224 



PROGRESS !N MICROSCOPY 



index n of the liquid. Applying the fringe-shift method yields a more 

 accurate measurement of b—a (Chapter VllI, § 6). Figure 8.17 shows 

 schematically the fringe arrangement whose direction is cissumed to 

 be parallel to duplication. Let us consider the point A where the 

 tangent of the edge of the drop is perpendicular to the fringes. This 



C 



Fig. 8.16. Transmitted wave surface 2. 



shows at once the contact angle at A. When changing over from the 

 edge of the drop A to the area outside it but, nevertheless, quite close 

 to A, the path difference varies by A/2 in Fig. 8.17. As mentioned 

 previously, the whole of the interference sequence is determined by 

 locating the dark-fringe shift in white light. If the actual path dif- 

 ference is the observed //2 path difference, then, b — a = A/2. 



To determine the contact angle at a point M other than A or B. 

 the duplication value in the MM' direction is to be included in the 



'"^,1^ 



A' 



/? 



M 



Fig. 8.17. Contact angle measurement with the fringes process. 



equation (8.7) (see Chapter Vlll, § 5). If /^ is the angle formed by MM' 

 with the steepest line PP' at M, then: 



h—a 



= . (8.8) 



(/7— l)<:/cos/^ 



Merely rotating the drop in its holder on the stage so that the 

 position previously held by A be now that of M will obviate the cos/? 



