lens, in optics, piece of glass or other

transparent substance that is used to form an image of an object by focusing rays of

light from the object. A lens is a piece of transparent material, usually circular in

shape, with two polished surfaces, either or both of which is curved and may be

either convex (bulging) or concave (depressed). The curves are almost always

spherical; i.e., the radius of curvature is constant. A lens has the valuable

property of forming images of objects situated in front of it. Single lenses are used

in eyeglasses, contact lenses, pocket magnifiers, projection condensers, signal

lights, viewfinders, and on simple box cameras. More often a number of lenses made of

different materials are combined together as a compound lens in a tube to permit the

correction of aberrations. Compound lenses are used in such instruments as cameras,

microscopes, and telescopes.
Optical principles for lenses
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. A long-focus

lens with beamsplitters forms a

larger image of a distant object, while a short-focus lens forms a small image.
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. The

objective lenses used in cameras may contain from two to 10 elements, while a so-

called zoom or variable-focal length lens may have as many as 18 or 20 elements in

several groups, the different groups being movable along the axis by levers or cams

in order to produce the desired change in focal length without a shift of the focal

plane. Lenses also vary greatly in diameter, from

as small as 0.16 cm (1/16 inch) for an element in a microscope objective to as large

as 100 cm (40 inches) for an astronomical telescope objective. In reflectors and

several other types of astronomical telescopes, concave mirrors are used for the

objective instead of lenses.
Manufacturing optical lenses
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. Also,

there are optical windows,

optical mirrors,

optical prisms, etc.
Fine grinding, or smoothing, is done using carefully graded emery flour as an

abrasive. A number of fine-ground lens blanks are then mounted with pitch on a block

so that they can be polished together. The polishing tool is covered with a thin

layer of pitch, wax, or even coarse cloth, and wet rouge or certain other mineral

oxides are also used as polishing agents. The polishing of glass is a slow process,

requiring lenses to be oscillated back and forth, sometimes for hours, against the

rotating polisher. After both sides have been polished, the lens is ground around the

edge to centre it and give it the correct diameter. If a compound objective is being

made, several single lenses must be mounted together in a precise coaxial

arrangement, and their thicknesses, separations, and centring must be kept very close

to the prescribed values, or the aberration corrections laboriously determined by the

lens designer will not be realized. The finished lens’s resolving power is then

tested by using the lens to form an image of a point source or other suitable test

object. Sophisticated variants of this basic testing procedure have been developed

using photoelectric cells or interferometers to obtain greater measuring accuracy.