SITING AND COVERAGE OF GROUND RADARS 87 
That is, 
SP’ — MP’ = SR — (MP’ — RP’), (41) 
and SR is constant; therefore, the difference of the 
distances of P’ from the fixed points S and M is 
constant. P’ describes a hyperbola, but its curva- 
ture is so small that it almost coincides with its 
asymptotes. 
The distance x to a maximum or minimum may 
be computed as follows 
i 2 j 
SP! = @+o[i+—e| . 
Since z is small compared to a + 6 
2 
SP =atb+ soy 
also 
Therefore from equations (40) and (41): 
ri hablar ass i ati er (eran LO RC 
MP RP’ = 5 (; aa )= Ps 
hence 
= (ear (43) 
a 
where n is odd for maxima and even for minima. 
SOURCE Pp 
Figure 30. Rectangular slit. 
The Rectangular Slit 
A problem similar to the straight edge is the 
rectangular slit (see Figure 30). Cornu’s spiral will 
be used to determine the field intensity along the 
plane PP’. With the slit in the central position, the 
only radiation at the plane is due to the wavefront 
in the interval As = MN. Equation (81) is used to 
determine what length Av corresponds to As. The 
resultant field strength at P is given by the chord 
of the spiral which has a length Av. Since the point 
of observation P is centrally located, this chord will 
be centered on the spiral. Thus, if Av = 0.5 the 
chord (see Figure 20) will extend from approximately 
0) 
Ficure 31. The Cornu spiral applied to obstacles and slits. 
