We must here digress a moment to draw attention to the three simple diagrams of Fig. 109. The object, O, in each case is assumed to be to the right of the lens. In the topmost diagram the object is so far away from the lens that all rays coming from a single point in it are practically parallel. These converge to a focus at F. If the distance between F and the centre of the lens is six inches, we say that the lens has a six-inch focal length. The focal length of a lens is judged by the distance between lens and image when the object is far away. To avoid confusion, this focal length is known as the _principal_ focus, and is denoted by the symbol f. In the middle diagram the object is quite near the lens, which has to deal with rays striking its nearer surface at an acuter angle than before (reckoning from the centre). As the lens can only deflect their path to a fixed degree, they will not, after passing the lens, come together until they have reached a point, F^1, further from the lens than F. The nearer we approach O to the lens, the further away on the other side is the focal point, until a distance equal to that of F from the lens is reached, when the rays emerge from the glass in a parallel pencil. The rays now come to a focus no longer, and there can be no image. If O be brought nearer than the focal distance, the rays would _diverge_ after passing through the lens. RELATIVE POSITIONS OF OBJECT AND IMAGE. [Illustration: FIG. 110.--Showing how the position of the image alters relatively to the position of the object.] From what has been said above we deduce two main conclusions--(1.) The nearer an object is brought to the lens, the further away from the lens will the image be. (2.) If the object approaches within the principal focal distance of the lens, no image will be cast by the lens. To make this plainer we append a diagram (Fig. 110), which shows five positions of an object and the relative positions of the image (in dotted lines). First, we note that the line A B, or A B^1, denotes the principal focal length of the lens, and A C, or A C^1, denotes twice the focal length. We will take the positions in order:-- _Position I._ Object further away than 2_f_. Inverted image _smaller_ than object, at distance somewhat exceeding _f_. _Position II._ Object at distance = 2_f_. Inverted image at distance = 2_f_, and of size equal to that of object. _Position III_ Object nearer than 2_f_. Inverted image further away than 2_f_; _larger_ than the object. _Position IV._ Object at distance = _f_. As rays are parallel after passing the lens _no_ image is cast. _Position V._ Object at distance less than _f_. No real image--that is, one that can be caught on a focussing screen--is now given by the lens, but a magnified, erect, _virtual_ image exists on the same side of the lens as the object.