The longer the focal length of a lens the larger the image, and the snorter the focal length the smaller the image. Suppose we photograph a tree and place the camera at such a distance from the tree that with a lens of three inches focal length we obtain a picture in which the image of the tree is one inch long.
Now, if with the camera at the same distance from the tree, we had used a six-inch lens instead of the three-inch lens, which means that instead of the lens being three inches from the film it would be six inches from it, then the image of the tree would be two inches long instead of one inch long in the picture. If we were using the same size film with both lenses, of course we should not be able to include as much of the subject we were photographing in the field of view of the picture made with the six-inch lens as we should obtain with the three-inch lens, because with the three-inch lens the tree would be, say, a quarter of the length of the picture, while with the six-inch lens it would be half the length of the picture. In other words, the three-inch lens would give us a smaller image, while the six-inch lens would give us a large image of the tree.
Fig. 18. Rays Bent by Double Prism.
Fig. 19. Lens Forming a Sharp Image.
Fig. 20. Images formed by a pinhole at various distances.
Fig. 21. A lens forms an image at only one point.
Short Focal Length Means Small Image.
The longer the focal length of a lens, the less subject we include in our picture, and the larger the images of objects are, while the shorter the focal length, the more subject we include in the picture and the smaller the images are.
In actual practice we must compromise between a lens which will include as large an area as possible in the field of view, and a lens which will give images as large as possible; consequently, for general all-around purposes it is best to use a lens whose focal length is somewhat longer than the longest side of the film. For a 2 1/22 x 4 1/4 film, for instance, we should use a lens of about 5 inches focal length.
It is most important not to use a lens of too short a focal length for the size of the film employed. There is a great temptation to do this. While a lens of 41/2 inch focus as compared with a lens of three inch focus means a big lens in place of a little lens, and a larger shutter and a somewhat larger camera in place of a smaller shutter and an extremely compact camera, it also means (and this is vastly more important than mere camera compactness) the making of pictures having good perspective instead of pictures with bad perspective; in other words, it means pictures the drawing in which looks right instead of pictures whose drawing looks wrong. The reason for this is that the perspective of a picture is determined by the point of view from which the lens makes the picture. If this perspective is not pleasing to the eye it will not be pleasing in the picture.
Long Focal Length, Larger Image.
Fig. 24 shows a picture made with a very short focus lens used close to the subject. This is a faithful rendering of the perspective that the eye saw from the viewpoint of the lens, but it is far from pleasing.
In Fig. 25 the same subject is shown photographed with a long focus lens, and in this picture the perspective is satisfactory. It likewise represents the perspective that the eye saw from the viewpoint of the lens.
It is a good rule to secure a lens which has a focal length at least equal to the diagonal of the film. A little more focal length is still better.
Lenses differ in another respect than their focal length. They differ in the amount of light they admit, and this is very important, because the more light admitted, the shorter the exposure can be. The chief object in using a lens instead of a pinhole is to transmit more light to the film, and the amount of light that is transmitted depends upon the area of the glass in the lens.
Fig. 24. Made With a Very Short Focus Lens.
Fig. 25. Made With a Long Focus Lens.
Suppose we place a piece of cardboard, instead of a film, in the back of a camera, and have a pinhole in the card through which we can look at the lens; then point the lens toward a window; the amount of light that reaches the eye through the hole in the card depends upon how much of the light from the window is passing through the lens; that is to say, it will depend on the area of the window which we could see if there was no glass in the lens. Of course, since the visible area of the window is bounded by the edges of the lens mount, we could see more if the lens were of shorter focal length so that the eye was closer to it. With a lens of long focal length only a small part of the window area is visible.
With a lens of half the focal length but of the same diameter as that shown in Fig. 26, four times as much of the window area is visible.
The brightness of the image projected by lenses of the same diameter varies inversely as the square of the focal length of the lens. It also varies as the area of the lens surface (aperture) which admits the light. The greater the lens aperture the more light it admits. Now the area of the lens aperture, of course, is proportional to the square of its diameter, so that all lenses in which the diameter of the aperture bears the same ratio to the focal length will give equally bright images. This means that the brightness of the image is determined not solely by the focal length, nor solely by the diameter of the lens aperture, but by the relation that exists between the lens aperture and the focal length of the lens, so that all lenses in which the diameter of the opening is, say, one-sixth of the focal length, will give equally bright images. Thus, in a lens of one-inch aperture and a focal length of six inches, the opening is one-sixth of the focal length, and in a lens of twelve inches focal length and two inches aperture, the opening is likewise one-sixth of the focal length. Both lenses are of the same f value. This means that both give an image of the same brightness, and will require the same exposure. Lens "apertures" are, therefore, rated according to the ratio between their diameter and their focal lengths; thus, one in which the opening is one-sixth of the focal length is marked f.6; one in which the opening is one-eighth,f.8, and so on, and the larger the aperture, the more light the lens transmits, and the more light it transmits the shorter the exposure needed.
Visible Area with Long Focus.
Fig. 27. Visible Area with Short Focus.