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A optical lens produces its focusing effect because light travels more slowly in the lens than in the surrounding air, so that refraction, an abrupt bending, of a light beam occurs both where the beam enters the lens and where it emerges from the lens into the air.
A single lens has two precisely regular opposite surfaces; either both surfaces are curved or one is curved and one is plane. Lenses may be classified according to their two surfaces as biconvex, plano-convex, concavo-convex (converging meniscus), biconcave, plano-concave, and convexo-concave (diverging meniscus). Because of the curvature of the lens surfaces, different rays of an incident light beam are refracted through different angles, so that an entire beam of parallel rays can be caused to converge on, or to appear to diverge from, a single point. This point is called the focal point, or principal focus, of the lens (often depicted in ray diagrams as F). Refraction of the rays of light reflected from or emitted by an object causes the rays to form a visual image of the object. This image may be either real—photographable or visible on a screen—or virtual—visible only upon looking into the lens, as in a microscope. The image may be much larger or smaller than the object, depending on the focal length of the lens and on the distance between the lens and the object. The focal length of a lens is the distance from the centre of the lens to the point at which the image of a distant object is formed.
Usually the image formed by a single lens is not good enough for precise work in such fields as astronomy, microscopy, and photography; this is because the cone of rays emitted by a single point in a distant object is not united in a perfect point by the lens but instead forms a small patch of light. This and other innate imperfections in a lens’s image of a single object point are known as aberrations. To correct such aberrations, it is often necessary to combine in one mount several lens elements (single lenses), some of which may be convex and some concave, some made of dense high-refractive or high-dispersive glass, and others made of low-refractive or low-dispersive glass. The lens elements may be cemented together or mounted at carefully calculated separations to correct the aberrations of the individual elements and obtain an image of acceptable sharpness (see also aberration). The precise mounting also ensures that all lenses are properly centred; that is, the centres of curvature of all the lens surfaces lie on a single straight line called the principal axis of the lens. A frequently used measure of the quality of any lens system is its ability to form an image that is sharp enough to separate, or resolve, two very close dots or lines in an object. Resolving power depends on how well the various aberrations in a lens system are corrected.The simplest compound lens is a thin cemented combination of two single lenses, such as that used in the objective (the lens nearest the object) of a small refracting telescope. Microscope objectives may contain as many as eight or nine elements, some of which may be made of different materials in order to bring all colours of light to a common focus, and thus prevent chromatic aberration.
In the manufacture of lenses, slabs of glass are cut with a glass saw or slitting disk; a piece of the desired type and shape is chipped to a rough, round blank, or the pieces may be heated to softness, rolled to a round shape, and pressed in a mold to the desired size and to approximately the desired curvature of the surfaces. The surfaces are then ground, or lapped, to the final form, using coarse emery, carborundum, or diamond as an abrasive. Lens surfaces are ground on an iron tool, either flat or suitably curved, using progressively finer grades of one of the abrasives mentioned above. In the grinding process, a rotating cup-shaped tool is mounted so that its axis of rotation intersects the axis of the lens at the centre of curvature of the desired spherical surface. The obliquity of the tool axis must be adjusted so that the rim of the tool cuts across the centre of the (concave) lens being generated. For convex lenses, the centre of the rotating tool face cuts the rim of the lens blank. As both tool and lens rotate about their respective axes, a spherical surface of the desired radius of curvature is generated on the lens.