Let us now turn to Fig. 123. At A is a distant object, say, a hundred yards away. B is a double convex lens, which has a focal length of twenty inches. We may suppose that it is a lens in a camera. An inverted image of the object is cast by the lens at C. If the eye were placed at C, it would distinguish nothing. But if withdrawn to D, the least distance of distinct vision,[23] behind C, the image is seen clearly. That the image really is at C is proved by letting down the focussing screen, which at once catches it. Now, as the focus of the lens is twice _d_, the image will be twice as large as the object would appear if viewed directly without the lens. We may put this into a very simple formula:-- Magnification = focal length of lens -------------------- _d_ [Illustration: FIG. 124.] In Fig. 124 we have interposed between the eye and the object a small magnifying glass of 2-1/2-inch focus, so that the eye can now clearly see the image when one-quarter _d_ away from it. B already magnifies the image twice; the eye-piece again magnifies it four times; so that the total magnification is 2 x 4 = 8 times. This result is arrived at quickly by dividing the focus of B (which corresponds to the object-glass of a telescope) by the focus of the eye-piece, thus:-- 20 ____ = 8 2-1/2 The ordinary astronomical telescope has a very long focus object-glass at one end of the tube, and a very short focus eye-piece at the other. To see an object clearly one merely has to push in or pull out the eye-piece until its focus exactly corresponds with that of the object-glass. THE TERRESTRIAL TELESCOPE. An astronomical telescope inverts images. This inversion is inconvenient for other purposes. So the terrestrial telescope (such as is commonly used by sailors) has an eye-piece compounded of four convex lenses which erect as well as magnify the image. Fig. 125 shows the simplest form of compound erecting eye-piece. [Illustration: FIG. 125.] THE GALILEAN TELESCOPE. [Illustration: FIG. 126.] A third form of telescope is that invented by the great Italian astronomer, Galileo,[24] in 1609. Its principle is shown in Fig. 126. The rays transmitted by the object-glass are caught, _before_ coming to a focus, on a concave lens which separates them so that they appear to meet in the paths of convergence denoted by the dotted lines. The image is erect. Opera-glasses are constructed on the Galilean principle. THE PRISMATIC TELESCOPE.