffraction field. The results of the approximate 
Fresnel-Kirchhoff theory are independent of the 
state of polarization in agreement with observation. 
If the angles of diffraction (a; and a, Figure 2) 
become. large, larger than a few degrees, for instance, 
the approximate theory no longer applies. The 
deviations from the Fresnel formulas then go in 
opposite directions for the two states of polarization. 
If the electric vector is parallel to the diffracting 
edge, the field in the shadow at large angles is 
slightly diminished as compared with that given by 
the Fresnel formulas; if the electric field is per- 
pendicular to the diffracting edge, the diffracted 
field in the shadow at large angles can become appre- 
ciably larger than the calculated one and, in the case 
of very large angles, the excess may reach the mag- 
nitude of, say, 6 to 15 db. In the region above the 
line of sight, the sign of the polarization effect is 
reversed (slight increase for polarization parallel to 
the edge, appreciable decrease for polarization 
perpendicular to the edge). : 
These effects are entirely analogous to those that 
are observed when the currents induced in the surface 
of the obstacle cannot be neglected and they have 
the same physical origin. 
360 
LTT 
Bail 
ABOVE LINE OF SIGHT 
Ficure 5. Phase lag (ordinate) of relative field 
strength (E/E) versus » (abscissa). 
