The focal length may, however, be found in another way. When an object is placed at a distance from a lens equal to twice the principal focal length of the latter, an image of the object is formed at the same distance upon the other side of the lens, inverted in position, but of the same dimensions as the original object. The object and image then occupy the equal conjugate foci of the lens, so that by causing them to assume these relative positions, and halving the distance at which either of them is from the lens, the focal length of the latter is known. These points will be seen on reference to Fig. 2, in which _L_ being the lens, and _P_ the principal focus, as before, rays from the point _C_ are brought together at the conjugate focus _C'_, at the same distance on the other side of _L_. In this case it manifestly does not matter whether the object be at one or the other of these points. [Illustration: Fig. 2.] So far we have been dealing with points on the line of the axis of the lens. The facts mentioned apply equally, however, to rays entering the lens at an angle to the axis, only that in this case they diverge or converge, correspondingly, upon the other side. It is evident, from Fig. 1, that no image is formed of a point situated at the distance of the principal focus; but Fig. 3, which is really an extension of Fig. 2, shows how the rays passing along secondary axes form an inverted image of the same size as the object, when the latter is situated at twice the focal length of the lens from this last. To avoid confusion, the bounding lines only are shown, but similar lines might be drawn from each and every point of the object; and if the lines _ALA'_, _BL'B'_ be supposed to be balanced at _L_ and _L'_ respectively, they will indicate the points at which the corresponding parts of the object and image will be situated along the lines _AB_, _B'A'_ respectively. Moreover, rays pass from every part of the object to every part of the lens, so that we must imagine the cones _LAL'_, _LA'L'_ to be filled with rays diverging on one side of the lens and converging on the other. The image so formed is a “real” image,--that is to say, it can be thrown upon a screen. [Illustration: Fig. 3.] The microscopic image, on the other hand, is a virtual image, which can be viewed by the eye but cannot be thus projected, for it is formed by an object placed nearer to the lens than the principal focal length of the latter, so that the rays diverge, instead of converging, as they leave the lens, and the eye looks, as it were, back along the path in which the rays appear to travel, and so sees an enlarged image situated in the air, farther away than the object, as shown in Fig. 4. In this case, as the diagram shows, the image is upright, not inverted.