Now the function of a lens is to obviate these drawbacks as far as possible; namely, to let more light through and form a brighter image, and to give sharper definition. In figure 2, the lens L collects all the light that falls upon it from the point B, and condenses it to the point _b_ on the surface T. The light from the point A that falls on the lens is also condensed and would be brought to a point or "focus" at _a_ beyond the surface T, but on the surface the light forms a patch of considerable size. Suppose that the lens is thirty times the diameter of the pinhole its area is 900 times as large, and the light that falls upon it is 900 times as much as the light that passes through the hole. Such an enormous gain of light is worth so much that photographers willingly put up with the very many imperfections of lenses for the sake of it, and if to this gain there is added the superior definition that is possible, it will be seen that lenses are indispensable to the photographer. To take a Daguerreotype portrait with a pinhole might have required several days if not weeks exposure of the plate and therefore would have been impossible, so that the gain in brightness of image is a great deal more than a mere convenience.
It will be observed in figure 1 that both points of light, A and B produce images on the surface T, although they are at different distances from it, but in fig. 2, although the effect of the lens is to concentrate the light from both points to two other points, one of these is beyond the surface T. This is a disadvantage inherent in lenses. They have so many other imperfections or "aberrations" that it is desirable to consider these separately. The reader should bear in mind that the one aim of opticians in perfecting lenses is to concentrate as much light as possible from each point in the object to a corresponding point, or as small as possible a dot, in the image, and the image should be flat because the plates used in photography are flat.
_Spherical Aberration._--The surfaces of lenses are always ground to spherical curves, and this fact makes it impossible for a single lens, such as that shown in figure 2, to bring to a point all the light that falls upon it from a point. If a pencil of light passes through a piece of glass with sloping sides it is bent or "refracted" towards the thicker part of the glass, and the greater the angle of inclination of the two sides the more is it refracted from its original path. In figure 3 it is clear that the two sides of the lens shown in section are inclined to each other at a continually increasing angle as they approach each other at the edges of the lens. The refracting effect of the lens increases from the centre outwards, and it increases to a greater extent than is necessary to bring the incident light to a point. The focus of the pencils of light that pass through the edges of the lens is nearer to the lens than the focus of the pencils that pass through its central part. In the figure two foci are shown, _a_ and _b_, but of course, in fact, intermediate parts of the lens produce intermediate foci, and what should be a point in the image, is spread out into a line on the axis of the lens, and all along this line is surrounded with the light that either is coming to a focus or that has come to a focus and has spread out again. On a screen placed at _b_ there would be a point of light surrounded by a halo, while at _a_, nearer the lens, the central focus or point is surrounded by a brighter or more condensed light, and the appearance is of a circular patch of light with a brighter boundary. This is positive spherical aberration. Negative spherical aberration is due to over correction, the focus of the light passing through the margins being furthest from the lens, and the appearances on a screen are of course reversed.