PHYSICS OF THE EIGHTEENTH CENTURY. 283 



of crown, with such a relation between their refracting angles that when 

 opposed they shall counteract each other's dispersive effects, and yet 

 leave a refracting effect. 



It will not be difficult to understand the principle of the achromatic 

 lens if we suppose, for the moment, that flint-glass has the same refract- 

 ing power as crown, and that we have a prism of each placed as in 

 Fig. 133 ; then a ray of light E F would be refracted in the directions 

 F L, L M ; and if the refracting angle A B c of the one prism equals the 

 refracting angle B c D of the other, the emergent ray L M would be 

 parallel to the incident ray 

 E F, but for the greater dis- 

 persive power of the flint- 

 glass, which would more 



than counteract that of the A\\\\\\\\\\ -^r~ 



other, and consequently LM Am ^^ 



would really only represent 

 the mean direction of a di- 

 verging bundle of coloured 

 rays due to the excess of the 

 dispersive effect of the flint- FIG. 133. 



glass. Now, by lessening 

 the refracting angle BCD 



of the flint-glass prism, we could make it such that the dispersive 

 effect of the flint-glass would neutralize the oppositely-directed dis- 

 persive effect of the crown, and B c N being that angle, the emergent 

 ray H K would be free from colour but it would plainly now be de- 

 viated from the original direction, by reason of the uncompensated 

 refractive action of the crown-glass prism. The result, then, is that 

 we obtain, without colour, a refractive effect, the direction of which is 

 due to the crown-glass prism. We have supposed that the refractive 

 powers of the two kinds of glass are equal, as the modification which 

 their slight difference would introduce into the arrangement can be 

 easily understood. But a more important modification of the above 

 explanation is required by the actual facts. The emergent rays have 

 been spoken of as without colour. Now, this is a result which, strictly 

 speaking, cannot be attained. The only thing that the adjustment of 

 the angle B c N can effect is the emergence from the system in parallel 

 directions of two given sets of prismatic rays, e.g., the red and the 

 green rays, the yellow and the violet, and so on. There will still exist 

 a certain small amount of dispersion. But, using a system of three 

 prisms instead of two, three spectra instead of two may be made to 

 overlap, so that an almost perfect achromatism is obtained. Fig. 134 

 will show the manner in which these principles are applied in the con- 

 struction of an achromatic lens. L L is a convex lens of crown-glass, 

 and //a concave one of flint-glass. A ray of light s falling on the 

 convex lens at F would be refracted exactly as by a prism ABC, whose 



