f distinct vision, and at the same
time to retain undiminished the angle it subtends at the eye, or, what
amounts to the same thing, the actual size of the image formed on the
retina.[22] It follows, therefore, that if a lens be of such short focus
that it allows us to see an object clearly at a distance of two
inches--that is, one-fifth of the least distance of distinct vision--we
shall get an image on the retina five times larger in diameter than
would be possible without the lens.

The two simple diagrams (Figs. 121 and 122) show why the image to be
magnified should be nearer to the lens than the principal focus, F. We
have already seen (Fig. 109) that rays coming from a point in the
principal focal plane emerge as a parallel pencil. These the eye can
bring to a focus, because it normally has a curvature for focussing
parallel rays. But, owing to the power of "accommodation," it can also
focus _diverging_ rays (Fig. 121), the eye lens thickening the necessary
amount, and we therefore put our magnifying glass a bit nearer than F to
get full advantage of proximity. If we had the object _outside_ the
principal focus, as in Fig. 122, the rays from it would converge, and
these could not be gathered to a sharp point by the eye lens, as it
cannot _flatten_ more than is required for focussing parallel rays.

[Illustration: FIG. 121.]

[Illustration: FIG. 122.]

USE OF THE SIMPLE MICROSCOPE IN THE TELESCOPE.

[Illustration: FIG. 123.]

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 But if withdrawn to D, the least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 imag