tlie Colours of Mixed Plates. 693 



the rings and other characteristic features of the halo 

 shown in this graph are fully in agreement with those 

 observed in experiment for this case. The total number 

 of rings seen in the halo increases when the plate is held 

 obliquely, as the path-difference between the undeviated 

 rays passing wholly through the two media is greater than 

 for normal incidence. 



As in the case of normal incidence, we have also to 

 consider a second set of rings in the halo due to light 

 diffracted from the edges of the wave-fronts towards the 

 less refrangible medium after traversing paths lying wholly 

 in one or the other of the two media, The course of such 

 diffracted rays is indicated by dotted lines for the three 

 cases dealt with above in fig. 2 (a), fig. 3 (a), and fig. 4. 

 The path-difference of such rays may be readily evaluated, 

 and the positions of the rings in the halo produced by them 

 may be found. 



The expressions for the path-differences are given by 



fit sec -KJr + 1 \ tan f' + ftan (45 + -^] — tan ^ > sin 6 \ 



— %t. tan (45 + |P) sin yjr f — t sec yjr'. I 



Fig. 2 (a). 



fit sec yfr + 1 tan yfr' + i tan / 45 + -^ )— tan ty I sin \jr' 



— \t . (an U5 + ¥\ sin 0-tsecf'. ! 



Fig. 3 (a). 

 [it cos-^ — t cos ylr' + ^t sin D . . . Fig. 4. 



When D = all the three expressions become identical 

 and equal to 



(fJLt COS t^— t COS-v/r'). 



The general result is the same as before — namely, that 

 owing to the superposition of the two sets the first few 

 rings in the halo vary in visibility with their position. It- 

 should be noticed that the rays diffracted towards the liquid 

 in fig. 2 will be superposed on those diffracted towards the 

 air in fig. 3, and vice versa. Hence the visibility of the rings 

 will not fluctuate in identically the same way on both sides 



