CHROMATIC ABERRATIONS. 31 
CHROMATIC ABERRATIONS. 
In describing the above third-order spherical corrections, we have as- 
sumed that the light source is monochromatic. If now white light be used, 
as is ordinarily the case, a given lens, although satisfactorily corrected for 
one particular wave-length, may be seriously defective for rays of another 
color, and chromatic aberrations may result. Any glass from which a lens 
may be ground shows noticeable dispersion, the refractive index for blue 
light being higher than that for red. The effect of any collective lens is, 
FIG. 24. 
therefore, to converge the blue rays to a point nearer the lens than that for 
the red rays (Fig. 24) ; the equivalent focal length of the lens varies accord- 
ingly with the wave-length. A simple positive lens shows chromatic under- 
correction for both location and size of image (Fig. 25), while a negative 
element shows chromatic overcorrection. The chromatic aberration of a 
simple collective lens can be readily detected by observing the image which 
L 
FIG. 25. 
it forms of a distant luminous point. At F (Fig. 24) the image is a blue 
disk with a marginal red fringe, while at F T the center is red and the margin 
blue. By combining two lenses, a positive of weak dispersion and a nega- 
tive of strong dispersion, it is possible to make both the image distance and 
also the equivalent focal length of the lens equal for two colors of the spec- 
trum. This applies to the paraxial rays. The lens is then achromatic for 
