There is a fixed relation between the principal focal length of a double convex lens and the position of the image of the object which may be expressed as follows: 1/_i_ = 1/_f_ - 1/_o_, in which _i_ and _o_ are the distances of the image and object, respectively, from the optical center and _f_ the focal length, from which we see that for all positions of the object from an infinite distance away from the lens to double the principal focal distance, the image will be on the other side, between a distance equal to the principal focal length and double this length. These are the limits of the image and object in the ordinary cases. If we place this expression in the following form: _i_ = _of_/(_o_ - _f_), and suppose the object to remain the same distance from various lenses, it will be seen that the image will be closer to the lens which has the shorter focal length. The principal focal distance, or, briefly, the focal length of the lens, depends on the curvature of the surfaces, and the greater the curvature the shorter the focal length. FORMATION OF IMAGE. [Illustration: FIG. 22.] 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. SPHERICAL ABERRATION. 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. CHROMATIC ABERRATION.