82 Mr. A. Schuster on the Elementary Treatment 



y/pk . (y/l — v/3)/2, that of the third \/pX . ( v / lT-\/7)/2, 

 and so on. 



The total effect of all the strips on one side of after the 

 first will therefore be 



1 



IT 



[(•7- S3) - (</ll- Si) + ( Vl5- v^ll) -. . . ]. 



The expression in square brackets converges towards the 

 limit -5420, and hence the effect of a wave of indefinite 

 extent from M T outwards will be *5420/7r=*1725. 



From this we may calculate the effect of the first strip OM 1? 

 for each half of the wave-front on either side of must produce 

 an amplitude of one half. As the effect of the second strip 

 counteracts that of the first, the latter must cause an am- 

 plitude at P, which is numerically represented by *6725, 

 the amplitude of vibration in the original wave being taken 

 as unity. It is now easy to calculate the amplitude of suc- 

 cessive diffraction-bands (fig. 3). P represents the point at 



Fig. 3. 

 



B 



/ 



which the amplitude is to be calculated, L A is a section of 



the plane wave-front, and A B a section of the screen which 



casts the shadow. The intensity at P will then be a maximum, 



to the degree of accuracy of which our method is capable, if 



the screen cuts off all strips on one side except the first, for 



q 



in that case PA=PO+ -,\, and the phase due to OA is the 



1 



same as that due to a distance PO + rr X. If the screen were 



o 



removed further away from it would expose parts of the 

 wave-front differing in distance by more than half a wave- 

 length from the latter value, and diminishing therefore the 

 total intensity. According to the strict calculation, the 

 resultant of OA shows a difference of phase slightly less than 

 that given here, and therefore the first maximum will be 

 reached when the is a little nearer to A, but the difference 

 is negligible. 



