This description of magnifying power does not apply to such instru ments as the solar or gas microscope, by which we look not at the object itself, but at its shadow or picture on the wall ; and the descrip tion will require some modification in treating of the compound microscope, where, as in the telescope, an image or picture is formed by one lens, that Image or picture being viewed as an original object by another lens.
It is nevertheless so important to obtain a clear notion of the real nature of the effect produced by a lens applied to the eye, that we will adduce the instance of spectacles to render the point more familiar. If the person who has been supposed to cross the street for the purpose of reading a bill had been aged, the limit to the power of adjustment would have been discovered at a greater distance, and without eo severe a test as tho supposed insect. The eyes of the very aged gene rally lose the power of adjustment, at a distance of thirty or forty inches instead of ten, and the spectacles worn in consequence are as much magnifying glasses to them as the lenses employed by younger eyes to examine the most minute objects. Spectacles are magnifying glasses to the aged because they enable such person' to see as closely to their objects as the young, and therefore to see the objects larger than they could themselves otherwise see them, but not larger than they are seen by the unassisted younger eye.
In saying that an object appears larger at one time, or to one person, than another, it is necessary to guard against misconception. By the apparent size of an object we mean the angle it subtends at the eye, or the angle formed by two lines drawn from the centre of the eye to the extremities of the object. In fig. 1, the lines a E and n E drawn from the arrow to the eye form the angle A E B, which, when the angle is small, is nearly twice as great as the angle o E D formed by lines drawn from a similar arrow at twice the distance. The arrow A B will therefore appear nearly twice as long as CD, being seen under twice the angle, and in the same proportion for any greater or lesser difference in distance. The angle in question is called the angle of vision, or the visual angle.
The angle of vision must however not be confounded with the angle of the pencil of light by which an object is seen. and which is explained in fig. 2. Here we have drawn two arrows placed in relation to the eye as before, and from the centre of each have drawn lines exhibiting the quantity of light which each point will send into the eye at the respective distances.
Now if E Y represent the diameter of the pupil, the angle E A F shows the size of the cone or pencil of light which enters the eye from the point A, and in like manner the angle E B F is that of the pencil emanating from B, and entering the eye. Then, since E a r is double EBF, it is evident that A is seen by four times the quantity of light which could be received from an equally illuminated point at B; so that the nearer body would appear brighter if it did not appear larger ; but as its apparent area is increased four times, as well as its light, no difference in this respect is discovered. But if we could find means to send into the eye a larger pencil of light, as for instance that shown by the lines G A fi, without increasing the apparent size in the same proportion, it is evident that we should obtain a benefit totally distinct from that of increased magnitude, and one which is iu some cases of even more importance than size in developing the structure of what we wish to examine. This, it will be hereafter shown, is sometimes done ; for the present, we wish merely to explain clearly the distinction between apparent magnitude, or the angle under which the object is seen. and apparent brightness, or the angle of the pencil of light by which each of its points is seen, and with these explanations we shall continue to employ the common expressions magnifying glass and magnifying power.
The magnifying power of a single lens depends upon its focal length, the object being in fact placed nearly in its principal focus, or so that the light which diverges from each point may, after refraction by the lens, proceed in parallel lines to the eye, or as nearly so as is requisite fur distinct vision. In fig. 3, A n is a double convex lens, near which When the focal length of a lens is very small it is difficult to measure accurately the distance between its centre and its object. In such cases the best way to obtain the focal length for parallel or nearly parallel rays is to view the image of some distant object formed by the lens in question through another lens of one inch solar focal length, keeping both eyes open and comparing the image presented through the two lenses with that of the naked eye. The proportion between the two images so seen will be the focal length required. Thus if the image seen by the naked eye is feu times as large as that shown by the lenses, the focal length of the lens in question is one-teuth of an inch. The panes of glass in a window, or courses of bricks in a wall, are con venient objects for this purpose.