in Theory and Practice. 403 



The intensity then becomes proportional to 

 1 . 2 N . X v 



^rh Sm Z 7T — Sill* 7T 7 A. 



This vanishes when 



N = m, 2m, 3m, &c. ; 



^=0, 1,2,3, &o. 

 The intensity of the central light, for which N = 0, will be 





(■?'*■> 



This can be made to vanish for only one angle for a given 

 wave-length. Therefore, the central image will be coloured 

 and the colour will change with the angle, an effect often 

 observed in actual gratings. The colour ought to change, 

 also, on placing the grating in a liquid of different index of 

 refraction, since X contains I, the index of refraction. 



It will be instructive to take a special case, such as light 

 falling perpendicularly on the plate. For this case, 



JS7 

 <£ = 0, X=I(l + cos^), and yu, = Isin^n= — . 



Hence 



The last term in the intensity will then be 



Sill 



As an example, let the green of the second order vanish. 

 In this case, Z = -00005. N = 2. Let a='0002 centim.,_and 

 1 = 1. 



Then X[20000+ \/(20000) 2 - (10000) 2 ] =w. 



Whence 



X = 



37300' 



where n is any whole number. Make it 1. 



Then the intensity, as far as this term is concerned, w r ill be 

 as follows : — 



