If a candle is held at a short distance in front of a concave mirror, as represented in Fig. 51, its image appears on the paper between the candle and the mirror, so that the rays from every point of the flame are brought to a focus, and produce an image just as the image is produced by a convex lens. If we study Fig. 52 the formation of this image will be clearly understood. First we must note that the rays A, C, _a_, and B, C, _b_, which pass through the centre of curvature of the mirror C, will fall perpendicularly on the surface, and be reflected back on themselves, so that the focus of the part a of the arrow will be somewhere on A _a_, and that of B on B _b_, and by drawing another ray we shall find it reflected to _a_, which will be the focus of the point A, and so also by drawing another line from B, we shall find it is reflected to _b_, which is the focus of the part B; and we might repeat this process for every part of the arrow, and for every ray from those parts. We now see that since the rays A _a_ and B _b_ cross each other at C, the distance from _a_ to _b_ bears the same proportion to the distance from A to B as their respective distances from the point C; or, in other words, the image is smaller than the object in the same proportion as the distance from the image to C is smaller than the distance from the object to C. Now, in dealing with the stars, which are at a practically infinite distance, the rays are parallel, and will be brought to a focus half-way between the mirror and its centre of curvature. In this case, therefore, the distance from the image to the mirror is equal to that from the image to the centre, so that we can express the size of the image by saying that it is smaller than the object, in proportion as its distance from the mirror is smaller than the distance of the object from C; and as it makes little difference whether we measure the distance of the stars from C or from the mirror, and as C is not always known, we can take the relation of the distances of the object and image from the mirror as representing the proportionate sizes of the two.