CHROMATIC ABERRATIONS. 
33 
piece it is thus possible to compensate the undercorrection in the objective 
so that the eye-piece has just as much greater magnification for red as the 
objective has for blue, and the result is an image practically free from color, 
even to the margin of the axis. This method was adopted by Abbe in his 
compensating oculars. 
In lenses of wide aperture the chromatic aberration varies from zone to 
zone. Thus in Fig. 27 the paraxial rays for blue and red unite in one point, 
P', while the marginal blue ray intersects the axis at P b and the marginal 
red ray at P r . In lenses of the same shape, the higher the refractive index 
the smaller the spherical aberration ; consequently, if the spherical aberra- 
tion is corrected for yellow rays, the blue rays show spherical overcorrection. 
The lenses may accordingly be considered as chromatically corrected in the 
axis and as having increasing chromatic overcorrection toward the margin. 
In simpler objectives no real correction is attempted. The zone of best 
chromatic correction is placed between the axis and the margin, so that the 
"circle of confusion" caused by the overcorrected marginal zone is equal 
to that caused by the undercorrected axial zone. All ordinary chromatic 
objectives are corrected by this method. Abbe was the first to point out 
FIG. 27. 
the importance of this chromatic difference of spherical aberration and its 
detrimental influence on the microscopic image. He showed how a micro- 
scope objective can be spherically corrected for two colors, or, in other 
words, chromatically corrected for two zones. Such an objective has the 
same quality of chromatic correction over the entire opening, the remnants, 
which are left uncorrected outside of the two zones, being too insignificant 
to cause trouble. 
The sine condition also varies for different colors, but is usually corrected 
only for the yellow-green. In the apochromatic objectives the sine con- 
dition is corrected for two colors. These objectives are the most highly 
corrected type yet devised. They are aplanatic for two colors (show no 
chromatic difference of spherical aberration and fulfill the sine condition 
for two colors) and are free from the secondary spectrum. 
As noted above, the corrections in the optical system are made only for 
a single, definite position of the object and image (tube length given) and 
for a definite thickness of cover-slip. For this reason it is essential for the 
best results that the tube length be correct and also the cover-glass thickness, 
otherwise the quality of the image may be seriously impaired. High-power 
dry-objectives are usually fitted with a correction collar to compensate for 
the change in spherical overcorrection resulting from the use of cover- 
glasses of different thicknesses. This defect may also be compensated for 
by changing the tube length, but less expeditiously. 
