Lens

Lens types

A compound lens is a combination of two or more lenses in which the second surface of one lens has the same radius as the first surface of the following lens and the two lenses are cemented together. Compound lenses are used instead of single lenses for color correction, or to introduce a surface which has no effect on the aperture rays but large effects on the principal rays, or vice versa. Sometimes the term compound lens is applied to any optical system consisting of more than one element, even when they are not in contact.

The diameter of a simple lens is called the linear aperture, and the ratio of this aperture to the focal length is called the relative aperture. This latter quantity is more often specified by its reciprocal, called the f-number. Thus, if the focal length is 50 mm and the linear aperture 25 mm, the relative aperture is 0.5 and the f-number is f/2. See Focal length

A compound lens made of two or more simple thin lenses cemented together is called a cemented lens.

Lens systems

A lens system consisting of two systems combined so that the back focal point of the first (the objective) coincides with the front focal point of the second (the ocular) is called a telescope. Parallel entering rays leave the system as parallel rays. The magnification is equal to the ratio of the focal length of the first system to that of the second. See Telescope

A photographic objective images a distant object onto a photographic plate or film. The amount of light reaching the light-sensitive layer depends on the aperture of the optical system, which is equivalent to the ratio of the lens diameter to the focal length. The larger the aperture (the smaller the f-number), the less adequate may be the scene luminance required to expose the film. Therefore, if pictures of objects in dim light are desired, the f-number must be small. On the other hand, for a lens of given focal length, the depth of field is inversely proportional to the aperture.

In general, photographic objectives with large fields have small apertures; those with large apertures have small fields.

The basic type of enlarger lens is a holosymmetric system consisting of two systems of which one is symmetrical with the first system except that all the data are multiplied by the enlarging factor m. When the object is in the focus of the first system, the combination is free from all lateral errors even before correction. A magnifier in optics is a lens that enables an object to be viewed so that it appears larger than its natural size. The magnifying power is usually given as equal to one-quarter of the power of the lens expressed in diopters. See Diopter, Magnification

(geological), a mode of occurrence of rock and ores in the form of a lens that tapers toward the edges. The dimensions of a lens vary, ranging from several meters in length and several centimeters in thickness to 1 km and more in length and several dozen meters in thickness.

a transparent body limited by two light-refracting surfaces; one of the main elements of an optical system. In the most useful lenses, both surfaces have a common axis of symmetry; among these, the most useful and easiest to produce are those with spherical surfaces. Less common are lenses with two mutually perpendicular planes of symmetry and with surfaces that are either cylindrical or toroidal. Such lenses are used in the eyeglasses prescribed for astigmatism of the eye and anamorphic attachments.

Optical glass and organic glass are the most commonly used materials for lenses. Special lenses for use in the ultraviolet region of the spectrum are made from crystals of quartz, fluorite, and lithium fluoride. Lenses for use in the infrared region of the spectrum are produced from special glasses, silicon, germanium, fluorite, lithium fluoride, and cesium iodide.

Description of the optical properties of axially symmetrical lenses usually involves the rays that are incident to the lens at a small angle with respect to the axis. These rays constitute what is called the parallaxial pencil of rays. The effect of a lens on these rays is determined by the position of its cardinal points (that is, of the principal points H and H’), at which the principal planes of the lens intersect the axis, and by the position of its front and back focuses F and F’ (see Figure 1). The segments HF = f and H’ F’ = f’ are called the lens’ focal lengths; when the media adjoining the lens have the same indexes of refraction, f is always equal to f’. The points O of intersection of the surfaces of the lens with the axis are called its vertexes. The distance between the vertexes is called the thickness.

Figure 1

The geometric values that characterize lenses and systems of lenses are considered positive if the directions of corresponding segments coincide with the direction of the light rays. In Figure 1, the rays pass through the lens from left to right and segment H’ F’ is oriented the same way; for this reason, f’ > 0 and f < 0.

Refraction at the surfaces of the lens alters the directions of the incident rays. If the lens transforms a parallel beam into a convergent beam, it is called a converging lens. A parallel beam becomes a divergent one after passing through a diverging lens. Rays that were parallel to the lens axis before refraction intersect at the principal focus F’ of a converging lens, for which f’ is always positive. The principal focus F’ of a diverging lens is the point of intersection not of the rays themselves but of their imaginary continuation in the direction opposite the direction of propagation of the light, so that f’ < 0. The externally distinguishing feature of thin converging and diverging lenses is that the edges are less thick than the center in the case of the former and thicker in the case of the latter.

The measure of the refracting power of a lens is its lens power Φ, which is a quantity inversely proportional to the focal length (Φ = 1/f’) and measured in diopters (m^-1). For converging lenses, Φ > 0, so that the lenses are called positive. Diverging lenses, for which Φ < 0, are called negative. Afocal lenses, for which Φ = 0, are also used; the focal length in these cases equals infinity. These lenses have neither a convergent nor a divergent effect on light rays but generate aberrations and are used in mirror-lens and lens objectives as aberration compensators.

All of the parameters determining the optical properties of a lens bounded by spherical surfaces may be expressed in terms of the radii of curvature r₁ and r₂ of the surfaces, the lens thickness along the axis d, and the index of refraction n of the lens’ materials. For example, the lens power and the focal length of a lens are given by the relationship

The radii r₁ and r₂ are considered positive if the direction from the vertex of the lens to the center of the corresponding surface coincides with the direction of the rays (r₁ > 0, r₂ < 0 in Figure 1). Equation (1) is valid only when applied to paraxial rays. The shape of a lens may differ given the same material and lens power. Figure 2 shows several ienses with the same optical power and different forms. The first three lenses are positive; the last three are negative. A lens is called thin if its thickness d is small in comparison to r₁ and r₂. A sufficiently accurate expression of the optical power of such a lens is obtained when the second term in equation (1) is omitted.

Figure 2

The position of the principal planes with respect to the vertexes may also be determined from the values of r₁, r₂, n, and d. The distance between the principal planes is relatively independent of the form and power of a lens and is approximately equal to [d(n— 1)]/n. In the case of a thin lens this distance is small; it may be assumed for practical purposes that the principal planes coincide.

When the positions of the cardinal points are known, the position of the optical image of a point produced by the lens (see Figure 1) is determined by the equations

x · x′ = f · f′ = f′²

(2) l′/l = -f/x = -x′/f′ = V

where V is the linear magnification of the lens, l and l’ are the distances from the point and its image to the axis (positive, if they are located above the axis), x is the distance from the front focus to the point, and x’ is the distance from the back focus to the image. If t and t’ are the distances from the principal points to the planes of the object and image, respectively, then (since x = t - f, x’ = t’ - f’)

f′/t′ + f/t = 1

(3) or

1/t′ + 1/t = 1/f′

In thin lenses, t and t’ may be measured from the corresponding surfaces of the lens.

It follows from equations (2) and (3) that as the image point (real source) approaches the focus of the lens the distance between the image and the lens increases. A converging lens gives a real image of a point when the point is located in front of the focus; when the point is located between the focus and the lens, the image is called virtual. A diverging lens always gives a virtual image of a luminous real point.

(lentil), a genus of annual herbs of the family Legurhinosae. The erect or partly climbing stem is 20–55 cm tall. The compound even-pinnate leaves have three to eight pairs of narrow leaflets, which end in short bristles measuring 1–60 mm long. The small white, pink, or violet-blue flowers are distributed singly or in groups of two or three on the axillary peduncle. The fruit is a pod; the flat or protuberant seeds are multicolored, monochromatic, or in patterns. The common lentil (L. culinaris) is classified into two groups according to the size of the seeds: the large-seeded plate-like group has a seed diameter of 5.5–9 mm, and the small-seeded group has a seed diameter of 2–5.5 mm.

There are five species in the Mediterranean region, Asia Minor, Transcaucasia, and Middle Asia. The common lentil, the only cultivated species, is distributed in many countries of Europe, Asia, and North Africa. In the USSR it is found in the southern European region, the Volga region, and Middle Asia. the plant is a food and feed crop.

Lentils are a spring crop, with a vegetative period of 75 to 115 days. The plants are relatively drought resistant, and the shoots can withstand brief frosts to –5°C. The best soils are loose loams and sandy loams rich in lime. The feed is poor on very acidic and solonetzic soils. In crop rotation, lentils follow winter and root crops. Like other legumes, lentils enrich the soil with nitrogen and are good predecessors for subsequent crops. Seeds are sown in rows spaced 15 cm apart. Phosphorus fertilizer (40–80 kg/ha of P₂O₅) and potassium fertilizer (60–100 kg/ha of K₂O) are applied during late-fall plowing or during spring cultivation. Granulated superphosphate is used during seeding. Harvesting operations are begun when the beans on the lower and middle section of the plant begin to ripen and the seeds of the upper beans finish ripening in swathes. Combines, reapers, and hay cutters are used for harvesting. When the swathes are dry, they are threshed by combines and grain threshers.

Mature lentil seeds contain 23–32 percent protein (in dry matter), as much as 60 percent starch, and as much as 2.5 percent fat; they also contain vitamins B₁ and B₂. The seeds of large-seeded lentils are used in the production of groats and flour for bread, sausage, confectioneries, and canned goods. The seeds of small-seeded lentils, the green mass, the chaff, and the straw are fed to agricultural animals. One hundred kg of grain contains 120 feed units and 21 kg of digestible protein. Ten varieties of lentils have been regionalized in the USSR, including Petrovskaia–4/105, Talinskaia-6, Penzenskaia-14, and Petrovskaia lubileinaia.

In 1976 the world area under lentil cultivation was about 1.8 million ha, the gross grain yield was 1.2 million tons, and the average yield was 6.8 quintals per ha. In the USSR lentils are grown on small areas; in 1976 the crop occupied 35,700 ha.