PHYSICAL ASPECTS OF IMAGE FORMATION 



45 



and Ox in a random direction d do not travel along the same paths. 

 Assuming the grating to be perpendicular in relation to the incident 

 light-beam, points O and Ox are reached by the incident rays at the 

 same time but the rays diffracted in the direction of (vibrations 

 originated by O^ lag slightly in relation to those originated by O. 

 Let us drop a perpendicular OH from O to OxX^. From O and H 

 the vibrations diffracted by O and Ox travel together in the direction 

 of Q. The lag of the vibrations diffracted by Ox equates OxH. To every 

 point of the slit AB there is a matching point of slit AxBx to which 

 the same inference applies. At all points of sHts AB and AxBx the 

 phenomenon is identical with that at O and Ox. Therefore all slits 

 may be substituted for their centres. 



The foregoing applies to the other slits too: the path difference 

 increases or diminishes, from one sht to another, by the distance OxH. 

 The vibration diffracted in the direction of d by shts AxBx, AoB^, 

 A3B3, lag by A, 2/1, 3A, etc., in respect of the vibrations diffracted by AB. 

 As the phenomena recur identically within one wave-length or whole 

 multiples thereof, nothing differentiates the sHt-originated vibrations. 

 Figure 1.57 shows there is no difference whatever between the vi- 



1 1 



I 1 I 



Fig. 1.57. The vibrations originated by the slits in the direction of are in phase. 



brations O, H, H\ H", etc., and phenomena occur as if the vibrations 

 originated by 0,0x, Oo, ... were not out of phase. The vibrations 

 diffracted by the slits in the direction of 6 are in phase. Then, am- 

 plitude of the light emitted by the grating in that direction equates 

 the sum of all the amplitudes emitted by the shts of the grating. 

 After passing through the objective Ox (Fig. 1.55) the maximum of 

 light is produced in the focal plane at S'x. The rays diffracted in the 



