196 PROGRESS IN MICROSCOPY 



Let us take the numerical instance mentioned in § 1 : 

 If f = 20// and n' = 1-525 the equation (7.6) yields: 



, 0-233 

 „=„'__-^ = 152. 

 20 



As stated above, the index is only approximated. Accuracy does not 

 extend beyond two places of decimals. 



Fringe-shifting method 



When /; < n, the equation (7.8) yields: 



n =n'-KXie. (7.9) 



As e and //' are determined, measuring the shift K of the figures now 

 evinces the index n of the object. Reverting to the previous example 

 {n = 1 -527 and e = 20 //) it is found that the fringe shift of the spectral 

 green line of mercury (A = 0-546/a) equates the fraction K == 1/2 27 

 of the fringe inter-space. Then: 



0-546 

 /; = 1-527-——= 1-515. 

 45-4 



Accuracy depends on the precision with which e and K are known. 

 Assuming that e be measured with a one-micron accuracy: Aeje = 1/20. 

 If K is determined with an accuracy within 1/40 of the fringe 

 inter-space, then, J /C/ AT = 1/20 since A^^ 1/2. The relative error 

 J{n' — n)J{n' — ti) is derived from: 



A(n'-n) Je JK 

 n'-n e K 



whence 



zl(//-70^0 001. 



In the example selected, the accuracy attained is correct to one 

 unit of three decimals. As stated previously, the aperture of the 

 incident beam is a prominent factor in measurement accuracy (cf. Chap- 

 ter VIII, § 2). 



When the thickness e is not known 



The Barer process consists in immersing the object seriatim, when 

 feasible, in two media whose indices //[ and n!^, are known. Now, 



