86 TECHNICAL SURVEY 
minimum at c’, etc., approaching a value ZZ’ for 
the unobstructed wave. Moving in the other direc- 
tion, into the shadow, the vector moves to the right 
from A, decreasing steadily to zero. 
The power intensity versus,v is plotted in Figure 
26, and the points B, C, D, etc., corresponding to 
those in Figure 25 represent the exposure of 1, 2, 3, 
etc., half-period zones below Mo. The maxima and 
minima occur a little before these points are reached. 
This curve may be plotted from the table of Fresnel 
integrals with the equations 
Fo20RLG, 
7=OR Ss; (38) 
<5 +0), 
where 2? is the relative power intensity compared to 
the unobstructed wave. The relative electric inten- 
sity is Pog? 
Wu (ee j (39) 
| 
U 
Figure 26. Relative power intensity—straight edge 
diffraction. 
Equation (39) is plotted in Figure 27. The portion 
of the curve for —v has been drawn to the right and 
is to be used with the right-hand ordinate. 
z RELATIVE INTENSITY 
z RELATIVE INTENSITY 
FicureE 27. Relative electric intensity—straight edge 
diffraction. 
The phase lag ¢ due to diffraction may be deter- 
mined from the angular position of the vector R in 
Figure 25. In the illuminated region the phase lag 
oscillates about the reference value, Z’Z, and is 
given by x 
Se 19. 
A tan ei 
At the shadow line the relative value is the same as 
Z'Z. In the shadow region the phase lag varies 
continuously along a parabolic curve and is given by 
04 20 
7) a) 
Z 03 15 = 
° (2) 
q 
= oo 10 
2 on 52 
2 o: 
fs 
o 0 Or 
2 re 
2 z 
Z-01 <q 
aw a 
as 
Ficur£ 28. Phase lag—straight edge diffraction. 
vet 
™> + 7 
The phase lag relative to that of the shadow line 
is plotted in Figure 28. The portion of the curve 
for —v is drawn to the right, and its ordinate, on 
the right, has a different scale from that used with 
the +» portion of the curve. 
Location of Maxima and Minima 
When the source is close to the diffracting edge, 
the positions of the maxima and minima in the 
illuminated region may be determined by the follow- 
ing analysis. The effect of the wave RM (Figure 29) 
at P’ may be considered to be due to the upper half 
of the wave (above FR), which is unaffected by the 
edge, and the lower half of the wave (below R), 
which is partly shielded by the edge. If RM contains 
an even number of half-period elements the inténsity 
at P’ is a minimum. If the number of half-period 
elements is odd the intensity is a maximum. That is 
MF’ — RP =, 
where n is an integer with values 1, 8, 5, etc., for 
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 S for loci. 
(40) 
Ficure 29. Path differences at a straight edge. 
