figure 6.
figure 7.
figure 8.

The axis of a lens is a straight line drawn through the center of its spherical surface; and as the spherical sides of every lens are arches of circles the axis of the lens would pass through the centre of that circle of which its sides are segments. Rays are those emanations of light which proceed from a luminous body, or from a body that is illuminated. The Radiant is that body or object which emits the rays of light—whether it be a self-luminous body, or one that only reflects the rays of light. Rays may proceed from a Radiant in different directions. They may be either parallel, converging, or diverging. Parallel rays are those which proceed equally distant from each other through their whole course. Rays proceeding from the sun, the planets, the stars, and distant terrestrial objects are considered as parallel, as in fig. 6. Converging rays are such as, proceeding from a body, approach nearer and nearer in their progress, tending to a certain point where they all unite. Thus, the rays proceeding from the object AB, (fig. 7.) to the point F, are said to converge towards that point. All convex glasses cause parallel rays, which fall upon them to converge in a greater or less degree; and they render converging rays still more convergent. If AB, fig. 7. represent a convex lens, and H G I parallel rays falling upon it, they will be refracted and converge towards the point F, which is called the focus, or burning point; because, when the sun’s rays are thus converged to a point by a large lens, they set on fire combustible substances. In this point the rays meet and intersect each other. Diverging rays are those which, proceeding from any point as A, fig. 8, continually recede from each other as they pass along in their course towards BC. All the rays which proceed from near objects as a window in a room, or an adjacent house or garden are more or less divergent. The following figures show the effects of parallel, converging and diverging rays in passing through a double convex lens.

figure 11.figure 9.figure 10.

Fig. 9, shows the effects of parallel rays, KA, DE, LB, falling on a convex glass AB. The rays which fall near the extremities at A and B, are bent or refracted towards CF, the focus, and centre of convexity. It will be observed, that they are less refracted as they approach the center of the lens, and the central ray DEC, which is called the axis of the lens, and which passes through its center, suffers no refraction. Fig. 10, exhibits the course of converging rays, when passing through a similar lens. In this case the rays converge to a focus nearer to the lens than the center; for a convex lens uniformly increases the convergence of converging rays. The converging rays here represented, may be conceived as having been refracted by another convex lens of a longer focus, and, passing on towards a point of convergence, were intercepted by the lens AB. The point D is the place where the rays would have converged to a focus, had they not been thus intercepted. Fig. 11, represents the course of diverging rays when falling on a double convex glass. In this case the rays D B, D A, &c., after passing through the lens, converge to a focus at a point considerably farther from the lens than its centre, as at F. Such rays must be considered as proceeding from near objects, and the fact may be illustrated by the following experiment. Take a common reading-glass, and hold it in the rays of the sun, opposite a sheet of writing-paper or a white wall, and observe at what distance from the glass the rays on the paper converge to a small distinct white spot. This distance gives the focal length of the lens by parallel rays. If now, we hold the glass within a few feet of a window, or a burning candle, and receive its image on the paper, the focal distance of the image from the glass will be found to be longer. If, in the former case, the focal distance was twelve inches,—in the latter case it will be thirteen, fifteen, or sixteen inches, according to the distance of the window or the candle from the glass.

If the lens A B, fig. 9, on which parallel rays are represented as falling, were a plano-convex, as represented at A, fig, 5, the rays would converge to a point P, at double the radius, or the whole diameter of the sphere of which it is a segment. If the thickness of a plano-convex be considered, and if it be exposed on its convex side to parallel rays, as those of the sun, the focus will be at the distance of twice the radius, wanting two-thirds of the thickness of the lens. But if the same lens be exposed with its plane side to parallel rays, the focus will then be precisely at the distance of twice the radius from the glass.

The effects of concave lenses are directly opposite to those of convex. Parallel rays, striking one of those glasses, instead of converging towards a point, are made to diverge. Rays already divergent are rendered more so, and convergent rays are made less convergent. Hence objects seen through concave glasses appear considerably smaller and more distant than they really are. The following diagram, fig. 12, represents the course of parallel rays through a double concave lens, where the parallel rays T A, D E, I B, &c., when passing through the concave glass A B, diverge into the rays G L, E C, H P, &c., as if they proceeded from F, a point before the lens, which is the principal focus of the lens.

figure 12.

The principal focal distance E F, is the same as in convex lenses. Concave glasses are used to correct the imperfect vision of short-sighted persons. As the form of the eye of such persons is too convex, the rays are made to converge before they reach the optic nerve; and therefore a concave glass, causing a little divergency, assists this defect of vision, by diminishing the effect produced by the too great convexity of the eye, and lengthening its focus. These glasses are seldom used, in modern times, in the construction of optical instruments, except as eye-glasses for small pocket perspectives, and opera glasses.

To find the focal distance of a concave glass. Take a piece of paste-board or card paper, and cut a round hole in it, not larger than the diameter of the lens; and, on another piece of paste-board, describe a circle whose diameter is just double the diameter of the hole. Then apply the piece with the hole in it to the lens, and hold them in the sun-beams, with the other piece at such a distance behind, that the light proceeding from the hole may spread or diverge so as precisely to fill the circle; then the distance of the circle from the lens is equal to its virtual focus, or to its radius, if it be a double concave, and to its diameter, if a plano-concave. Let d, e, (fig. 12,) represent the diameter of the hole, and g, i, the diameter of the circle, then the distance C, I, is the virtual focus of the lens.[9]