4 6 
METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
By using oblique light, it is often possible to include in an objective the 
first diffracted beam (as indicated in Fig. 36, where .-1 is the source of light 
and PL\ the first diffracted beam which would be transmitted were the 
incident beam the pencil LP) and thus to render visible details half as large 
as that indicated by equation (8) ; wherefore the value of a condenser of 
large aperture, equal at least to that of the objective. The smallest 
possible detail resolvable is accordingly 
* = - (9) 
20. 
FIG. 36. 
Any increase in the numerical aperture of an objective enhances its re- 
solving power and also the brightness of the image. The numerical aperture 
(n sin ) may be increased either by increasing u or by raising the refractive 
index of the medium between the objective and the object. Thus if with 
a dry objective of numerical aperture 0.85 (sin w = o.85; M = 58i3 ; ) an 
immersion liquid (cedar oil) of refractive index 1.51 be used, the numerical 
aperture of the combination is no longer 0.85 but n times 0.85 = 1.28 approxi- 
mately. As noted above (page 37), the relative brightness of an image is 
directly proportional to the square of the numerical aperture of the objec- 
tive; the image observed through the immersion liquid appears therefore 
I 28 2 
- = 2.28 as bright as when observed without the liquid, even with the 
o. 85 
same magnification. With the dry objective the smallest resolvable detail 
in sodium light of wave-length 0.000589 mm. is 
X 0.000589 
2a 2-0.85 
= 0.00035 mm - 
while with the oil immersion 
X 0.000589 
= 0.00025 mm. 
2nsin u 2- 1 .51 -0.85 
