OX A CERTAIN CLASS OF FRAUNHOFERS DIFFRACTION-PHENOMENA- 3 



2) ^ e %ee09{ma ~ B) ^ n r(c)+i n . l 2n(cost>id)J n (c) + cos(3nd)J* n (c)+ ) 



o 



+ i"- 1 .2n(cos(2nd)J 2,l {c)+cos{4nd)J in {c)+ \ 



when n is odd. 



Supposing n is very large compared with c, we can show that the 

 sum of the series within the brackets is negligible. 



The convergent series for J n {c) can be written 



c n P / <? c 4 \ 



/n(c)= 2 n ll{n)\}~\2\n+\) ~ 2!2*(n+l)(n + 2)J 



"A3! 2«(n+l);n + 2)(n + 3)~ 4! 2 8 C«+l)(/i + 2)(« + 3)(n + 4)/ ~ J 



If c<8. (w + 2), the terms in parenthesis are always positive, 

 so that 



Consequently the series 



J "(c) cos d + J" 2 "(c) cos 2n£ + 



c" 



^ 2"//(n) ' 2 2 "//(2») 

 th 



+ ^ ##»-> x + > which again is less 



an (w) — r — /ecvi > îl ver ^ sma11 c i uantit y wnen M 



is large. Similarly, we can prove that the other series within the 

 brackets are negligible; accordingly we arrive at the result 



Si c cos (ma — Ô) 

 e = n J°(c) {na = 27z) 



The expression for the intensity of the diffracted ray for the 



