471 Mr. H. P. Waran : Interferometer Method of determining 



displacement vertically between the two sets that represented 

 the phase difference. The fringes due to the latter acted as 

 the reference marks from which to measure the distance to 

 the bands corresponding- to the former, and a slight lateral 

 shift given to the latter system of bands by rotating the 

 wave-length drum a little served to identity the two in 

 practice, as shown in fig. d (PL VIII.) . 



For mercury, which was the next metal studied, the 

 arrangement had to be. slightly modified, and the specially 

 made ebonite trough described above and shown in fig. 1 and 

 PL VIII. fig. e, had to be used. A modification had to be intro- 

 duced in it in the form of a narrow partition to divide the 

 mercury chamber into two longitudinal halves, so that, as 

 with the silver, we might get half the plate covered with 

 mercury, leaving the other half free as shown in part section 



fig. i. 



We may proceed now to consider the theory of the 

 method and the process employed for the actual evaluation 

 of the phase difference from a measurement of the displace- 

 ment of the metal fringes from the normal system. 



Let t = the thickness of the parallel plate 



and /ui = the refractive index for the wave-length \ used, 

 which maybe calculated out from the given optical constants 

 of the plate, using Cauchy's formulae. 



Then the path difference between two adjacent beams 

 emerging out of the plate because of the multiple reflexions 

 is given by the relation 



2 fjbt cos r = n\, . (1) 



where r is the angle of incidence for these rays within the 

 plate. 



If we count this as the path difference for the starting- 

 band of the Lummer system of fringes, we have a bright 

 band at every position corresponding to an increase in the 

 path difference by X. Thus for the pth band we have 



2 fit cos {r-8r p )={n+p)\. .... (2) 

 Subtracting (1) from (2), we have, since Sr p is small, 



2yui sin r Sr P — p\ (3) 



Further, we have the relations 



sin i = fj, sin r, , 



and sin i p = /m sin ?>, 



sin i — sin i P — jjl (^sin r — sin r p 



+ r v . i — ? 

 2 S1U -* 



= fju . 2 . cos — ^—^ sin — 



