LAW OF FOCI.

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.