Let us now see how an image is formed by a convex lens, and suppose that CD is the section of a double convex lens (fig. 22), O the optical center, and AB an object at a greater distance from the optical center than double the focal length. Rays will pass out in all directions from the object and some will fall on the lens. A ray from A will pass through the optical center and will not be deviated; others will be incident at various points, for example, E and G, and if we apply the law of refraction we will find that AE and AG will intersect each other and AO at the point A['], provided we do not consider the figure of the lens, forming one point of the image A['] B[']; similarly for rays from other points of the object, as, for example, B, we can construct the focus B['], and thus obtain the image A['] B['], which is inverted and smaller than the object AB. The relative size of the image and object will be directly as the conjugate foci, and these can be found at once from the equation of the lens.
If, however, we consider the form of the lens, we will find that all the rays emerging from one point on the object are not brought to the same focus, because the rays incident on the edges of the lens are refracted to a greater extent than those falling on the center, and will be brought to a focus at a shorter distance from the lens than those passing through the central part. This confusion or wandering of the foci from one point is called spherical aberration, or aberration of form, and is due solely to the geometrical form of the lens.
In what has been said about the visual image we have supposed that the light was monochromatic, or homogeneous. Let us see what will happen if the light is polychromatic, say, for example, sunlight, and let a beam of sunlight be intercepted on a screen after passing through a double convex lens. It will be observed, as in figure 23, that the violet rays are brought to a focus nearest the lens, and the red farthest away, and circles of light will be seen on the screen; this wandering of the colored rays from a common focus is called chromatic aberration and depends on the dispersive properties of the material of which the lens is made. Here is a defect that can not be corrected by a stop, but as the refractive and dispersive properties of a substance do not vary together, it is possible to combine two substances, one with high refractive and low dispersive properties and the other with the reverse properties. If proper curves are given to them they will correct each other, thereby producing coincidence of the visible and chromatic foci. Such a combination gives an achromatic lens, which is usually composed of a double convex of crown glass cemented to a diverging meniscus of flint glass, as shown in section in figure 24. This combination is not absolutely achromatic, but sufficiently so for all general purposes.