80 Lord Rayleigh on Achromatic 



careful consideration. We will suppose in the first place that 

 the lights issuing from the various parts of the aperture are 

 without permanent phase-relation, as when the slit is backed 

 immediately by a flame, or by the incandescent carbon of an 

 electric lamp. Regular interference can then only take place 

 between lights coming from corresponding parts of the two 

 images ; and a distinction must be drawn between the two 

 ways in which the images may be situated relatively to one 

 another. In Fresnel's experiment, whether carried out with 

 mirrors or with bi-prism, the corresponding parts of the 

 images are on the same side ; that is, the right of one corre- 

 sponds to the right of the other, and the left of one to the left 

 of the other. On the other hand, in Lloyd's arrangement the 

 reflected image is reversed relatively to the original source : 

 the two outer edges corresponding, as also the two inner. 

 Thus, in the first arrangement the bands due to various parts 

 of the slit differ merely by a lateral shift, and the condition of 

 distinctness is simply that the width of the slit be a small 

 proportion of the width of the bands. From this it follows as 

 a corollary that the limiting width is independent of the order 

 of the bands under examination. It is otherwise in Lloyd's 

 method. In this case the centres of the systems of bands are 

 the* same, whatever part of the slit be supposed to be opera- 

 tive, and it is the distance apart of the images (6) that varies. 

 The bands corresponding to the various parts of the slit are 

 thus, upon different scales, and the resulting confusion must 

 increase with the order of the bands. From (1) the corre- 

 sponding changes in u and b are given by 



du=—n\D db/b 2 ; 

 so that 



du/A=—n db/b (4) 



If db represents twice the width of the slit, (4) gives a measure 

 of the resulting confusion in the bands. The important point 

 is that the slit must be made narrower as n increases, if the 

 bands are to retain the same degree of distinctness. 



If the various parts of the width of the slit do not act as 

 independent sources of light, a different treatment would be 

 required. To illustrate the extreme case, we may suppose 

 that the waves issuing from the various elements of the width 

 are all in the same phase, as if the ultimate source were a star 

 situated a long distance behind. It would then be a matter of 

 indifference whether the images of the slit, acting as proxi- 

 mate sources of interfering light, were reversed relatively to 

 one another, or not. It is, however, unnecessary to dwell 

 upon this question, inasmuch as the conditions supposed are 



