The spherical aberration may be considerably diminished by making the most advantageous use of single lenses. Thus the aberration of a plano-convex lens, whose convex side is turned towards parallel rays, is only of its thickness, whilst, if the plane side be turned towards the object, the aberration is 41 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 31 times its thick ness; but when the most convex side receives or transmits them, the aberration is only 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 aplanatic 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 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.
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, the 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 without any essential difficulty in practice; for the dispersive power of flint-glass is so much greater than that of crown-glass, that a convex lens of the former, the focal length of which is 7j inches, will produce the same degree of colour with a convex lens of crown-glass whose focal length is 41 inches. Hence a concave lens of the former material and curvature will fully correct the dispersion of a convex lens of the latter, and will yet diminish its refractive power only to such an extent as to make its focus ten inches. The correction for chromatic aberration in such a lens would be perfect, if it were not that, although the extreme rays, violet and red, are thus brought to the same focus, the dispersion of the rest is not equally compensated ; so that what is termed a secon dary spectrum is produced, the images of ob jects seen through such a lens being bordered on one side with a purple fringe, and on the other with a green fringe. Moreover such a lens is not corrected for spherical aberration ; and it must of course be rendered free from this, to be of any service, however complete may be its freedom from colour.