406 Prof. Henry A. Eowland on Gratings 



The total integral will then be 



ba/ju 

 sin ?i ■— -j __ a p w 



-f- —Jj^ — + (pV"+M»ds [ 1 + e ib ^ + ^h* + &c] , 



sin -|£ %lL 



As before, multiply this by the same with the sign of i 

 changed to get the intensity. 



Example 1. — Equal Distances. 

 The space a contains n' — l equidistant grooves, so that 



. bail 

 sin — — 



. baa 

 An 



Hence the displacement becomes 

 baa 



>aul tbfi J J 



sin n 



sin , 

 In' 



As the last term is simply the integral over the space -/ in 



a different form from before, this is a return to the form we 

 previously had except that it is for a grating of nnf lines 



instead of n lines, the grating-space being — . 



Example 2. — Two Grooves. 

 n>m bay. 



But baa = 2^7r. Hence this becomes 

 2e^*coswN^. 



The square of the last term is a factor in the intensity. 

 Hence the spectrum will vanish when we have 



