greater angle, causing the image to appear much larger. If we take a watch or other small circular object and place it at A, which we will suppose is a distance of 50 yards, we shall find that it will be only visible as a circular object, and its apparent magnitude or the angle under which it is viewed is then stated to be very small. If the object is now moved to the point B, which is only 5 feet from the eye, its apparent magnitude will be found to have increased to such an extent that we can distinguish not only its shape, but also some of the marking. When moved to within a few inches from the eye as at C, we see it under an angle so great that all the detail can be distinctly seen. By having brought the object nearer the eye, thus rendering all its parts clearly visible, we have actually magnified it, or made it appear larger, although its actual size remains exactly the same. When the distance between the object and the observer is known, the apparent magnitude of the object varies inversely as the distance from the observer.
Let us suppose that we wish to produce an image of a tree situated at a distance of 5000 feet. At this distance the light rays from the tree will be nearly parallel, so that if a lens having a focal length of 5 feet is fastened in any convenient manner in the wall of a darkened room the image will be formed 5 feet behind the lens at its principal focus. If a screen of white cardboard be placed at this point we shall find that a small but inverted image of the tree will be focussed upon it. As the distance of the object is 5000 feet, and as the size of the received image is in proportion to this distance divided by the focal length of the lens, the image will be as 5000 ÷ 5, or 1000 times smaller than the object.
If now the eye is placed six inches behind the screen and the screen removed, so that we can view the small image distinctly in the air, we shall see it with an apparent magnitude as much greater than if the same small image were equally far off with the tree, as 6 inches is to 5000
feet, that is 10,000 times. Thus we see that although the image produced on the screen is 1000 times less than the tree from one cause, yet on account of it being brought near to the eye it is 10,000 times greater in apparent magnitude; therefore its apparent magnitude is increased as 10,000 ÷ 1000, or 10 times. This means that by means of the lens it has actually been magnified 10 times. This magnifying power of a lens is always equal to the focal length divided by the distance at which we see small objects most distinctly, viz. 6 inches, and in the present instance is 60 ÷ 6, or 10 times.
When the image is received upon a screen the apparatus is called a camera obscura, but when the eye is used and sees the inverted image in the air, then the apparatus is termed a telescope.
The image formed by a convex lens can be regarded as a new object, and if a second lens is placed behind it a second image will be formed in the same manner as if the first image were a real object. A succession of images can thus be formed by convex lenses, the last image being always treated as a fresh object, and being always an inverted image of the one before. From this it will be evident that additional magnifying power can be given to our telescope with one lens by bringing the image nearer the eye, and this is accomplished by placing a short focus lens between the image and the eye. By using a lens having a focal length of 1 inch, and such a lens will magnify 6 times, the total magnifying power of the two lenses will be 10 × 6 = 60 times, or 10 times by the first lens and 6 times by the second. Such an instrument is known as a compound or astronomical telescope, and the first lens is called the object glass and the second lens the magnifying glass, or eye-piece.
We are now in a position to understand how virtual images are formed, and the formation of a virtual image by means of a convex lens will be readily followed from a
study of Fig. 73. Let L represent a double convex lens, with an object, AB, placed between it and the point F, which is the principal focus of the lens. The rays from the object AB are refracted on passing through the lens, and again refracted on leaving the lens, so that an image of the object is formed at the eye, N. As it is impossible for the eye to follow the bent rays from the object, a virtual image is formed and is seen at A1B1, and is really a continuation of the emergent rays. The magnifying power of such a lens may be found by dividing 6 inches by the focal length of the lens, 6 inches being the distance at which we see small objects most distinctly. A lens having a focal length of 1/4 inch would magnify 24 times, and one with a focal length of 1/100th of an inch 600 times, and so on. The magnifying power is greater as the lens is more convex and the object near to the principal focus. When a single lens is applied in this manner it is termed a single microscope, but when more than one lens is employed in order to increase the magnifying power, as in the telescope, then the apparatus is termed a compound microscope.
Unlike a convex lens, which can form both real and virtual images, a concave lens can only produce a virtual image; and while the convex lens forms an image larger