Lenses

Type of physical science: Classical physics

Field of study: Optics

A lens is a device made from glass or another transparent material that causes light rays entering one of its sides either to diverge or converge as the rays leave the other side. The two scientific instruments made from lenses, the telescope and the light microscope, led to a further understanding of the universe and the nature of life.

Overview

A lens is a device made from glass or another transparent material that causes light rays entering one of its sides either to diverge or converge as the rays leave the other side. In general, light rays passing through a convex lens surface are brought together, or converged; light rays passing through a concave lens surface are spread apart, or diverged. Lenses are made with various combinations of flat, convex, and concave surfaces in order to converge or diverge light rays to a desired degree. For a transparent object to act as a lens, however, at least one of its surfaces must be curved--that is, either convex or concave.

The diverging or converging effects of lenses depend on the behavior of light as it passes through transparent materials. Light travels at its maximum velocity in a vacuum. As it passes through transparent matter of any kind, its velocity is slowed. The degree to which the velocity is slowed is a measure of the refractive index of a transparent material, which is equivalent to the ratio of the velocity of light in a vacuum to the velocity of light in the transmitting medium. Because all materials transmit light at a slower velocity than a vacuum, the value for the refractive index is always greater than one. For convenience, however, the refractive index of air (1.00029) is usually taken as 1, as if air transmitted light with the same velocity as a vacuum. Glass and the plastic materials used to make lenses have a refractive index of about 1.5.

As light rays pass from a transparent material of one refractive index to a material with a differing refractive index, the light rays may be bent from their paths. The degree of bending, or refraction, as the bending is termed, depends on two factors: the magnitude of the difference in refractive index of the two materials and the angle at which the light strikes the surface of the second transparent material. If light strikes the surface of the second material at an angle exactly perpendicular to the surface, no refraction occurs and the light is transmitted without a change in direction. At any other angle, the light rays are bent from their paths as they pass through the surface. As the angle at which light strikes the surface becomes more acute, the degree of bending increases. For a transparent material of a given type, the degree of bending for light striking the surface at a fixed angle is always the same. For another material of greater refractive index, the degree of bending for this angle will be greater.

If parallel light rays pass from air through a glass plate with flat surfaces, the light rays are all bent to the same degree and exit the other side also as parallel rays. Yet, if parallel light rays pass from air through a glass surface that is convex or concave, each point on the surface is presented to the light at a different angle. Therefore, the degree of refraction is different for every point on the surface. For a convex lens in which the surface is part of a sphere, a ray of light passing through the center of the lens at an angle perpendicular to the surface is not refracted and exits the other side of the lens traveling in the same direction. All rays parallel to this ray that strike the lens surface at progressively greater distances from the center are bent to progressively greater degrees. As a result, the parallel rays entering on one side are converged or focused to a point at some distance on the other side of the lens. The distance from the center of the lens to this point is the focal length of the lens. In general the smaller the radius of curvature of a convex lens, the shorter the focal length. A lens that has symmetrically curved surfaces will have focal points on either side at the same distance from the center of the lens.

Light traveling in either direction through a lens follows exactly the same pathways.

Therefore, if a light source is placed at the focal point of a convex lens, the light rays will exit the opposite side as parallel rays traveling in a direction perpendicular to the long axis of the lens.

These characteristics allow lenses to form images of objects placed on one of their sides. For convex lenses, the images take two forms, depending on whether an object is placed outside or inside the focal point of the lens. Whether the object is a light source or reflects light coming from another source, light rays travel from its surfaces in all directions. Rays of light traveling from points over the surface of an object placed outside the focal point on one side of a convex lens are all focused into a series of corresponding points in a vertical plane at some distance from the focal point on the other side of the lens. If a screen is placed in this plane, the image of the object can be seen directly by an observer. An image of this type is called a real image.

A real image has two characteristics that are highly significant for instruments based on convex lenses: The image is inverted, and it is typically magnified--that is, it is larger than the original object. The degree of magnification depends on the focal length of the lens and the placement of the object with respect to the focal point. As the object moves closer to the lens, the image plane moves farther from the lens on the opposite side and is magnified to a greater degree. The greatest magnification is produced when an object is placed as close as possible to the focal point of a lens of very short focal length. Objects placed inside the focal point of a convex lens do not form a real image: There are no points in any plane in which rays from object point are brought to focus. As a result, the image cannot be focused on a screen. Nevertheless, the image can be seen by looking directly into the lens on the opposite side from the object. This type of image, which cannot be focused on a screen but can be viewed by looking into the lens, is called a virtual image. A virtual image is typically magnified but not inverted.

The total collection of points forming the virtual image can be seen directly by the human eye because the rays apparently radiate outward from all points in an image plane that is placed at some distance behind the actual object. These diverging light rays are focused into a real image on the retina by the lens of the eye, which acts as a more or less typical convex lens.

Applications

A number of highly useful devices, with great technical, scientific, and social value, are based on lenses. The simplest is the single hand-held convex lens in which an erect, magnified virtual image is formed of an object held inside the focal point of the lens. A projector is a similarly simple device in which an object such as a photographic plate, illuminated strongly by an intense light, is held just outside the focal point of a convex lens. The rays leaving the lens are focused into a real image on a screen. A camera is also a simple instrument, in which a convex lens forms a real image of an object that lies outside its focal length. A photographic film is placed in the plane of the real image focused by the lens.

More complex optical devices such as microscopes and telescopes use several lenses in combination. In the light microscope, the object is held just outside the focal point of a convex lens of very short focal length. This lens, called the objective lens, focuses a real image that is highly magnified and inverted. The objective lens is placed at one end of a tube. At the opposite end of the tube is a second convex lens that is placed so that the real image formed by the first lens falls inside the focal point of the second lens. This lens, called the ocular lens, forms a virtual image that is magnified further but remains in the orientation focused by the first lens--that is, inverted. The virtual image formed by the ocular lens is viewed by looking directly into this lens. The total magnification produced by the microscope is the product of the magnification of the objective and ocular lenses.

More complex light microscopes have a rotating turret containing a series of objective lenses of decreasing focal length so that the object can be viewed at successively higher magnifications. On most microscopes, the combination of objective lenses allows an object to be viewed at a total magnification ranging from about ten to one thousand times. To correct for inherent faults in the glass lenses used in light microscopes, the objective and ocular lenses are constructed from a series of lenses placed close together, usually as many as eight to ten for the objective and two to three for the ocular. The individual lenses in the objective or ocular lenses are mounted so close together that they act, in effect, as a single highly corrected lens.

Most light microscopes have another converging lens, the condenser lens that focuses on an intense spot of light on the object from a source such the sun or an incandescent bulb. This lens works only to increase the illumination of the object and has no imaging functions.

Although there is no limit to the degree of magnification obtainable by a light microscope, there is a definite limit to the amount of fine detail that can be seen in an object.

This limit, called the resolving power or resolution of the microscope, is fixed essentially by the wavelength of light used to view the object. As shorter wavelengths are used to illuminate the object, progressively smaller features can be seen, to a limit of about 0.2 micrometer for a high-quality microscope using the shortest visible wavelengths at the blue end of the spectrum.

The maximum useful magnification is that which will increase the size of an image of points with this dimension to the level, allowing them to be distinguished clearly by the human eye. For practical purposes, this degree of magnification is about one thousand times. Magnification past this range does not increase the detail visible in the image.

Telescopes are very similar in construction to a light microscope. In these instruments, the object typically lies far beyond the focal point of the objective lens. As a result, this lens--which is placed at one end of a tube--focuses an inverted real image of the object that is not greatly magnified. A second ocular lens is placed at the opposite end of the tube, placed so that the real image formed by the objective lens falls just inside its focal point. This lens forms a magnified virtual image of the object that remains inverted. The practical total magnification, which depends primarily on the ocular lens, ranges from a minimum of two to several hundred times.

When used for viewing astronomical objects, the fact that a telescope forms an inverted image is not a handicap. For terrestrial objects, telescopes include a series of prisms that turn the image right side up. A set of binoculars, for example, consists of two side-by-side telescopes, one for each eye, that include prisms that turn the image upright.

The human eye is a simple optical device in the sense that it employs a single convex lens in a manner similar to a camera. The lens focuses a real image of objects that lie beyond the focal point of the lens on the retina at the back of the eye, which converts the image into a series of nerve impulses that are reconstructed by the brain into a sensory image. In contrast to optical devices, which use glass or plastic lenses of fixed focal length, the lens of the human eye is a flexible structure that is adjusted in focal length by small muscles that surround the lens. By contracting, these muscles increase the curvature of the lens and thus its focal length. When the muscles are relaxed, the reduced curvature allows objects lying at farther points to be focused sharply on the retina. As the muscles contract, the curvature of the lens increases and the focal length decreases, allowing objects closer to the eye to be focused.

In many individuals, the distance from the lens to the retina is too long or too short.

When the distance is too long, the fully relaxed lens focuses the image in a plane in front of the retina, so that the image formed on the retinal is out of focus. As objects are placed closer to the eye, a point is reached at which a clear focus is obtained. Persons with this defect are called near-sighted, or myopic; in severe cases, only objects placed a few centimeters from the eye can be focused clearly. When the distance from the lens to the retina is too short, the fully relaxed lens focuses the image in a plane that falls behind the retina. Although this image can be focused still by contraction of the eye muscles, there is a limit to which this accommodation can be made; therefore, objects closer than several meters or more from the eye cannot be focused. Persons with this defect are called farsighted, or hyperopic. Both nearsightedness or farsightedness can be corrected by means of a glass or plastic lens placed in front of the eye.

The lens of the human eye loses its flexibility gradually from the time of birth onward.

For most individuals with normal vision, the loss of flexibility has progressed far enough by the age of forty to interfere with the eye's ability to change focus to accommodate objects placed at the closest distances. The lens of a baby's eye, for example, is so flexible that objects placed as close as 7 centimeters can be focused clearly. The nearest point of focus for persons in their twenties and thirties is about 10 to 15 centimeters. By age forty, the point of closest focus has receded to about 22 centimeters in a person with normal vision. By the age of fifty, the nearest point of focus lies at about 40 centimeters, so that objects must be held nearly at arm's length to be sharply focused. By the age of sixty, the average person of normal vision cannot focus objects sharply that are closer than about 200 centimeters.

Context

Lenses have been known from ancient times. The Roman dramatist and statesman Seneca, for example, noted that small and indistinct objects could be enlarged and seen more clearly if viewed through a glass globe filled with water. Glass droplets, or spheres, were used for the same purpose and for focusing the sun's rays for heating or burning objects. Hand-held convex lenses and eyeglasses were made in Europe by the late thirteenth century.

The first recorded systematic studies of lenses and their properties were made by the Arabian scholar Abu `Ali al-Hasan ibn al Haytham in the early part of the tenth century. Much later, the study of lenses was put on a fully scientific footing in Europe and England by Sir Isaac Newton, Christiaan Huygens, Rene Descartes, Carl Friedrich Gauss, and others; by the early 1800's, the work of these scientists had laid out the fundamentals of lens optics. Means for correcting the defects inherent in glass lenses were worked out by the mid-1800's, allowing glass lenses of very high quality to be made.

The two primary scientific instruments developed from these investigations--the telescope and the light microscope--first appeared in Europe around the beginning of the seventeenth century. The original inventor of the telescope is unknown. Yet, Hans Lippershey is known to have made a number of telescopes in Holland in 1608. In 1609, Galileo made the first compound telescope designed from optical principles. With his telescopes, Galileo saw astronomical details, such as the craters on the Moon and the satellites of Jupiter. He also made the observations leading to his deduction that the earth revolves around the sun, contrary to the formerly held belief that Earth is the center of the solar system. Galileo also noted that the same arrangement of lenses used in the telescope could also be used to magnify small objects. He stated, for example, that by means of his lens system he could make flies appear "as big as lambs."

The first instruments designed specifically as microscopes were probably made during the same period as telescopes, around the beginning of the seventeenth century. Although the inventors remain uncertain, credit is usually given to one or more Dutchmen, including Hans Janssens and his son Zacharias, and Lippershey. Some of the earliest instruments designed specifically as light microscopes used a single lens, and others were compound instruments with two lens placed at either end of a tube. Perfection of the light microscope required another 250 years of effort to correct the defects inherent in glass lenses. By the late nineteenth century, light microscopes had been developed to their ultimate degree of resolution.

It is difficult to overestimate the effects of the telescope and light microscope on science and human society. Research with the light microscope put astronomy on a firm scientific footing and led to a fundamental understanding of the universe and its nature. The light microscope opened the microscopic world to view and set off an explosion of new findings in biology that changed the concept of the nature of life. Both instruments and discoveries made through their application continue to lie at the forefront of scientific investigation.

Other applications of lenses--including the camera, projector, and lenses for the correction of human vision--have been equally as important to human society, so much so that it is difficult to imagine how life would be without them.

Principal terms

FOCAL LENGTH: the distance from the center of a convex lens to the focal point

FOCAL POINT: the point at which parallel rays entering one side of a convex lens are brought to a point of focus on the other side of the lens

REAL IMAGE: an image that can be focused on a screen

REFRACTION: the bending of light rays as they pass from a medium of one refractive index to a medium with a different refractive index

REFRACTIVE INDEX: the ratio of the velocity of light in a vacuum to the velocity in a transmitting medium

RESOLVING POWER: the ability of a lens or optical device to image small details in an object

VIRTUAL IMAGE: an image that can be seen only by looking directly into a lens

Bibliography

Bradbury, Savile. THE EVOLUTION OF THE LIGHT MICROSCOPE. New York: Pergamon, 1967. This highly readable book presents a complete description of the theory and development of the light microscope. Many illustrations of lenses, their action, and microscopes from the earliest models to contemporary instruments are included.

Hughes, Arthur. A HISTORY OF CYTOLOGY. New York: Abelard-Schuman, 1959. A well-written and informative history that ties the development of the light microscope to the explosion of research in cell structures.

Sears, Francis W., Mark W. Zemansky, and Hugo D. Young. UNIVERSITY PHYSICS. New York: Addison-Wesley, 1982. Chapter 40, "Lenses and Optical Instruments," presents an understandable discussion of the principles of optics based primarily on algebra. Earlier chapters in this standard college-level work describe the nature and propagation of light and image formation.

Spencer, Michael. FUNDAMENTALS OF LIGHT MICROSCOPY. New York: Cambridge University Press, 1982. One of the standard textbooks in light microscopy. Although intended for the college-level reader, the descriptions of optics and instruments are accessible to the average reader.

Wilson, Michael B. THE SCIENCE AND ART OF BASIC MICROSCOPY. Bellaire, Tex.: American Society for Medical Technology, 1976. A primer in light microscopes and their applications that starts with basic principles and leads to lens theory and the construction, operation, and application of various types of light microscopes. This booklet is clearly and simply written and is understood easily by a nontechnical reader.

Polarization of Light

Reflection and Refraction