CHAPTER V. 
OPTIC AXIAL ANGLE. 
/ 
In petrographic microscopical analysis the optic axial angle is an impor- 
tant characteristic which separates birefracting minerals into two great 
classes uniaxial and biaxial. Optic axial interference figures have long 
attracted the attention of observers and are still considered among the most 
interesting and beautiful phenomena in the whole realm of optics. Until 
recently they have been studied solely in convergent polarized light and 
the methods applicable thereto are in consequence better known and more 
fully developed than those requiring the use of parallel polarized light and 
the universal stage methods first successfully applied by Fedorow. We 
shall accordingly begin with the methods for measuring the optic axial 
angle of minerals in convergent polarized light. 
CONVERGENT POLARIZED LIGHT. 
There are several different lens combinations which can be used to advan- 
tage for obtaining and observing interference figures under the microscope 
in convergent polarized light;* and of these, the one suggested by Amicif in 
1830 has been found to be the best suited for optical measurements. With 
this method the primary interference image, which is formed in the upper 
focal plane of the high-power objective, is magnified and reproduced as 
a secondary image in the upper part of the microscope tube, where it can be 
observed either with a magnifying glass or an ocular with cross-hairs and 
micrometer scale. The small Amici-Bertrand lens, by means of which 
this change of microscope to conoscope is effected, must be inserted at such 
a point between the ocular and objective that the secondary interference 
image observed through the ocular is as sharp and clear as possible. 
Both theory and observation show, however, that all parts of the inter- 
ference figure thus formed are not in perfect focus at the same time. Fig. 
32, page 39, illustrates the path of a light beam from the condenser lens to 
the eye of the observer. From this figure it is evident that the upper focal 
surface of the objective for light-waves entering in all possible directions is 
not a plane, but consists of two coaxial convex, warped, eggshell-shaped sur- 
faces, the mean locus of which roughly approximates a spherical surface. 
In the introduction it was shown that in view of the corrections of the objec- 
tive for a fixed object and image distance, it is not possible to correct the 
objective so that the image in the upper rear focal plane shall also be a plane 
image free from the errors of central and oblique spherical and chromatic 
aberrations. These defects are common to all interference figures and can 
*Thc conditions best adapted for observations in convergent light have been discussed in detail by S. 
Czapski. Neues Jahrb. B.B. 7. 506-515. 1891 ; and by E. A. \Vtilfing. Neues Jahrb. B. B. 12, 405-446. 1898. 
tAnn. Chim. Phys. (3), 12, 114. 1844. 
E. Bertrand. Bull. Soc. Min. Fr., I, 27. 97. 1878. 3, 98, 1880; 8, 29. 1885; for other lens combinations 
see A. v. Lasaulx. Neues Jahrb. 1878. 377; C. Klein. Nachr. d. K. Ges. d. Wiss. zu Gdttingen. 1878. 461; 
Sitz. Br. K.Preuss. Akad.d. Wiss. 1893. No. 18; H. Laspeyres, Zeitschr. Kryst. 4, 460, 1880; 25.380. 1896; 
A. Lacroix, Minor, d. 1. France, 15-16. 1893; F. Becke. T. M. P. M.. 14, 375. 1895; H. Leak, Zeitschr. 
Kryst. 25. 379. 1896; Neues Jahrb. B. B. 10, 429, 1896. 
