1)11 I ''KACTION OK KADIO \VA\KS 



131 



20 



15 z 



< 



a 



< 

 10 cc 



z 



c O 

 < 



_J 

 li. 



o° 



UJ 



_1 



(9 



'0 1 2 3 4 5 



v 



Figure 28. Phase lag — straight edge diffraction. 



maxima and 2, 4, 6, etc., for minima. The difference 

 MP' — RP' is a constant, and the locus of the 

 point P' is a hyperbola having M and $ for loci. 

 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 a; to a maximum or minimum may 

 be computed as follows 



SP' = (a + b) 1 + 



(a + by 

 Since x is small compared to a + b 



x- 



SP' = a + b + 



2(o + b) 



also 



MP' = b + - h . 



Therefore from equations (40) and (41): 



1 \ n\ 



MP' - RP' = %{\- 



2 \b a + b 



hence 



->/ 



b (a + b) n\ 



■ (42) 



(43) 



where n is odd for maxima and even for minima. 

 a. 



SOURCE 



Figure 30. Rectangular slit. 

 154.10 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 (31) 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 Ay = 0.5 the 

 chord (see Figure 20) will extend from approximately 

 C = -0.25 to C = +0.25. The resultant R ^ 0.5 

 substituted in equation (37) gives a power intensity 

 of )i relative to the unobstructed wave and a field 

 strength of 0.353. 



The field intensity at P' is due to the same length 

 Av but taken over a different portion of the spiral. 

 For this purpose, it is desired to use distances along 

 the plane PP', x, instead of s (Figure 30). 



a + b 



-4 



b\ (a + b) 



2a 



(44) 



Figure 29. Path differences at a straight edge. 



Thus the portion of the spiral nO in Figure 31 from 

 v = 0.9 to v = 1.4 has an average value of v = 1.15 

 which multiplied by the radical term of equation (44) 

 gives x. The chord connecting these points is 0.43, 



