Action of Lenses. generaily resembling that of a flat bean or lentil, being 585 814. The rays of light issuing from any point, c, towards any surface, a b, are said to form a cone or pencil of diverging light. It is evident that to make all such rays converge or meet again in one place, as f, beyond the transparent body, a b, it would be necessary, while the middle ray or axis of the pencil, c df, did not bend at all, for the others to be bent more and more, in proportion as they fell upon the body farther and farther from the centre, d. A lens, or glass, of which the surface is ground, to have a regular convexity or bulging, as if it were a portion cut off from the surface of a ball or sphere, possesses the property of so converging or collecting the rays to a point. In fig. 193, a b is such a glass, similarly ground on both sides; the ray, c d, falling on its middle, goes straight through to f; the oblique ray, c e, is bent down a little, first, on entering the surface at e, and then as much more on leaving the opposite surface with equal obliquity, and so arrives at f; the ray, c a, for corresponding reasons, is still more bent, and equally arrives at ƒ;-and similarly for any other rays that might be examined. The point, s, is usually called a focus (the Latin for fire-place), because when the light of the sun is thus gathered, the heat concentrated with it is powerful enough to set combustibles on fire. Oblique pencils, as form o and x, have a focus similarly determined: it always lies in 586 Varieties of Lenses. the line joining the origin of the luminous pencil with the centre of the lens. It is important to understand here that rays of light meeting at any focal point in the air or in any other transparent medium, do not at all disturb one another like solid masses clashing, but simply cross and pass onwards, as sketched here at letters 3, f, p. 815. Lenses are of different shapes, as represented in fig. 194. That marked 1, having both sides convex, is called a double convex lens. A glass convex only on one side, and plane or flat on the other, as 2, does as effectually gather the rays, but with half the power, and the point of meeting, or focus, is therefore proportionately more distant. Such a glass is called a plano-convex lens. Then the gathering or converging power of any glass, whether doubly or singly convex, is in proportion to the degree of its convexity or the bulging of the surfaces, for the less it bulges, the more nearly does it approach to being a plane glass, and the more it bulges, the more obliquely will the rays, at any distance from the centre, fall upon its surface, and the sooner, therefore, in consequence of their being more bent, will they all meet the axis-ray to form a focus ;—hence No. I would converge much more quickly than No. 3, which represents nearly a common spectacle glass; and a very minute globe is the form most powerfully converging of all. The surfaces of No. I are portions of a small globe; those of No. 3 are smaller comparative portions of a globe much larger. Concave lenses, as No. 4, which is a double concave, and No. 5, which is a plano-concave lens, in obedience to the same law of refraction, spread rays, or bend them away from the axis of the pencil, in the same degree that similarly convex lenses gather them. A concave lens, therefore, receiving the converging pencil of rays from a convex lens, might restore them to their former nearly parallel direction. Very useful purposes, as will be afterwards explained, are served in optics, by certain combinations of differently formed lenses. A lens may be The Camera Obscura. 587 convex on one side and concave on the other, as at No. 6, called a meniscus lens, because it resembles the crescent moon, and its effect will be according to the curve which predominates. A person recollecting the case of the "multiplying glass," described at page 581, might say,—but is not a convex lens merely a multiplying glass of a much greater number of faces, and if so, why, instead of one image, does it not make thousands? The answer is, that the multiplying glass, by every face, bends a set of rays, capable of forming a distinct and complete image; but the lens has no surface large enough to bend more than single rays, it concentrates all into focal points, which form a general image of great vividness and beauty. "When the light proceeding towards a lens from every point of an object placed before it, is collected in corresponding points behind it, a perfect image of the object is there produced. The CAMERA OBSCURA, the SOLAR MICROSCOPE, and the MAGIC LANTERN are merely arrangements whereby an image so formed is received upon a suitable white surface in a dark place." a 816. If a lens, such as a common spectacle glass, a (fig. 195), be placed to fill up an opening made in the window-shutter of a darkened room, then, from any object before that opening-as the cross here represented, all the light which different points radiate towards the lens will be con Fig. 195. centrated or gathered together in corresponding focal points behind the lens within the room, and if a sheet of paper be held there at the distance of the focal points, a beautiful inverted image of the object will be seen upon the paper. In these few words, we have described that most interesting arrangement called the Camera obscura or dark chamber; and when a lens is chosen of proper size and focal distance, and a screen, or the wall of the chamber (if at the required distance), is properly prepared to receive the light, the most admirable portraiture is instantly produced of the whole scene which the window commands. 817. It appears in fig. 195 that the image, formed beyond a lens by the gathered light, is in an inverted position, for the light from the top of the object darts through the opening or glass in a descending direc. tion, and that from. the pottom rises to the opening, and in the same direction passes beyond it. It is necessary, therefore, in a camera obscura, to place a small mirror diagonally behind the lens, so as to throw all the light which enters, downwards to a broad table, upon which the picture may be conveniently contemplated from any side. The camera obscura gives useful assistance to young painters, by enabling them to study perspective outlines and the effects of light, shade, and colour, more profitably than they can at first, by looking at the objects themselves. The modern art of Photography (which means writing by light) fixes the otherwise transient image upon the screen of the camera. This is effected by coating the screen of the camera with a chemical preparation sensitive to light. The discovery made by Daguerre, in 1830, has proved to be one of the most glorious in the whole domain of science. This subject will be again noticed under the chemistry of light. A similar but less vivid effect is produced by merely making a small hole in the shutter of a dark room, and letting the light which enters by it fall on any white surface beyond. The whole landscape is at once dimly portrayed upon the surface. Barry, the eminent painter, while lying on a sick bed, in fever, mistook such a scene appearing on the ceiling of his room for a supernatural vision. If the opening be very small, the picture will be tolerably defined, but very feebly illuminated: but if the opening be of considerable size, the mixing of the pencils will be so great as to leave no particular object distinguishable. In either case, however, if a lens be introduced to fill the opening, it will converge every entering pencil of light to an exact point, and a perfect picture instantly starts into view. 818. The distance from a lens at which an image is formed, or the focal distance, depends, first, upon the refractive or bending power of the lens, that is, on its form and substance; and, secondly, upon the direction of the rays of light when they reach the lens, as to whether they are divergent, parallel, or convergent. Rays diverging from a point, a (fig. 196), to fall on a comparatively flat or weak lens at L, might meet only at the point, d, or even further off; while, with a stronger or more convex lens, they might meet at c or at b. A lens weaker still might only destroy the divergence of the rays, without being able to give them any convergence at all, and then they would all proceed parallel to one another, as Conjugate Foci of Lenses. 589 seen at e and f. If the lens were yet weaker, it might only destroy a part of the divergence, causing the rays from a, after passing through, to go to g and h, instead of to i and k, in their original direction. In an analogous manner, light coming to the lens in the contrary directions from b, c, d, &c., might, according to the strength of the lens, be all made to come to a focus at a or at l, or in some more distant point; or the rays might become parallel, as m and n, and therefore would never come to a focus, or they might remain divergent. It may be observed in the above figure (196), that the farther an object is from the lens, the less divergent the rays are which fall from it upon the lens ; or the more nearly do they approach to being parallel. Proceeding from b, there is much divergence in the exterior rays, from less, from d less still, and rays from a great distance, as those represented by c and ƒ, appear quite parallel. If the distance of the radiant point be very great, they really are so nearly parallel that a very nice test is required to detect the nonaccordance. Rays, for instance, coming to the earth from the sun, do not diverge the thousandth of an inch in a thousand miles. Hence where we wish to make experiments with parallel rays, we take those of the sun. Any two points so situated on the opposite sides of a lens, as that, when either becomes the radiant point of light, the other is the focus of such light, are called conjugate foci. An object and the image of it formed by a lens are always in conjugate foci, and as the one is nearer the lens, the other will be in a certain propor. tion more distant. 819. The principal focus of a lens, by the distance of which from the glass we compare or classify lenses, is the point at which the sun's rays, or any parallel rays, are made by it to meet; and thus, by holding the lens in the sin, and noting at what distance behind |