DIFFRACTION' OF RADIO WAVKS HY A I'AHAHODIC ('YI,I\1)KH 107 



H ~ --liMiTT X 



^ > 1 (7.4.3) 



.sin irn d'\Vn{Z{))/dfl 



S,, = .S,i defined by (7.16), 



S,, = .S,, with 'r„(zo)/'Wn(zo) in plaoe of U,.U)/Wn{2o), 



S,, = S,, with 'V,.U)/"]VnU) in phice of V„{z^)/W„U), 



^3., ^ i^'Mo / exp ( - l'^'ag)A i'iar'") da/Ai'{a), (7.47) 



•'« exp (i2jr/3) 



(7.46) 



S3Z '^ ^fi 



■'i 



00 exp (-i2ir/3) 



exp ( — ?' ag)Ai'{ai ") da/Ai'{a), 



Szi + Szz ~ ^■i¥o^,(^), 



^((^r) = ? ^^ / exp { — l^'^ag)Ai'{m '*^^) rfQ:/.4/'(a) 



•/« exp {iiir/Z) 



^00 exp (— i2ir/3) 



/ exp { — i'^ag)Ai'{ai^^^) da/ Ai'{a), 



Jo 



H ~ lAhlg ' + ^.(^)J, ^ < 



(7.48) 

 (7.49) 



(7.50) 



(7.51) 



H 



-2/3 



M,Z 



exp(-a,^i ) 



'^.{g) + g-' = -^'''I: 



rf {-as)[Ai{a's)f' 

 exp(-o,grz ) 



g < (7.52) 

 ^ < (7.53) 



^(-aOUKaO]^' 

 a,' = sth zeroof Ai'(a), a[ = -1.019, -47(ai') = 0.5357, 

 Ai'ia^i"^') = -z^''5/'(a:)/2 = -^''V[27^.W(flI)], (7.54) 



A/"(«) = aAi(a). 

 When g is large and positive, 



^.(g) fi'"' - a-^gy" exp (-^VVl2), (7.55) 



'S32 + *^'33 '^^ —iMig 



+ 



"Kl - ^)" 



Lr(l + 0). 



"- exp [-ir + 2^fe(l - i8)/(l + &) ] (7-56) 

 sin K^ + ^ + V2) 



The change in sign of the second term on the right in going from (7.36) 

 to (7.56) comes from (12.2) and the analogous expre.s.sion for 'Wn{z[^) 



