Interference-Bands. 79 



FresnePs Bands. 

 In this experiment the two sources of light which are 

 regarded as interfering with one another must not be inde- 

 pendent ; otherwise there could be no fixed phase-relation. 

 According to FresnePs original arrangement the sources 1; 

 2 are virtual images of a single source, obtained by reflexion 

 in two mirrors. The mirrors may be replaced by a bi-prism. 

 Or, as in Lloyd's form of the experiment, the second source 

 may be obtained from the first by reflexion from a mirror 

 placed at a high degree of obliquity. The screen upon which 

 the bands are conceived to be thrown is parallel to OjC^, at 

 distance D. If A be the point of the screen equidistant from 

 Oi, 2 , and P a neighbouring point, then approximately 



where 



1 2 =6, AP=u. 



Thus, if X be the wave-length, the places where the phases 

 are accordant are determined by 



u = n\D/b, (1) 



n being an integer representing the order of the band. The 

 linear width of the bands (from bright to bright, or from dark 

 to dark) is thus 



A = \D/6 (2) 



The degree of homogeneity necessary for the approximate 

 perfection of the nth band may be found at once from (1) and 

 (2). For, if du be the change in u corresponding to the 

 change dX, then 



du/A = ndX/X (3) 



Now clearly du must be a small fraction of A, so that dX/X 

 must be many times smaller than 1/n, if the darkest places 

 are to be sensibly black. But the phenomenon will be tole- 

 rably well marked, if the proportional range of wave-length 

 do not exceed 1/(2??), provided, that is, that the distribution 

 of illumination over this range be not concentrated towards 

 the extreme parts. 



So far we - have supposed the sources at 1; 3 to be mathe- 

 matically small. In practice the source is an elongated slit, 

 whose direction requires to be carefully adjusted to parallelism 

 with the reflecting surface, or surfaces. By this means an 

 important advantage is obtained in respect of brightness with- 

 out loss of definition, as the various parts of the aperture give 

 rise to coincident systems of bands. 



The question of the admissible width of the slit requires 



H2 



