IMI'I'H ACTION OK KAIMO WAVES 



133 



to the two parts ill' the spiral Z' to ./ and A' to Z. 

 The resultant amplitude is obtained by adding the 

 two vectors Z'.I and KZ. The sum is R lor a point 

 midway between ■/ and A". The head of the vector 

 is always in the direction Z along the spiral. Typical 

 patterns for narrow obstacles are shown in Figure 33. 



Jl^rtAH/Wl/li-'l 



Av=0.5 



-5 +5— V — * 



Figtjke 33. Diffraction of narrow obstacles. 



is.4.12 Multiple Slits and Obstacles 



Slits or obstacles with parallel sides may be treated 

 by means of the Cornu spiral and the resultant sum 

 of the vectors obtained. Thus, with two slits of a 

 width such that Ay = 0.5 and spaced so that Ay = 0.5 

 may be located on the spiral as JK and Im in 

 Figure 31. The total R is the vector sum of R and 

 R". The field strength pattern is then obtained by 

 sliding the two lengths along the spiral holding their 

 spacing fixed. 



In similar fashion two narrow obstacles would 

 cause two absent sections such as JK and Im and 

 three open sections Z'J, Kl, and mZ. The three 

 vectors, obtained by joining these three latter pairs 

 of points, are combined to give the resultant ampli- 

 tude R. 



15.4.13 Limitations of Fresnel's Theory 



Neither Huyghens' principle nor Fresnel's theory, 

 on which the above treatment is based, is rigorous, 

 and their limitations must be kept in mind when 

 making applications to radio and radar problems. 



In the development of the theory no mention was 



made of the effect of the shape and composition of 

 the edge. Actually within a region of about one 

 wavelength around the edge the wavefront is 

 affected by the presence of the edge. In Figure 34 

 the region of the edge disturbance is DE, and first 

 half period of the wave front is DF. The first half 



tf\t 



[•" 



I 



IL 



Figure 34. Edge effects. 



turn of the Cornu spiral is due to DF. The position 

 of F depends on the point considered. When DE is 

 an appreciable part of DF, the simple Fresnel theory 

 should not be depended upon. This occurs when the 

 field point is at Q, lying at a large angle of diffraction, 

 or at R, close to the edge. 



Near the diffracting edge, a certain amount of re- 

 flection occurs, especially near R. This reflection is 

 divergent and decreases rapidly in intensity as one 

 recedes from the edge. When the edge is blunt or 

 has a large radius of curvature, the amount reflected 

 is increased and the field is affected over a greater 

 distance. Since the angle is near grazing, the nature 

 of the reflecting surface is not important. If Fresnel's 

 theory is applied to spheres and cylinders, the results 

 may be only approximate. 



When the edge and the electric vector are parallel, 

 the theory gives good results. When the electric vec- 

 tor is perpendicular to the edge, the field strength in 

 the shadow region may be several times larger than 

 that obtained with the electric vector parallel, and 

 the theory should then be used only for small angles 

 of diffraction. 



Other discrepancies are due to ignoring the ob- 

 liquity factor and the effect of the inclination of the 

 wavelets with respect to each other. The theory does 

 not give the correct phase angle for the diffracted 

 wave. 



The same objections may be raised for apertures 

 and obstacles whose dimensions are of the order of 

 a wavelength. 



