Dll'I'K ACTION OK KVUIO WAVES 



125 



Figure 16. Fresnel zones in the shadow region. 



Figure 17. Fresnel zones on the shadow line. 



In Figure 17 the observer is at the geometrical 

 edge of the shadow. Only one-half of the wave is 

 effective and the electric intensity is reduced to 

 one-half, considering the unobstructed wave as unity. 

 Outside the edge, Figure 18, at a distance ab the 

 electric intensity is that due to the half of the 

 wave, plus such portions of the zones between a and 

 b that are uncovered. If an even number of zones is 

 uncovered there is approximately a minimum of 

 radiation received at the line a, that is, the half 



a b 



Figure 18. Fresnel zones in the illuminated region. 



wave plus the effect of the two zones, x /i + m\ — mi, 

 for the case shown. If a were moved to the right so 

 that slightly less than one zone were uncovered there 

 would be a maximum, Yi + wh, in which case m\ is 

 greater than one-half owing to the partial screening 

 of the other zones, which, if allowed to operate, 

 would reduce the effect due to the right-hand half 

 of the central zone. For this reason the fringes 

 formed outside the shadow may exceed the electric 

 intensity of the unobstructed wave. As a is moved 

 to the left, more zones are uncovered, and the 

 maxima and minima are spaced approximately 

 according to the radii of the zones; that is, the 

 distances are proportional to the square roots of 

 1, 2, 3, etc. 



15.4.6 



Fresnel Integrals 



The preceding discussion is approximate and 

 provides a qualitative picture of diffraction phenom- 

 ena. The problem will now be formulated quanti- 

 tatively by the method of Fresnel. Since the applica- 

 tions in view all have to do with diffraction by 

 straight edges, slits, etc., the theoretical approach 

 will be limited to diffraction of cylindrical waves by 

 long edges parallel to the axis of the cylinder. The 

 diffraction images of the source will then be bright 

 bands also parallel to this axis, and the whole prob- 

 lem may be reduced to the consideration of rays in 

 a plane perpendicular to the axis. The fact that in 

 the applications to be discussed later the illumina- 

 tion is due to a point source rather than a line source 

 is probably of little importance provided the distance 



