MEASURING REFRACTION INDICES— POLARIZING MICROSCOPES 207 



the area (1) to area (2), the tip B' in contact with f?i, a.., may be 

 rounded off (0 varies from zero to Q in the area B'). There is no need 

 to change over to white light. 



Immersion measurement 



In chemical microscopy, the method is suitable for measuring the 

 index of a melted autectic. We have seen that, in Kofler's method, 

 a glass powder of known index is immersed in the liquid (§ 4). In the 

 differential method, the glass particles are substituted for readily 

 purchasable tiny glass spherules. 



Figure 7.36 is a vertical cross-section of the specimen, passing 

 through the centre O of such a spherule of index /?', radius r, and 

 which is immersed in a liquid whose index n is being measured. Let 



(I). 



Fig. 7.36. Index measurements by immersion of spherules in the liquid. 



US observe the specimen through a microscope whose duplication d 

 is set at right angles to the fringes. The specimen's horizontal view 

 takes on the appearance shown in Fig. 7.37. Since duplication is 

 very weak, it is not shown in Fig. 7.37. It is assumed to be in the 

 direction XX' . If the indices of both spherule and liquid, n' and n 

 respectively, are equal, the fringes within the imaged spherule are 

 spaced as are the outer ones and in alignment with each other. 



When n = /;', all fringes, save the central one, are shifted. Let us 

 measure the shift d of one of the fringes along the diameter XX' which 

 is at right angles to the fringes. As mentioned previously, the two 

 duplication-originated waves are not shown in Fig. 7.37. Their path 

 difference at random point A along XX' is J + 6 and, outside the 

 sphere, d. A simple calculation shows that: 



6 =2d{n'-n)i2ind 



(7.21) 



