306 U. NAGAOKA. 



âR = ^ + -^-^ {ax + by + r.^)- .,7^ 



.j^, a'x + b'y-^c z , 1 , / , ?' , / n- à:^+ (/'+ f-'^ 



-i) 



Let the direction cosines «jf OL be }c, u., v, ;in(l those oï OD be 

 ;/, /^', y' ; then ( 4 ) becomes 



i') 



J22 = (;r a: + //. y + i^z) + -:^-rr {" x + n y + •. z)-— j' — -, 



^ it 1 i\ 



1 / / / /so ^" + ?/ + •'^' 



M/ï'= (;/a; + u-'y + v's) + -^-jr, {nx + //.'^ + v'a)- — 



2ii;' 



In Fraunhofer's diitraction phenomena, // and B! are supposed to l^e 

 very large compared with a;, y z, so tli:it we can neglect the terms 

 containing B, <3r Pi in the denominator. 'Huis 



âli - âR = {)( - ;/) X + {/J. - //) y + 'c^ - v') ?:. 



Writing 



- 



- ^') = n, 



the expression for the intensity of the dittVacted Jiglit becomes 

 (T) I = Mod-.fdae'^'-'"-'"^-""^ 



where the integration extends o\er the wh(jle aperture. 



In Fresnel's diffraction phenomena, we can no Jonu'er neuiect the 



terms -5- and -^. Thus tlie expression f(.)r AR + âR' ljec(3mes very 



complicated. It is, however, somewhat simphfied Ijy taking in the 

 Une LD as shown in Fig. 2. Thereby ;/= — )(, //= — ti, >= — v, 

 because OL and OD are in one Une. Tlius 



