ACHKOMATIC COMBINATIONS. 



from the lens, the red image E' being nearest, the violet v' most 

 distant from the lens, the dispersion being E' v'. Now this dis- 

 persion may be increased or diminished by increasing or diminish- 

 ing the concavity or the diverging power of the tens i/ I/. It is 

 evident, therefore, that such a form may be assigned to the lens 

 I/ i/, as will give the dispersion E' v' any desired magnitude. 



Let L L and i/ i/ (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 E, the distance v E being therefore its dispersion. But 

 instead of allowing the rays transmitted through the lens L L to 

 form this series of images, we will suppose them intercepted r by 

 the lens i/ L', and since the images would fall within its focal 

 length, the effect of L' i/ 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 E, that the dis- 

 tance of v from the lens will be more increased than that of E, 

 by a space exactly equal to v E, 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 



ACHEOMATIC 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 



117 



