MICROSCOPE. 



335 



towards the object, the aberration is 4| times 

 the thickness of the lens. Hence, when a plano- 

 convex lens is employed, its convex surface 

 should be turned towards a distant object, 

 when it is used to form an image by bringing 

 to a focus parallel or slightly-diverging rays; 

 but it should be turned towards the eye, when 

 it is used to render parallel the rays which are 

 diverging from a very near object. The single 

 lens having the least spherical aberration is 

 a double convex, whose radii are as 1 to 6. 

 When the flattest face is turned toward parallel 

 rays, the aberration is nearly 3f times its thick- 

 ness ; but when the most convex side receives 

 or transmits them, the aberration is only T Jjths 

 of its thickness. The spherical aberration may 

 be still further diminished, however, or even 

 got rid of altogether, by making use of com- 

 binations of lenses so disposed that their op- 

 posite aberrations shall correct each other, 

 whilst magnifying power is still gained. For 

 it is easily seen that, as the aberration of a con- 

 cave lens is just the opposite of that of a con- 

 vex lens, the aberration of a convex lens placed 

 in its most favourable position may be cor- 

 rected by a concave lens of much less power 

 in its most unfavourable position ; so that, 

 although the power of the convex lens is weak- 

 ened, all the rays which pass through this com- 

 bination will be brought to one focus. This is 

 the principle of the uplunatic doublet proposed 

 by Sir J. F.W. Herschel, consist- 

 ing of a double-convex lens of 

 the most favourable form, and a 

 meniscus with the concave of 

 longer focus than the convex.* 

 A doublet of this kind may be 

 made of great use in the mi- 

 croscope, as we shall hereafter 

 show. 



But the spherical aberration is not doublet. 

 the only imperfection with which the optician 

 has to contend in the construction of micro- 

 scopes. A difficulty equally serious arises from 

 the unequal refrangibility of the different coloured 

 rays, which together make up white or colour- 

 less light,t so that they are not all brought to 

 the same focus, even by a lens free from sphe- 

 rical aberration. It is this difference in their 

 refrangibility which causes their complete sepa- 

 ration by the prism into a spectrum ; and it 

 manifests itself, though in a less degree, in the 

 image formed by a convex lens. For if pa- 

 rallel rays of white light fall upon a convex 

 surface, the most refrangible of its component 

 rays, namely, the violet, will be brought to a 

 focus at a point somewhat nearer to the lens 

 than the principal focus, which is the mean 

 of the whole ; and the converse will be true of 

 the red rays, which are the least refrangible, 

 and whose focus will therefore be more distant. 



* The exact curvatures to be given to these sur- 

 faces will be found in the original memoir, Phil. 

 Trans. 1821. 



t It has been deemed better to adhere to the 

 ordinary phraseology, when speaking of this fact, 

 as more generally intelligible than the language in 

 which it might be more scientifically described, 

 and at the same time leading to no practical error. 



jFig.158. 



A 



HerscheVs 



Diagram illustrative of chromatic aberration, 



A B, rays of white light refracted by a convex 

 lens ; C, the focus of the violet rays, which then 

 cross and diverge towards E F ; D, the focus 

 of the red rays which are crossed at the points 

 E E, by the violet ; the middle point of this 

 line is the mean focus, or focus of least aber- 

 ration. 



This is easily proved experimentally. If a 

 lens be so fixed as to receive the solar rays, 

 and to illuminate a white screen at any dis- 

 tance between the lens and the mean focus, the 

 luminous circle will have a red border, because 

 the red rays will there form the exterior of the 

 cone ; but if it be removed beyond the mean 

 focus, ihe circle will have a violet border, be- 

 cause the violet rays will then be outermost. 

 As the spherical aberration would be mixed up 

 with the chromatic in such an experiment, the 

 undisguised effect of the latter will be better 

 seen by taking a large convex lens, and co- 

 vering up its central part, so as to allow the 

 light to pass only through a peripheral ring; 

 and since the greater the alteration in the course 

 of the rays, the greater will be the separation 

 of the colours, (or dispersion, as it is techni- 

 cally called,) this ring will exhibit the pheno- 

 menon much better than would be done by the 

 central portion of the lens. Hence, in prac- 

 tice, the chromatic aberration is partly obviated 

 by the same means used to diminish the sphe- 

 rical aberration, the contraction of the aper- 

 ture of the lens, so that a very small portion 

 of the whole sphere is really employed. But 

 this contraction is attended with so much in- 

 jury to the performance of the microscope in 

 other respects, that it becomes extremely de- 

 sirable to avoid it. In no single lens can any 

 correction for chromatic aberration be effected ; 

 and it requires a very nice adjustment of two, 

 three, or even more, to accomplish this with 

 perfection. 



The correction is accomplished by bringing 

 into use the different dispersive powers of va- 

 rious materials, which bear no relation to their 

 simple refracting power. As the effects of con- 

 cave lenses are in all respects the converse of 

 convex, it is obvious that, if a concave lens of 

 the same curvature be placed in apposition 

 with the convex, in such an experiment as 

 that just alluded to, the dispersion of the rays 

 will be entirely prevented, but neither will any 

 change in the course of the rays take place. 

 If, however, we can obtain a substance of 

 higher dispersive power in proportion to its 

 power of refraction, it is obvious that a con- 

 cave lens of less curvature formed of it will 

 correct the dispersion occasioned by the convex 

 lens, without altogether antagonising the re- 

 fraction of the latter. This is accomplished 



