THE OPTICAL ELEMENTS OF THE MICROSCOPE LENS SYSTEM. 49 
THE OPTICAL ELEMENTS OF THE MICROSCOPE LENS SYSTEM. 
The primary purpose of the lens system is to present to the eye an en- 
larged image of an object and to render details visible which would other- 
wise not be detected. If the lens system were perfect the image would be 
similar to the object in every respect; all light- waves emerging from any 
given point in the object and entering the system would converge to the 
corresponding point in the image, a condition which would be fulfilled for 
any and all colors of visible light; the image points would be either strictly 
points or areas so small as to appear to the eye to be points; and the image 
would be a true representation of the original. These conditions involve 
not only correction for the spherical aberrations, for the chromatic aberra- 
tions, and the chromatic differences in spherical aberration, but require at 
the same time that the angular aperture of the ray pencil emerging from 
each point in the object be large, in order that the resolution and illumina- 
tion be satisfactory. If only low-angular apertures were to be used, the 
effects of diffraction with high powers would be so serious as practically to 
destroy the definition in the image. To meet all these requirements simul- 
taneously is unfortunately a physical impossibility, since they are in part 
mutually exclusive; in the actual construction, a compromise is therefore 
made and those aberrations are decreased which are the most serious under 
the stipulated conditions of observation. 
It is the task of the optician to produce with the means at his disposal 
(i) glasses and minerals of different refractive indices and dispersion, all 
definitely known, (2) differences in the shapes of the component spherical 
lenses, (3) their distances apart a lens system which shall meet these re- 
quirements in the best manner possible with the serious aberrations reduced 
to within negligible limits, so that the circles of confusion or "blur circles" 
in the image from all causes combined subtend an angle of less than 2' at 
the eye of the observer and appear, in consequence, as points. In design- 
ing the different parts of the microscope care is taken to assign to each par- 
ticular part that portion of the burden it is best adapted to carry. 
THE OBJECTIVE. 
In the optical system of the microscope the major corrections are effected 
in the objective itself; for satisfactory work it is essential that the lens 
system of the objective be corrected spherically and satisfy the sine condi- 
tion, i.e., be aplanatic; also that it be corrected for chromatic aberration 
and the chromatic difference of spherical aberration. The object field in 
the microscope is limited in practice to small areas near the axis and the 
aberrations (as astigmatism, curvature of field, and distortion, which result 
from oblique rays from points far removed from the axis) are practically 
negligible in the construction of high-power objectives, which are corrected 
primarily for rays entering under wide aperture from points on or very 
near the axis. 
Objectives are classified, according to the degree of their correction for 
aberrations, as achromats, semi-apochromats, and apochromats. In the ordi- 
nary achromatic objectives the spherical corrections are made chiefly for the 
yellow- green, which, visually, is the brightest part of the spectrum. In such 
