418 Mr. R. T. Glazebrook on 



only a small quantity from o>; while, since Q'Qi is small com- 

 pared with PQ', the angle Q 1 PQ / is small compared with w. 

 Hence, if Q'R be drawn at right angles to PQi, the light from 

 P arrives at R in the same phase as at Q/, and the difference 

 in phase at Q Jl between the waves coming from A and P is 

 QiQ' — QiR= QiQ^l — cos a) ) > an( i to the same approximation 

 this is equal to ^kXco 2 . So that if we consider as well the light 

 coming from a point k' lines below A, the extreme difference 

 of phase in the various waves which reach the point Qi is 

 ^(k + k')\co 2 ; k + k f will be the total number of lines in the 

 grating. 



Thus in one of Prof. Rowland's gratings we have 



a = 213 centim., 



37 

 o,= 2^ about, 



k+k'= 14250; 



and hence the difference in phase is about 7X/10. Hence the 

 aperture of the grating is too large to give the best defini- 

 tion : for that purpose the difference of phase in the various 

 secondary waves arriving at the point in question should not 

 be greater than X/4. 



We may conveniently express this difference of phase in 

 terms of the number of lines, the radius of the grating, and 

 the distance between the lines. Let a be the distance between 

 the lines; then 



(k+k') 



and the difference of phase is 



For good definition this difference of phase must not be greater 

 than X/4. Since in the case above the difference of phase is 

 7X/10, we must reduce the number of lines, keeping the 

 distance between them the same, in the ratio of <^/10 to ^/28, or 

 rather more than 2 to 3. Hence by covering up rather less 

 than one third of the grating we should expect to produce 

 better definition. 



In another grating of Rowland's, cr = jyjTTT- centim., a =520 



centim., k+k! — 160,000; and in this case the difference of 

 phase comes out to be about 4*8 x X. The grating is much too 



