Concave lens

“ In refraction, I added "The focal length f is considered negative for concave lenses." (Though this wouldn't be true for concave lenses with lower index of refraction than the surrounding medium.) I suggest also adding, "Incoming parallel rays are focused by a convex lens into an inverted real image one focal length from the lens, on the far side of the lens. Rays from an object at finite distance are focused further from the lens than the focal distance; the closer the object is to the lens, the further the image is from the lens. ”

“ A concave lens must of necessity render originally parallel rays divergent. The principal focus of the convex lens is the point at which the rays which pass through it, near and parallel to its axis, converge. The science of optics is one that needs to be taught. ”

“ A great many people of all ages suffer from short-sight. For one reason or another the distance between lens and retina becomes too great for a person to distinguish distant objects clearly. The lens, as shown in Fig 117a, is too convex—has its minimum focus too short—and the rays meet and [Pg 250] cross before they reach the retina, causing general confusion of outline. This defect is simply remedied by placing in front of the eye (Fig. 117b) a concave lens, to disperse the rays somewhat before they enter the eye, so that they come to a focus on the retina. ”

“ Thus it is possible to correct a system by combining a convex and a concave lens, if both have aberrations of the same amount but of opposite signs. In this case the power of the crown lens must preponderate so that the resulting lens is of the same sign, but of a little less power. Correction of the spherical aberration in strong systems with very large aperture can not be brought about by means of a single combination of two lenses, but several partial systems are necessary. Further, under-corrected systems must be combined with over-corrected ones. ”

“ Lenses with sharp edges (thicker at the centre) are convergent or positive lenses. Lenses with blunt edges (thinner at the centre) are divergent or negative lenses. The first group comprises:— (1) The bi-convex lens; (2) the plano-convex lens; (3) the convergent meniscus. The second group:— (4) The concave lens; (5) the plano-concave lens; (6) the divergent meniscus (Fig. 8) .
Principal Focus.—A lens is usually a solid of revolution, and the axis of revolution is termed the principal axis of the lens. When the surfaces are spherical it is the line joining the centre of curvature. ”

“ Another very useful form of doublet was proposed by Sir John Herschel, chiefly like the Coddington lens, for the sake of a wide field, and chiefly to be used in the hand. It is shown in Fig. 9; it consists of a double convex or crossed lens, having the radii of curvature as 1 to 6, and of a plane concave lens whose focal length is to that of the convex lens as 13 to 5. ”

“ Here a convex lens produces a distant, and therefore magnified image of a near transparent object, which is strongly enlightened by a lamp placed behind it; a concave mirror is generally put behind the lamp to throw as much of the light as possible on the object, which is some group of figures painted on a glass slide, and is inverted so that the image may be cast in an erect position, on a wall or a white sheet, at a proper distance. ”

“ Nos. 3, 4, 5, 6 have two spherical surfaces. When a lens is thicker at the middle than at the sides it is called a convex lens; when thinner, a concave lens. The names of the various shapes are as follows:—No. 1, plano-convex; No. 2, plano-concave; No. 3, double convex; No. 4, double concave; No. 5, meniscus; No. 6, concavo-convex. The thick-centre lenses, as we may term them (Nos. 1, 3, 5) , concentrate a pencil of rays passing through them; while the thin-centre lenses (Nos. 2, 4, 6) scatter the rays (see Fig. 105) .
Fig. 104.—Six forms of lenses. THE CAMERA.
Fig. ”

“ They are free from chromatic aberration, being subject only to that of the eye glass, which is never considered.
They are shorter, cæteris paribus, for the focal length of a concave speculum is only half its radius, whereas that of a glass lens with equal surfaces is the whole radius.
They give brighter images, for there is less light lost in their reflexions, than in the refraction through an object glass. ”

“ It is seen from the equations giving the distances of the cardinal points from the vertices that the first principal focus F is always behind S1, and the second principal focus F′ always in front of S2, and that the principal points are within the lens, H′ always following H. If one of the radii becomes infinite, the lens is plano-concave (fig. 9, 5) .
(3) If the radii are both positive. These lenses are called convexo-concave. Two cases occur according as r2 > r1, or < r1. (a) If r2 > r1, we obtain the mensicus (fig. 9, 3) . Such lenses are always collective ”

“ The field lens is a positive meniscus with a noticeable amount of concavity in the rear face while the eye lens is a “crossed” lens, the outer curvature being about 1⁄6 of the inner curvature. The marginal field in this ocular is a little better than in the conventional Huygenian.
A commoner modification now-a-days is the Mittenzwey form, Fig. 101b. This is usually made with 2:1 ratio of focal lengths, and the field lens still a meniscus, but less conspicuously concave than in the Airy form. The eye lens is the usual plano-convex. ”

“ The direct light of the lamp G, as well as that reflected by the mirror and passing through the lens c, is so concentrated as to project a brilliant beam of light through the painted slide, which being in the conjugate focus of the large plano-convex lens d, the pictures on the glass are refracted in a magnified form on the white cloth P Q.
The magic lantern, therefore, consists of a box to hold the lamp, a concave mirror, and a convex lens to concentrate the light on the slide, and a second convex lens to throw the image on the screen. ”

“ What will happen will be this: assuming the second lens to be away, the rays will 86emerge from the first (convex) lens and form a coloured image at A. But if the second flint-glass concave lens be interposed it will, by means of its action in a contrary direction, undo all the dispersion due to this first lens and a certain amount of deviation, so that we shall get the combination giving an almost colourless image at B.
Fig. ”

“ Concave lenses should never be used for work within the far point; but they may be used in all cases to improve distant vision, and in very short-sighted persons to remove the far point so as to enable fine work such as sewing or reading to be done at a convenient distance. The weakest pair of concave lenses with which one can read clearly test types at a distance of 18 ft. ”

“ Double concave lenses produce effects which are just the reverse of those we have been considering. Instead of increasing in thickness from the edges to the centre, they follow the contrary plan, and increase from the centre to the edges. Consequently, instead of the rays meeting at the focus, they diverge from each other, and gradually spread out, as shown in fig. ”

“ The single lens has a very small sharp field, hardly 10° in angular extent, the image falling off rapidly in quality as it departs from the axis. If plano-convex, as is the eye lens of common two-lens oculars, it works best with the curved side to the eye, i.e., reversed from its usual position, the spherical aberration being much less in this position. ”

“ The real romance of the construction of this huge telescope centres on the making of the lenses and mirror. First-class lenses for all photographic and optical purposes command a very high price on account of the care and labour that has to be expended on their production; the value of the glass being trifling by comparison. Few, if any, trades require greater mechanical skill than that of lensmaking; the larger the lens the greater the difficulties it presents, first in the casting, then in the grinding, last of all in the polishing. ”

“ Should the lenticular elasticity no longer admit of a sufficient scope for refraction, we must then either adjust the distance of the objects, as we see a far-sighted individual do, by holding the book proportionably farther off, or we must afford the eye assistance by accommodating it with movable auxiliary lenses, spectacles, which replace the lost power of adjusting forms to the natural eye. This power of accommodating the focus disappears beyond recall if the lens has sustained an injury, or if we remove it entirely, from its having grown turbid. ”

“ It will only be necessary to mention that the prisms used in the eye-pieces are made by cutting a double convex lens in two, and reversing the halves. They are so placed that the centre of each prism is just in the centre of each eye; but as the eyes of different people vary in distance, an arrangement is generally added so that the eye-pieces may slide from side to side. Being cut from lenses, the prisms have a magnifying power; consequently other means are provided for sliding them up and down to suit the length of focus in different eyes.
Fig. 68.—Stereoscope. ”

“ I find it impossible to focus a red object, such as the filament of an electric lamp screened by a properly selected deep red glass, when placed at the ordinary distance of distinct vision—some nine or ten inches from the eye—without the aid of a convex lens. In this case one is not too short-sighted but too long-sighted to see the object distinctly; in other words, the lenses of the eye cannot refract the red rays sufficiently to produce well-defined images upon the retina, and the refraction has to be increased by artificial means. ”

“ When very high powers are required, a single plano-convex lens is sometimes used, but although there is less loss of light in this case, the field of view is so contracted in comparison with that given with other eyepieces that the single lens is seldom used. ”

“ The cover slip is not only a protection for our object but for our objective. Water you may argue cannot harm the lenses of the objective. Perhaps not, we will not argue the point but, when the water dries on the objective, it leaves a certain amount of deposit on the glass and this deposit must be rubbed off. The less often the lenses are rubbed the better for them, glass especially very highly polished optical glass, is far more easily scratched than many [299] people imagine and a scratched lens is an inefficient lens. ”