ACHROMATIC COMBINATIONS. 
from the lens, the red image R' being nearest, the violet v' most 
distant from the lens, the dispersion being r' v'. Now this dis¬ 
persion may be increased or diminished by increasing or diminish¬ 
ing the concavity or the diverging power of the lens l' l\ It is 
evident, therefore, that such a form may be assigned to the lens 
1 / l', as will give the dispersion r' v' any desired magnitude. 
Let L L and l' l (fig. 37, p. 113) be two lenses made of dif¬ 
ferent materials, the former being a convergent, and the latter a 
divergent lens. Let o be a white object placed at such a distance 
from the lens L L, that its violet and red images would be formed 
at v and r, the distance v r being therefore its dispersion. But 
instead of allowing the rays transmitted through the lens ll to 
form this series of images, we will suppose them intercepted by 
the lens L' l\ and since the images would fall within its focal 
length, the effect of l' v will be to throw the images to a greater 
distance from it; but its effect upon the violet image v, will be so 
much greater than its effect upon the red image R, that the dis¬ 
tance of V from the lens will be more increased than that of R, 
by a space exactly equal to v r, and consequently the two images 
will be made to coalesce, and the system will thus be rendered, 
for all practical purposes, achromatic. We say for all practical 
purposes, inasmuch as although the conditions here supposed will 
produce the coincidence of the red and violet images, they will 
not rigorously produce the coincidence of all those of the inter¬ 
mediate colours. Nevertheless, the general effect will be the 
production of an image sensibly exempt from chromatic con¬ 
fusion. 
A compound lens, which produces such an effect, is called an 
ACHROMATIC LENS. 
68. The materials which have been found most valuable for 
achromatic lenses, are flint and crown-glass, which differ con¬ 
siderably in both their refractive and dispersive powers. The 
refractive and dispersive powers of these sorts of glass, vary 
according to the proportions of their constituents, but they may 
always be rendered such as to fulfil the conditions necessary for 
an achromatic lens. 
69. The forms of the lenses shown in fig. 38, are those of a 
plano-concave of flint, and a double convex of crown glass. It 
is neither necessary nor expedient that these forms should be 
adhered to. The crown-glass lens may be double-convex with 
unequal convexities, or it may be plano-convex or even meniscus. 
The flint-glass lens may be in like manner double-concave, with 
unequal concavities, or it may be plano-concave, or concavo- 
convex. In the same way the curves of the surfaces may be 
indefinitely varied, the compound lens having still the same focal 
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