of Problems on the Diffraction of Light. 



79 



sa 



point P the amplitude due to s at P is --, where a is the am- 

 plitude at s ; and this agrees with the more complete result 

 obtained by Stokes for the case where the angle between the 

 normal to s and the radius vector to P is so small that its 

 square may be neglected. 



We are now prepared to subdivide the wave-front into 

 rectangular elements. 



From P (fig. 1) draw a perpendicular P to the wave- 

 Fig. 1. 



front and consider a central strip S S 1 , of width h, subdivided 

 into smaller areas, the middle one having a length t. The 



effect of this area at P ; as regards amplitude, is —, the ampli- 

 tude of the wave being unity, and t and h being small com- 

 pared to a wave-length. The amplitude of the strip S S 1 can 



be expressed in the form — , where fc is a quantity to be deter- 

 mined. If the effect due to S S 1 is known, that due to the 

 whole wave-front may be calculated ; for on any portion 

 having a length tf a rectangular strip Q Q 1 could be erected, the 

 effect of which could be determined by applying the same factor 

 which converts the effect of the central element at into the 



strip S S 1 ; that is to say, if — is the effect of S S 1 , — will be 

 J ' pX 7 pX 



the effect of the complete wave ; and as this is unity, it fol- 

 lows that fc=\/p\: hence the effect due to a strip of width J z 



and of indefinite length will be —j=> A similar reasoning 



shows that the phase due to such a strip differs by half a right 

 angle from the phase due to the central portion at 0. 



In order to find the effect at P of a wave-front bounded by 



H2 



