SITING AND COVERAGE OF GROUND RADARS 719 
Figure 11. Fresnel zones. 
Neglecting \?/4, the radius 7; = +~/od and the 
radii, ro = V/20A, rs = +/3bA, etc., and in general 
Tm = Vimbo . (11) 
The corresponding areas are approximately 7b), 
2rb\, 3rbA, and mmbdA. The area of the central zone 
is rbA, and each succeeding ring or zone is slightly 
greater. 
The effect which one of the zones produces at P 
is proportional to its area and inversely proportional 
to its distance from P. These factors compensate as 
the radius increases, so that the successive zones 
may be regarded as producing equal and opposite 
effects at the point P. The zones become less effective 
further from the center owing to the increased 
obliquity, since the effect at P is proportional to 
i + cos @ (see Figure 10). The resultant effect may 
be represented by a series of terms of alternate sign 
which decrease slowly at first and then more rapidly, 
eventually becoming zero, thus: 
S = mi — m2 + mz, etc., 
1 1 1 
= 9M is (Gm = m2 + sm) 
lee 
1 
3 ma + 5) be + 5a. 
It can be shown that all terms except the first cancel 
so that 
S= em 5 (12) 
The resultant effect of the entire wavefront is equal 
to one-half of that due to the central zone. 
The secondary wavelets from the central zone 
unite into a disturbance whose phase is midway 
between the center and the rim. This may be shown 
by dividing the first zone into rings such that the 
effect of each ring at the point P is equal in ampli- 
tude, and the phases range over half a complete 
period. The electric vectors corresponding to these 
subdivisions may be combined to obtain the resultant 
phase as in Figure 12. The vector for the central 
area of the first zone is AB with succeeding sur- 
rounding rings represented by BC, CD, etc. These 
vectors fall along the perimeter of a half circle, as a 
consequence of which the resultant amplitude is 
2/x times the sum of the amplitudes of the individual 
vectors. The vectors for the second zone are shown 
dotted. 
In Figure 13 is shown the first' six half-wave zones 
and the phases relative to the center of the first zone 
are indicated. A set of alternate black and white 
zones as shown at the top is known as a zone plate. 
If a screen is provided which has an aperture of 
the same diameter as the first zone, it will be found 
