The form of simple convex lens most free from aberration is that in which the curves of the two surfaces form parts of a sphere, the radii of the curves being as 1 to 6; the focal length being rather less than twice the length of the radius of the most convex surface. This form of lens comes very near to a plano-convex lens, which is consequently the best form for a simple lens.
Dispersion, or Chromatic Aberration.—The rays of light have so far been considered as simple. They are, however, in reality compound, consisting of a number of primary-coloured rays, of which seven kinds are easily distinguishable, viz. red, orange, yellow, green, blue, indigo, and violet. The coloured rays of the sun are, as is well known, often seen separated by the action of the triangular glass bars or prisms forming the lustres of a chandelier; the separation arising from the different refrangibility of the coloured rays, by which each is refracted to a different degree from that of the others. This is shown in [Pl. XII.] fig. 19, representing a ray of white light entering a triangular prism, at the surface of which the paths of the rays become different according to the degree of their refrangibility, whence they emerge separately, forming a spectrum at v r; the most refrangible violet rays (v) being most refracted, the less refrangible red (r) least so, the intermediate rays being refracted to intermediate degrees according to their respective refrangibilities. This separation of the coloured rays is called dispersion; and as different substances or media disperse the coloured rays over a larger or smaller space, so as to produce spectra of different lengths, they are said to possess different dispersive powers. Thus the dispersive power of flint glass and balsam are about equal, while that of crown glass is considerably less.
The extent to which dispersion is produced by the same medium also depends upon the angle of the prism, being greater as the angle is larger; increased obliquity of the incident light also increases the dispersion, so that the spectrum produced by a small prism may be equal to that produced by a larger one upon which the light is less obliquely incident.
In consequence of the dispersion of light, rays passing through a convex lens do not meet at a single point or focus ([Pl. XII.] fig. 20), but form as many foci as there are coloured rays.
When the spectrum is received upon a convex lens, the coloured rays are brought to a focus, and the light appears again white; for it is only when the primary-coloured rays are parallel, and seen close together, that they produce the impression of white or colourless light. The spectra produced by different dispersive media not only differ in length, but also in the breadth of the coloured spaces not being in the same ratio to each other; hence the spectra are said to be irrational, or the dispersion is said to be irrational.
Vision.—The visibility of an object depends upon the rays of light which emanate from each point of its surface presented to the eye being brought to a focus upon the ret´ina or expansion of the nerve of sight lining the inside of the back of the eye; so that, an image of each point being impressed upon the retina, the sum of the images forms the compound image of the entire object.
The manner in which the image is formed is shown in [Pl. XII.] fig. 21, in which, to prevent confusion, the rays coming from three points of the arrow only have been represented. The rays diverging from these three points, a b c, form cones in contact by their bases; the apex of each cone outside the eye being situated at the points a b c, the common base of each being situated at the crystalline lens x, immediately behind the pupil or rounded aperture in the coloured curtain of the eye, called the iris, i i, and which limits the base of the cones. The apices of the cones within the eye, a´b´c´, are formed by the rays brought to foci upon the retina by the crystalline lens. The marginal cones of rays coming from the object cross within the eye, so that the uppermost rays from the object become lowermost upon the retina, and thus an inverted image of the object is formed. This appears to the eye to be erect, because the eye or rather the mind judges the parts of an object to be situated in that direction in which the rays coming from them are impressed upon it. Hence, as in fig. 21, the rays impressed upon the retina at the lower part a´, appear to come from the upper part of the cross, although they are lowermost in the image, and so on for the other rays. For distinct vision the rays of each cone must be parallel, or nearly so.
Angle of Vision.—The marginal rays coming from the object cross at a point corresponding to the centre of the pupil, and thus form an angle, as seen in fig. 22, where the cones are omitted, to avoid confusion; this angle is the angle of vision. Now the size which objects appear to possess is measured by this angle, or by the linear magnitude of their images (i. e. their size estimated in one direction, as of length or breadth) upon the retina. When the object is distant, the angle and its linear magnitude are small, and it appears small and distant; whilst if it be large, or if small and brought near the eye, the reverse will be the case.
Magnification.—Hence an object may be made to appear larger, or may be magnified, by increasing the linear magnitude of its image upon the retina, which can be done by bringing it nearer the eye, as shown in fig. 22, where the image of b formed at b´ is larger than the image of a formed at a´. But when an object is brought nearer the eye than about 8 or 10 inches (for the distance varies with different persons), its image becomes indistinct and misty; and this because the rays composing the cones are too divergent to meet at a focus upon the retina, as shown in fig. 23. By interposing a convex lens, however, between the eye and the object, the too divergent rays may be made to meet at a focus upon the retina, as in fig. 24, the object at the same time being rendered apparently larger or magnified, from the refracting action of the lens upon the cones.
Aplan´atism (a, not, πλανἁω, to wander).—The effect of spherical aberration in rendering the image of an object seen through a lens indistinct and misty may now be intelligible. In order that such image may be distinct, the rays emanating from each point of the object must converge at one spot upon the retina. But since, when spherical aberration exists, the marginal rays are more refracted than the central ones, they will meet at foci before those formed by the latter; and when the foci of one set are coincident with the retina, so that the image would otherwise be distinct, the latter is rendered confused and indistinct by the rays of the other set.