Fig. 28.—Path of a Ray through a Convex Lens.
Fig. 29.—Path of divergent Rays through a Convex Lens.
If the rays of light are not parallel, as in the case of the source of light being near the lens, they do not converge so rapidly as when they proceed from a distant object, consequently the focus for near objects is longer in proportion to their distance. In [fig. 29] for instance, if a candle be placed as shown, and a screen on the other side of the lens, a point will be found where the image of the candle is seen upon it in a reversed position. The distance between these two points is always relative, and they are called conjugate foci. Thus, the candle may change places with the screen with a similar effect, as long as the exact position of the two points is preserved. If the candle is placed farther off, we must diminish the distance between the screen and the lens, and vice versâ. In fact, the nearer the object, the longer the focus; the farther it is off, the shorter the focus. Half an hour’s experiment with a double convex lens, a piece of white cardboard, and a small candle, will teach the student more about the properties of convex lenses than a chapter of explanation. A common magnifying-glass, or even an old spectacle lens, will serve the purpose of more expensive instruments.
Fig. 30.—Conjugate Foci.
We now proceed to speak of the images formed by lenses. In [fig. 31] we have a flower placed on one side of a lens. As it is not at an infinite distance, the rays sent out by its various parts are convergent, and not parallel, consequently they do not meet at the sidereal focus, but at a point beyond it, according to the rule already laid down. The rays proceeding from the exact centre of the flower striking the lens exactly in the middle at right angles, suffer no change, the others being refracted in proportion to their angles of incidence.
Fig. 31.—Images formed by Convex Lenses.
The rays proceeding from the flower cross each other at a certain point: hence the image on the screen is reversed. The dimensions of the image will depend on the distance of the object from the lens. This is a fact we meet with every day, when using an opera-glass or a telescope. Images formed by convex lenses upon a screen are called by opticians real images, in contradistinction to those which are the result of mere reflection, as in the case of plane mirrors. These latter are known as virtual images and are produced by convex lenses as well as by plain reflecting surfaces. In [fig. 32], for instance, the unreversed image of the insect seen by the eye is not a real image, but a virtual one,—a fact that might be easily proved by placing a screen in the position of the eye, when it would be found that no image would be formed.