42 METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
From equation (23) it is evident that the magnification increases with D, 
the optical tube length. This fact furnishes a convenient method for 
changing the magnification in low-power objectives; in medium to high- 
power objectives, however, the corrections are such that the quality of the 
image is more sensitive to change in the tube-length and suffers noticeably 
if great changes are made. The slight remnants of spherical aberration 
resulting from the use of cover-slips of different thicknesses from that for 
which the objective is corrected may be remedied by altering the tube 
length. (The mechanical tube length, /. e., the distance from top to bottom 
of the draw-tube, is altered and with it the optical tube length defined above.) 
THE FIELD OF THE MICROSCOPE. 
The apparent field of the microscope is determined by the apparent 
diameter A'"B'" (Fig. 30) of the diafram A"B" in the eye-piece as viewed 
from the eye-circle. The image thus seen subtends usually an angle of 20 
to 36 at the eye-point. As indicated by the diagram, the ocular diafram 
frames the image from the objective and sharply limits the apparent field. 
The diameter of the apparent field is measured by use of a camera lucida. 
The real field, on the other hand, is measured by means of a micrometer on 
the stage. It varies with the focal length of the objective and with the 
optical tube length. The greater the magnification of the microscope the 
smaller the field. The diameter of the field is not affected by the numerical 
aperture of the objective, as is evident from Fig. 30, and can also be shown by 
observing the field in a microscope and then reducing the aperture by means 
of the condenser diafram. 
THE PHYSICAL SIGNIFICANCE OF THE NUMERICAL APERTURE. 
In the above paragraphs the optical system of the microscope has been 
treated from the standpoint of geometrical optics. From each point of the 
object a bundle of light rays has been considered to emanate, each individual 
ray being supposed capable of separate treatment, irrespective of the others. 
Such separation and individual treatment of the rays is, however, physi- 
cally not justifiable beyond a certain limit. The rays are simply the 
energy flow lines or the paths along which the wave impulse is transmitted. 
In case the object to be imaged is not self-luminous, but is lighted by trans- 
mitted light as in the microscope, the light on emerging from the object 
suffers diffraction (Fig. 34) ; a diffraction pattern is formed in the rear focal 
plane of the objective, and the image in turn is derived from this diffraction 
pattern. Abbe was the first to recogni/e the secondary character of the 
image observed in the microscope and its dependence on diffraction. He 
proved that not only is the degree of similarity of the image to the object 
directly proportional to the number of diffraction spe-tra entering the objec- 
tive, but that the limit of resolution is reached when the iirst diffraction 
spectrum no longer enters the objective. Different objects produce different 
diffraction patterns in the focal plane of the objective; but if the aperture 
of the objective be so small that only the central clement of the diffra< 
pattern of each object is transmitted, the result is an equally illuminated field 
