84 TECHNICAL SURVEY 
2 a ee ie A Ee ae 
Fieure 20. Cornu spiral. 
half-periods is AZ, which is thus the resultant effect 
at P of the upper half of the wavefront. A similar 
result is obtained for the lower half. 
It may be remarked that the superiority of the 
dimensionless variable » over s shows itself in the 
fact that one Cornu spiral suffices for all situations 
of the diffracting edge, while the use of s would have 
necessitated the construction of a special spiral for 
each specific set of values, a, b, and X. In Figure 20 
the values v = 1 and v = 2 are marked and corres- 
pond to path differences A = d/4 and A=), 
respectively. 
Equation (30) shows that the electric field strength 
in the diffraction region which is due to a certain 
section of the wavefront is proportional to the 
corresponding value of R. Hence, it follows that the 
power per unit area is proportional to R*. Let W 
denote peak power per unit area at the point P for 
a certain arbitrary value of R. Then 
W=K-:- RF, (36) 
where K is a certain constant. When the whole wave 
is acting, the integration limits extend from v = 
— otov = + @, that is, along the full length of 
the Cornu spiral. The coordinate difference between 
the foci of the spiral being (1,1) (see Figure 20) it 
follows that their distance is R = +/2, so that the 
corresponding peak power per unit area Wo is, by 
equatiori (36), Wo = 2K which defines K as 4Wo. 
Hence it follows that equation (36) may also be 
written as 
Ls 
Were. (37) 
Straight Edge Diffraction 
Using Cornu’s spiral the diffraction pattern due to 
a straight edge may be obtained. In Figure 23 is 
shown a diffracting edge at Mo. At P the upper 
half of the wave is effective, and on Figure 22 the 
amplitude is AZ of length 1/+/2. The square of this 
is one-half, which by equation (37) is multiplied by 
¥% to get for the power intensity at the edge of 
the shadow. The electric field intensity is }, 
Consider next a point such as P’ at a distance x 
above P (see Figure 23). To be specific, the point 
Figure 21. Division of wavefront into half-period zones. 
