DIFFRACTION <>!• HAIMO WAVES 



It can be shown that al 

 so that 



terms except the first cance 



ZONE 12 3 4 5 



S = -y/M . 



(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 



RESULTANT 



Figure 12. Phase of a zone. 



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/ir 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 

 that the electric intensity of the wave at the point P 

 is doubled (mi = 2S) and the power intensity is four 

 times as great as for the unobstructed wave. If the 

 aperture is increased to include the second zone, the 

 intensity at P will be reduced nearly to zero. The 



Figure 13. Polarity of zones. 



disturbances from the second zone are out of phase 

 with those of the first zone and equal in magnitude 

 and therefore cause cancellation. 



15.4.4 



Reflection from Rough Surfaces — 

 Rayleigh's Criterion 



A rough surface may destroy all phase relations 

 between the elements on the wavefront. The second- 

 ary wavelets start from the elevated portions of the 

 surface first, since these portions are struck first by 

 the incident wave, and the lower portions send out 

 secondary disturbances at various other times in 

 random phase. It is impossible to arrange any zone 

 system on such a surface for there are all possible 

 phase differences irregularly distributed over the 

 reflected wavefront and each point on the surface 

 acts as an independent source radiating in all 

 directions. 



In Figure 14 is shown a plane surface xy with 

 incident rays SB and SA falling on a raised portion 

 and a crevice respectively and being reflected to P. 

 The path difference is SA + AP - (SB + BP). 

 Since BP and AP are practically parallel, the path 

 difference may be taken as BA — BK. 



BA = 



H 



sin V ' 

 BK = BA ■ cos 2* . 



