186 PROGRESS IN MICROSCOPY 



The equations to be used are, therefore: 



, \n > n (;; —u)e\ , ., . ,. 



b > a\ , ; ,[ \ = c-a = b-c = {b~d)2 



\n < n {n-u)e\ ^ ^' 



(7.5) 



, r. ] = a—c = c—b = {a—b)2 

 n < n {n—n)e\ ^ '^ 



a > b 



These data are not ahered if the two waves i^i and E^ are inter- 

 sected as shown in Fig. 7.3, i.e. if 6 > J. There remains to determine 

 whether n' > n or n' < n. To solve the problem once and for all, 

 a sample (whose index is known), is measured. 



Let us take a numerical example: 



(1) Testing the adjustment. A sample, whose index is known to be 

 /; = 1-550 and of thickness e = 10//, is immersed in a medium (index 

 n'~= 1-527). Then, {n-n')e = 0-23//. 



Having set the instrument for the first-order purple to be developed 

 around both images, these appear in two different shades. A[ is, as 

 before, still the left-hand image and A'., the right-hand one. The tints 

 observed in both images are correlated to the path differences 565-f 

 + 0-23 = 0-588// and 0-565- 0-23 = 0-542//. According to Newton's 

 scale, the image correlated to 588 // is indigo and the one correlated 

 to 0-542 // is red. If it is found that the left-hand image {A[) is indigo, 

 a = 0-588 // and the arrangement is either that shown in Fig. 7.6 

 or 7.7. In the present case, the sample is determined (« > /?'), and 

 the figure observed is correlated to Fig. 7.7. In this way the position 

 of the microscope element which can take effect on J can be determined. 

 In this position, the left-hand image (^i) forms part of the lower wave 

 (the direction of light is shown next to each figure). If, now, an unde- 

 termined sample is dealt with, it is ascertained that, for above mentioned 

 position of the adjusting element, the only possible arrangements are 

 those shown in Figs. 7.4 and 7.6. 



(2) Measuring the path difference of an undetermined sample. The 

 sample is immersed in a medium, of known index n' . Observation 

 in the polarizing interference microscope discloses that when the field 

 around the images is purple (c = 565 //), the left-hand image {A[) is 

 bright yellow {a = 0-332 //) and the right-hand image (^o) green 

 {b from 0-747 // to 0-826 //). Then, b > a. However, calibrating the 

 known sample reveals that the left-hand image belongs to the lower 

 wave, thus correlating with Fig. 7.4. The sample index n is lower than 

 the index of the medium in which the sample is immersed. Detecting 



