An Elementary Text-book of the Microscope / including a description of the methods of preparing and mounting objects, etc.

by J. W. Griffith

In this consideration, we imply that there are only two sets of rays, the central and the marginal; but the central and marginal rays are not separate, for the rays possess every intermediate degree of obliquity, hence the foci and images are really innumerable.

Now there are evidently two methods of destroying or correcting spherical aberration, viz. by excluding the marginal rays, or by altering their direction.

The exclusion of the marginal rays is often adopted; and is effected by means of a diaphragm, or stop as it is called. This consists of a plate of metal, with a round aperture in the middle, and it is placed behind the lens; but it has the serious defect of diminishing considerably the amount of light transmitted.

The alteration of the direction of the marginal rays is produced by refraction, a thin plano-concave lens being placed in front of the convex one ([Pl. XII.] fig. 25). The doubly convex lens is composed of crown glass, and the concave lens of flint glass, which has a higher refractive and dispersive power than crown glass. In this way we get a compound lens, which, if the two lenses had the same refractive power, would simply amount to a plano-concave lens with the marginal portions removed. But as the concave lens consists of more highly refracting material than the convex, if the curve and thickness of the two lenses be properly adapted, the marginal portions of the concave correct the too great convergence of the marginal rays produced by the convex lens, and so the rays are brought to nearly the same focus. An idea of this action may be obtained from fig. 25, the dotted lines indicating the direction which the rays would take, if passing through the convex lens only.

A lens in which the spherical aberration is corrected is said to be aplanatic.

Achrómatism.—Supposing the spherical aberration of a lens to be corrected, there still remains the chromatic aberration (p. 173); for although the central or mean coloured rays may meet at a focus, the other coloured rays belonging to the same compound or ordinary ray will meet at different foci, so that a series of coloured images of the object will be formed at different distances from the lens; hence, at whichever focus the object is viewed, it will appear coloured.

Now the coloured primary rays can only be made to coincide in direction, so that the light parts of an object may appear white, by refraction. And the correction is produced by the same plano-concave lens as that which corrects the spherical aberration. But in this case the relative dispersive powers of the media composing the convex and the concave lenses form the point to be considered. If the dispersive power of the media of which the convex and concave lenses are composed were the same, the dispersive power of the convex lens would be in excess, and the coloured rays in each compound ray could not become parallel. But by forming the concave lens of a more highly dispersive medium, with a less proportional mean refraction than the convex, when the curves of the surfaces and the relative thickness of the lenses are properly adjusted, the dispersive action of the concave lens may be made equal to that of the convex; and being exerted in the opposite direction, the coloured rays will become parallel and meet at a single focus.

This may be elucidated by considering the lenses as composed of prisms. Thus, let fig. 28 represent the compound lens, the two halves of the doubly convex lens acting as two triangular prisms (fig. 19) with their bases opposed, converging the compound white rays w w, and dispersing the coloured elementary rays, which would form spectra at s s. In the plano-concave lens the triangular prisms may be considered as placed with their apices towards each other, and so would tend to disperse the coloured rays in the opposite direction, to form spectra at t t. Then, supposing the dispersions to be equal and in opposite directions, the coloured rays would become parallel and meet at a definite focus, the colour being destroyed. At the same time, the spherical action of the concave lens being opposite to that of the convex, the converging action of the latter will be diminished, so that the focus of the compound lens will be longer than that of the convex alone; but as the dispersive power of the concave is greater relatively than that of the convex, the mean refraction is less altered than the refraction or dispersion of the separate coloured rays; so that the concave wholly opposes or corrects the dispersion produced by the convex, while it only partially corrects its mean refraction.

A lens in which the chromatic and spherical aberrations are corrected or destroyed is commonly called achromatic; although the term properly applies to the correction of the colour only.

If in a compound lens the chromatic aberration is only partially corrected, so that the red rays still meet at a focus beyond the violet, as in a simple uncorrected lens (fig. 20), the lens is said to be under-corrected, or the aberration to be positive; while if the correcting action of the plano-concave lens be too great, so that the violet rays meet before the red, as in a simple concave lens, the lens is said to be over-corrected, and the aberration is called negative. Although the positive chromatic aberration of the extreme rays passing through a convex lens may be corrected by the negative aberration of a concave lens, there still remains a certain amount of uncorrected colour, arising from the irrationality of the spectra of the two refracting media. This evil cannot be overcome, and the remaining colour is said to arise from the secondary spectrum.