SITING AND COVERAGE OF GROUND RADARS 81 
with H in feet, f in mc, and W in degrees. Thus for 
100 mc regular reflection may be obtained over 
ridges as high as 35 ft for a grazing angle of 1°, but 
for 3,000 mc’ the roughness could not exceed 1 ft 
in height at this angle. 
Diffraction at Obstacles 
The preceding considerations of Fresnel zones in 
a wavefront will now be applied to the problem of 
radio wave diffraction past hills, ridges, or nearby 
objects. These obstacles will be treated as though 
they were straight edges, narrow screens, or rec- 
tangular slits. 
In Figure 15 is shown a distant source of radiation 
DISTANT 
SOURCE 
! 
! 
1 
| 
| 
| 
1 
| 
| 
| 
Figure 15. Interference of waves at an edge. 
and a diffracting edge. The illuminated edge is 
considered to send out secondary cylindrical wavelets 
which interfere with the plane waves which are not 
shielded by the edge. The dotted and solid lines are 
spaced a half wavelength apart. In the unshaded 
region the intersection of two dotted or two solid 
lines indicates reinforcement and the intersection of 
a dotted and a solid line indicates cancellation. 
The loci of maxima and minima are parabolas 
along which the relative intensities are practically 
constant. In the shadow region, where only the 
wavelets from the edge are propagated, the relative 
beatles 
Ficure 16. Fresnel zones in the shadow region. 
Fiaure 17. Fresnel zones on the shadow line. 
intensity falls off continuously as the angle of 
diffraction is increased, since the angle 6 (see Figure 
10) approaches 90°. 
In Figure 16 is shown the zone system obtained 
because of a diffracting edge with the source of 
radiation at a distance behind the paper and with 
the edge viewed from a screen on which diffraction 
fringes are formed. The observer is within the 
shadow region a distance bc, and the zone system 
is largely obscured as indicated by the dotted lines. 
The radiation received at c comes from the exposed 
zones, and its intensity is equal to a series of the 
form m — m2+m3---, etc., where m is the 
electric intensity due to the exposed portion of the 
first uncovered zone, etc. The sum of this series is 
a fraction of m since the outer zones tend to cancel 
As c is moved to the right, that is, further into the 
shadow, m, will decrease very rapidly without passing 
through maxima and minima. 
In Figure 17 the observer is at the geometrical 
edge of the shadow. Only one-half of the wave is 
D 
y 
d ; 
Ficure 18. Fresnel zones in the illuminated region. 
