MEASURING REFRACTION INDICES — POLARIZING MICROSCOPES 183 



respectively, we have seen (Chapter VI, § 1) that the object-originated 

 path difference, i.e. the path diiference between the ray (1) that passes 

 through the object and the ray (2) passing next to it, is: 



d = {n'-n)e. (7.1) 



However, the interference microscope brings in the path difference 

 J (adjustable as required) between the two waves T^ and 2*2 in the 



^ f r, ^ ^ I I ^2 



-^'; 



■^, 



"L-U ^2 1 i I \ \ r, 



Fig. 7.2. Duplication of the transmitted Fig. 7.3. Duplication of the transmitted 



wave {n > n). wave ( J < (5 and n > n). 



plane areas where there is no object (Fig. 7.1). Hence, the path 

 differences at A[ and A', between the two waves I-^ and I^, shall be 

 (in the case of Fig. 7.1) 



at ^; A-d=A-{n'-n)e, 



at A'. A + d =A + {n'-n)e. 



It is worth noting that there is no need to apply the terms "ordinary" 

 or "extraordinary" to the images A[ and A', as, generally, in full- 

 dupHcation instruments, all the rays were ordinary and extraordinary 

 rays seriatim, or conversely (Figs. 3.20, 3.25, 3.27, 3.28). Throughout 

 the following the left-hand image shall be denoted A[. The interference 

 theory shows that, when the path difference between the two interfering 

 waves is not excessive, a typical tint is developed, featuring the above- 

 mentioned path difference. These tints are detected versus the path 

 difference in Newton's scale shown hereunder. Therefore, three tints 

 are perceived at A[, A', and the remainder of the field. Let us assume 

 that these tints correlate the path difference whose numerical values 

 (in microns, for instance), deduced from Newton's scale are a, b, c, 

 respectively. Then: 

 at ^i J — in'—ft)e=a, .. 



at A'. J + in'-n)e = b. 



Around A[ and A'„ 



whence 



A =c 



(n'-}i)e = c-a=^b-c ^{b- a)!2 . (7.4) 



13 



