GRATINGS IN THEORY AND PRACTICE' 533 



The second series of integrals will be 



/ 



The total integral will then be 



8inw ^ri * 



sin^i L *&, ^ Jo 6 JL 



i 



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' 1 equidistant grooves, so that y^ = y z y\ 



= etc., = -, 

 n' 



metals with some one metal, such as iron. Malting the iron spectrum 



-. a 

 v tt>n^ n 



Hence the displacement becomes 



bttu 

 sin n . 



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 nn' lines instead of n lines, the grating space 



being . 



EXAMPLE 2. Two GROOVES 



But ba/jt = 2 ATT. Hence this becomes 



. v\_ y 



a 



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

 spectrum will vanish when we have 



~n~ ' 

 4 A theorem of Lord Rayleigh's. 



