Focus being secured, the relative linear proportions of image and object are equal to those of the relative conjugate focal distances. Thus image and object are the same size when they are equally distant from the principal points, while if the focal distance of the image is one-third that of the object the image is one-third the size of the object.
The ratio of image to object is also equal to that of the extra-focal distance of the image to the focal length, and to the ratio of the focal length to the extra-focal length of the object. That is to say, if the image is one-third the size of the object, fq (in fig. 3) is one-third the focal length, while p f2 is three times the focal length. The size of the image, therefore, varies directly with its distance from the back principal focus, and inversely with the distance of the object from the front principal focus. If you halve the latter distance you must double the distance of the plate from the back principal focus to secure definition, and the image is then doubled in size.
These rules are of great importance in practical work. Suppose, for example, we wish to copy a diagram or negative on the scale of one-quarter full size. With a 6-in. lens we must set the object four focal lengths, or 24 in. from the front principal focus of the lens, and the plate one-quarter of a focal length from the back principal focus—that is i\ in. If, however, we wished to enlarge the image four times we should set the object one-quarter of a focal length from the front principal focus, and the plate four focal lengths from the back focal point. Or, having once set up the camera, if we wish to alter the scale slightly—say reduce the image to three-quarters its present size—we reduce its distance from the principal focus in the same ratio and increase the distance of the object in the inverse ratio, which means that we multiply it by four thirds or add one third. It should be noted that such adjustments can seldom be made so accurately as to ensure perfect focus—they must always be supplemented by visual examination of the image.
With different lenses used upon an object at a fixed focal distance the size of the image varies with the focal distance of the plate from the lens. In the case of very distant objects the plate is placed at the principal focus, and the size of the image then varies directly with the focal length of the lens. Thus an 8-in. lens will produce an image just twice the size of that formed by a 4-in. lens, if the object is distant. With a near object the camera has to be racked out to secure focus, and size then depends on the focal distance, which is greater than the focal length.