Michelson, Albert Abraham

views updated May 11 2018

MICHELSON, ALBERT ABRAHAM

(b. Strelno, Prussia [now Poland], 19 December 1852; d . Pasadena, California, 9 May 1931)

physics, optics, metrology.

Precision measurement in experimental physics was Michelson’s lifelong passion. In 1907 he became the first American citizen to win a Nobel Prize in one of the sciences, being so honored “for his precision optical instruments and the spectroscopic and metrological investigations conducted therewith.” Michelson measured the speed of light in 1878 as his first venture into seientific research, and he repeatedly returned to the experimental determination of this fundamental constant over the next half century. Never fully satisfied with the precision of former measurements, he developed and took advantage of more advanced techniques and tools to increase the accuracy of his observations. He died, after several strokes, during an elaborate test of the velocity of light in a true partial vacuum over a mile-long course at Irvine, California; but the value later published by his colleagues (299,774 ±11 km./sec.) was probably less precise than Michelson’s own optical determination over a twenty-two-mile course between mountains in southern California during 1924–1926 (299,796 ± 4 km./see.).

Born to parents of modest means in disputed territory between Prussia and Poland, Michelson at the age of four emigrated with his parents, Samuel and Rosalie Michelson, to San Francisco via New York and Panama. The elder Michelson became a merchant to gold-rush miners in California and later in Virginia City, Nevada, while his son was sent after the sixth grade to board first with relatives in San Francisco and then with Theodore Bradley, the headmaster of Boys’ High School there. Bradley seems to have aroused young Michelson’s interest in science and to have recognized and rewarded his talents in the laboratory. At Bradley’s suggestion Michelson competed for a state appointment to the U.S. Naval Academy; but when three bovs tied for first place in the scholastic examination and another was appointed, young Michelson decided to take his case, with a letter of recommendation from his congressman, to the White House. In 1869 he traveled to Washington, saw President Grant, and gained his appointment to Annapolis.

Graduating with the class of 1873, Michelson went to sea lor several cruises before being reassigned to the academy as instructor in physical sciences. On 10 April 1877 Michelson married Margaret Heminway from a prosperous New York family; this marriage lasted twenty years and produced two sons and a daughter.

While teaching physics in 1878, Michelson became interested in improving upon Foucault’s method for measuring the speed of light terrestrially. In July 1878, with a $2,000 gift from his father-in-law, Michelson was able to improve the revolving-mirror apparatus and to perfect his experiment—the fourth terrestrial measurement of the speed of light. He was preceded by Fizeau, Foucault, and Cornu. Simon Newcomb, superintendent of the Nautical Almanac Office, became interested in his work. In consequence, his first scientific notices and papers were published in 1878–1879, and he began to collaborate with Newcomb on a government-sponsored project to refine further the determination of the velocity of light. He obtained a leave of absence to do postgraduate study in Europe during 1880–1882. He studied with Helmholtz in Berlin, with Quincke in Heidelberg, and with Cornu, Mascart, and Lippman in Paris.

In the winter of 1880–1881, while working in Helmholtz’ laboratory, Michelson thought of a means to try a second-order measurement of Maxwell’s suggestion for testing the relative motion of the earth against the ubiquitous, if hypothetical, luminiferous ether. Drawing on the credit that Alexander Graham Bell maintained in his account with the Berlin instrument makers Schmidt and Haensch, Michelson designed an apparatus called an interferential refractometer, which he then used to test for relative motion, or an “aether-wind,” by comparing the speed of two pencils of light split from a single beam and caused to traverse paths at right angles to each other upon a base that could be rotated between observations. At different azimuths it was expected that the recombined pencils forming interference fringes would shift past a fiducial mark and thereby give data from which could be calculated the “absolute motion” of the earth, with respect to the ether or the “fixed” stars, as it hurtles through space. This first ether-drift experiment was tried in Berlin, then at the Astrophysicalisches Observatorium at Potsdam, with disappointingly null results. The instrument itself was amazingly sensitive and versatile; but errors in experimental design, pointed out by A. Potier and later by H. A. Lorentz, together with the null results themselves and the theoretical difficulties with regard to what was meant by “absolute velocity,” later led Michelson to consider the experiment a failure. The hypotheses of A. J. Fresnel concerning a universal stationary ether and of G. G. Stokes concerning astronomical aberration were thus called into question.

The undulatory theory of light as generally accepted in the 1880’s simply assumed a luminiferous medium. This “aether” must pervade intermolecular spaces, of both transparent and opaque materials, as well as interstellar space. Hence, it should be at rest or stationary in the universe and therefore provide a reference frame against which to measure the earth’s velocity. Michelson boldly denied the validity of this hypothesis of a stationary ether, but he always maintained the need for some kind of ether to explain the phenomena of the propagation of light. Ad hoc hypotheses soon seemed necessary to explain why no relative etherwind or relative motion appeared to be detectable in Michehon’s interferometer at the surface of the earth. This curious puzzle piqued the interest of Lorentz, W. Thomson (later Lord Kelvin), and FitzGerald, among others.

In 1881 Michelson resigned from active duty, and the next year he joined the faculty of the new Case School of Applied Science in Cleveland, Ohio. There he set up improved apparatus, helping to check Simon Newcomb’s velocity-of-light measurements and testing various colored lights for indexes of refraction in various media. In 1885 Michclson began a collaborative project with Edward W. Morley of Western Reserve, a senior experimentalist (and primarily a chemist) with an elaborate laboratory. Their first effort, undertaken at the suggestion of W. Thomson, and of Rayleigh and Gibbs, was to verify the Fizeau experiment, reported in 1859, that supposedly had confirmed Fresnel’s drag coefficient by comparing the apparent velocities of light moving with and against a current of water. This “ether-drag” experiment worked out well and corroborated the suppositions of Fresnel, Maxwell, Stokes, and Rayleigh concerning astronomical aberration and an all-pervasive immaterial luminiferous medium.

Michelson and Morley next redesigned the 1881 ether-drift experiment to increase the path length almost tenfold and to reduce friction of rotation by floating a sandstone slab on a mercury bearing. During five days in July 1887 Michelson and Morley performed their test for the relative motion of the earth in orbit against a stationary ether. Their results were null and so discouraging that they abandoned any effort to continue with the tests they intended in the following autumn, winter, and spring. The sensitivity they had achieved with this new interferometer, about one-fourth part in one billion, was its own reward, however; and both innovators began to think of other uses for such instruments. Although the experimenters quickly forgot their disappointment, theorists, and notably FitzGerald, Larmor, Lorentz, and Poincaré, made much of their failure to find fringe shifts and to corroborate Fresnel and Stokes’s wave theory of light.

Michelson accepted an offer in 1889 to move to the new Clark University at Worcester, Massachusetts. Concurrently he began to carry out a monumental metrological project that he and Morley had envisioned to determine experimentally the length of the international meter bar at Sèvres in terms of wavelengths of cadmium light. Adapting his refractometer as a comparator for lengths that could be reduced through spectroscopy and interferometric techniques to nonmaterial standards of length, Michelson found in 1892–1893 that the Paris meter bar was equal to 1,553,163.5 wavelengths of the red cadmium line. So elegant were the success and precision of this project that Michelson became internationally famous.

In 1893 Michelson moved to the new University of Chicago to head its department of physics. There he began to develop his interests in astrophysical spectroscopy. Diffraction gratings, a new harmonic analyzer, and the echelon spectroscope, as well as a large-scale vertical interferometer, were designed by and built for Michelson around the turn of the century. He was clearly recognized as one of the foremost experimental physicists of the nation and was invited to give the Lowell lectures at Harvard in 1899, later published as Light Waves and Their Uses (Chicago, 1903). Also in 1899, Michelson remarried, having been divorced, and took as his second wife Edna Stanton, who bore him three daughters.

When Einstein’s three famous papers of 1905 appeared, one of uhich inaugurated the special theory of relativity by dispensing with the idea of an ether and by elevating the velocity of light into an absolute constant, Michelson was much too busy with prior commitments and with receiving honors to pay much heed.

The relation between Michelson’s experimental work and Einstein’s theories of relativity is complex and historically indirect. But the influence of his ether-drift tests on Lorentz, FitzGerald, Poincaré, W. Thomson, Lodge, Larmor, and other theoreticians around 1900 is less problematic and quite direct. Although scholars continue to debate the role of his classic ether-drift experiment, Michelson himself in his last years still spoke of “the beloved old ether (which is now abandoned, though I personally still cling a little to it).” He advised in 1927 in his last book that relativity theory be accorded a “generous acceptance,” although he remained personally skeptical.

From 1901 to 1903 he had served as president of the American Physical Society, and in 1907 he received the Copley Medal from the Royal Society (London) in addition to the Nobel Prize. In all, during his half-century as an active scientist he was elected to honorary membership in more than twenty-five societies, was awarded eleven honorary degrees, and received seventeen medals. In 1910–1911 he served as president of the American Association for the Advancement of Science, and from 1923 to 1927 he presided over the National Academy of Sciences.

During World War I, Michelson returned to the navy as a sixty-five-year-old reserve officer. He helped perfect an optical range finder and demonstrated tolerances for imperfections in striated optical glasses. After the war the Eddington eclipse expedition of 1919 made Einstein and relativity theory almost synonymous with esoteric modern science. Although legend has much inflated the role of the Michelson-Morley experiment in supposedly providing the basis for Einstein’s first work on the principle of relativity applied to electrodynamics, Michelson’s corroborations of the speed of light as a virtual constant did in fact prove significant equally for the special and for the general theories of relativity.

Early in the 1920’s Michelson began to spend more time in California at Mt. Wilson, in Pasadena, and at the California Institute of Technology. Besides teaching, his main work for almost a decade had been to perfect ruling engines for the production of better diffraction gratings. But administrative duties at the University of Chicago also weighed heavily upon him. In southern California, he could work and play in several well-equipped laboratories and also indulge his interest in tennis, billiards, chess, and watercolor painting. Tests for the rigidity of the earth (or earth-tide experiments) were followed by work with H. G. Gale toward an elaborate test near Chicago for the effect of the earth’s rotation on the velocity of light. Other studies of the application of interference methods to astronomical problems led to the construction in 1920 of the celebrated stellar interferometer on the Hooker 100-inch telescope that measured the amazing angular diameter of α Orionis (Belelgeuse), which was found to have a disk subtending 0.047” arc, or approximately 240 million miles in diameter. Still other tests and a geodetic survey under Michelson’s supervision in southern California prepared the way for a measurement of the velocity of light between mountain peaks. The Mt. Wilson to the San Jacinto Mountains measurement (eighty-two miles) was scuttled because of smog in 1925; the Mt. Wilson to Mt. San Antonio measurement (twenty-two miles) was completed in 1926, and the value remains one of the best optical determinations ever made.

Meanwhile, George Ellery Hale, director of the Mt. Wilson Observatory, had invited to southern California Michelson’s friend and successor at Case, Dayton C. Miller, who had worked with Morley on other ether-drift tests in 1900–1906 and had achieved eminence in acoustics. Miller was supposed to perfect the original Michelson-Morley experiment for all seasons and at a 6,000-foot altitude. After many vicissitudes he did so in 1925–1926 and, to the consternation or delight of a divided profession, Miller announced in his retiring address as president of the American Phvsieal Society that he had finally found the absolute velocity of the solar system: about 200km./sec. toward the head of the constellation Draco! This challenge spurred Michelson to take up ether-drift tests once again. In conjunction with F. G. Pease and F. Pearson, several very elaborate interferometers were built and operated briefly from 1926 through 1928 but to little avail. Neither Michelson nor his team—nor any other experimentalists later in the 1920’s—were able to corroborate Miller’s slight but positive results; and so Einstein stood verified largely on the authority of Michelson’s reiterated word.

Michelson’s second book, Studies in Optics, was published in 1927, the year before the Optical Society of America dedicated its annual meeting to him on the fiftieth anniversary of his scientific career. Michelson had used “Light Waves as Measuring Rods for Sounding the Infinite and the Infinitesimal,” as the title of one of his last papers. When he died in 1931, he was hardly less a believer in the wave theory of light and its concomitant ether. Although he supported Einstein with few reservations, he was secure in the knowledge that he had indeed sounded the nature of light and found its field both infinite and infinitesimal.

BIBLIOGRAPHY

I. Original Works. Michelson’s books are Light Waves and Their Uses (Chicago, 1903); and Studies in Optics (Chicago, 1927). Translations and 78 articles are listed in Harvey B. Lemon, “Albert Abraham Michelson: The Man and the Man of Science,” in American Physics Teacher, 4 (Feb. 1936), 1–11.

MS and memorabilia material are widely scattered, but the best collection is held by the Michelson Laboratory, Naval Weapons Center, China Lake, California. See D. Theodore McAllister, “Collecting Archives for the Hisiory of Science,” in American Archivist, 32 (Oct. 1969), 327–332; and Albert Abraham Michelson: The Man Who Taught a World to Measure, Publication of the Michelson Museum, no. 3(China Lake, Calif., 1970). See also holdings of the Bohr Library, American Institute of Physics, Center for History and Philosophy of Phvsics, 335 East 45th Street, New York, N.Y. 10017.

II. Secondary Literature. See Bernard Jaffe, Michelson and the Speed of Light, Science Study series (Garden City, N.Y., 1960); Dorothy Michelson Livingston, “Michelson in the Navy; the Navy in Michelson,” in Proceedings of the United States Naval Institute, 95 , no. 6 (June 1969), 72–79, a collection of papers and memorabilia that forms the basis for a biography of her father, The Master of Light (New York, 1973); Robert A. Millikan, “Albert A. Michelson,” in Biographical Memoirs. Sational Academy of Sciences, 19 , no. 4 (1938), 120–147; “Proceedings of the Michelson Meeting of the Optical Society of America,” in Journal of the Optical Society of America, 18 , no. 3 (Mar. 1929), 143–286; Robert S. Shankland, “Albert A. Michelson at Case,” in American Journal of Physics, 17 (Nov. 1949), 487–490; and Loyd S. Swenson, Jr., The Ethereal Aether: A History of the Michelson-Morley-Miller Aether-Drift Experiments 1880–1930 (Austin, Tex., 1972); Gerald Holton, “Einstein, Michelson, and the ‘Crucial Experiment,’” in Isis, 60 , no. 202 (Summer 1969), 133–197; Jean M. Bennett, et al., “Albert Michelson, Dean of American Optics-Life, Contributions to Science, and Influence on Modern-Day Physics,” together with Robert S. Shankland, “Michelsoi’s Role in the Development of Relativity,” in Applied Optics, 12 , no. 10 (Oet. 1973), 2287 and 2253; Loyd S. Swenson, Jr., “The Michelson-Morley-Miller Experiments Before and After 1905,” in Journal for the History of Astronomy, 1 , no. 1 (1970), 56–78.

Loyd S. Swenson, Jr.

Albert Abraham Michelson

views updated May 23 2018

Albert Abraham Michelson

1852-1931

American Physicist

Albert Michelson was a renowned physicist whose work in optics inspired, among others, Albert Einstein (1879-1955). He made the first accurate determinations of the speed of light and helped to disprove the existence of "ether," previously thought to permeate all space.

Michelson was born in Strzelno, Poland, to Samuel and Rozalia Michelson. The Michelson family left Poland for the United States when Albert was three, his father eventually becoming a successful merchant in San Francisco. Michelson entered the U.S. Naval Academy at age 17, where he performed well in his academic studies but rather poorly in seamanship. He graduated in 1873 and was a science instructor at the Academy until 1879.

In 1878 Michelson began what was to be his life's passion—obtaining accurate measurements of the speed of light. He first used crude homemade equipment to arrive at reasonable values. Knowing he would need to study optics in order to obtain the accuracy he desired, Michelson spent two years in Paris, Berlin, and Heidelberg. During this period, he resigned from the Navy to be able to concentrate on his research. Upon returning to the United States in 1882, he calculated that the speed of light was 299,853 km/sec, the most accurate measurement to be made until his own revision nearly 30 years later.

Accepting a professorship in physics at Case University in Cleveland, Ohio, Michelson began a collaboration with Edward Morley (1838-1923) to try to prove or disprove the existence of "ether," a substance that was thought to permeate space, allowing electromagnetic radiation to be transmitted. The Michelson-Morley experiment was elegant and decisive, using the wave-like properties of light in a device called an interferometer.

When light waves meet and are slightly out of phase (meaning the crests and troughs do not match each other exactly), observers see a series of bright and dark bands. The bright bands represent places where two crests meet and reinforce each other, while the dark bands show where a crest and a trough meet and cancel each other out. Someone holding two fingers very close together in front of a light can see these dark and light bands between their fingers if they look closely and carefully.

Michelson and Morley realized that as the Earth moved in its orbit it would be in motion across the ether. That meant that, if the ether existed, a light shining in different directions would be moving with different velocities with respect to the ether. They set up an "L"-shaped set of mirrors and bounced beams of light from a single source from the mirrors at either end of the "L." As the light returned to the origin, they looked for bands, because differences in the travel times of the beams of light would cause the beams to be out of synch with each other. When repeated experiments showed no bands, Michelson and Morley reluctantly came to the conclusion that "ether" did not exist. This conclusion not only rattled conventional science, but also set the stage for the later theory of relativity. For this experiment and his groundbreaking work on the speed of light, Michelson was awarded the Nobel Prize in Physics in 1907, the first American to receive this honor. It is important to note that from the perspective of Michelson and Morley this experiment was a failure, as they were attempting to show that ether existed. However, from their "failure" came a number of advances in our understanding of the physical universe, proving in the end more profitable than most experimental "successes."

Of Michelson's work, Einstein said: "My honored Dr. Michelson, it was you who led the physicists into new paths, and through your marvelous experimental work paved the way for the development of the theory of relativity."

Michelson commented in 1894: "The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. . . . Our future discoveries must be looked for in the sixth place decimals." The irony of this quote is that Michelson's own work set the stage for discoveries in relativity that would overturn our view of the universe. Also of interest, this statement was made shortly before the discoveries of x-rays and radioactivity, which led to studies of the atom, quantum physics, and other areas that are still being fruitfully explored today.

In addition to his scientific accolades, Michelson served as the first chair of the Physics Department at the University of Chicago and was president of the National Academy of Sciences from 1923-1927. He married twice during his life, having three children in each marriage, and died in 1931 at the age of 78.

P. ANDREW KARAM

Albert Abraham Michelson

views updated May 11 2018

Albert Abraham Michelson

The American physicist Albert Abraham Michelson (1852-1931) is important for his determination of the velocity of light and the study of optical interference.

Albert Michelson was born on Dec. 19, 1852, in German Poland. The family emigrated to the United States in 1854. He took the competitive examinations for congressional appointment to the U.S. Naval Academy. Although he qualified for the appointment, the place was awarded to another boy. Young Michelson traveled to Washington, was unsuccessful in getting President Grant to appoint him to the academy, but then persuaded the commandant to accept him.

Michelson graduated from the Naval Academy in 1873. Two years later he was appointed instructor in physics and chemistry there. He resigned his commission in 1880 and spent 2 years studying in Berlin, Heidelberg, and Paris. He was then appointed to the Case School of Applied Science at Cleveland, Ohio, as professor of physics. In 1889 he moved to Clark University as professor of physics, and in 1892 he was invited to head the department of physics at the new University of Chicago, a position which he held until 1931.

With few exceptions, all of Michelson's work bore directly on problems involved in the study of light; he was thus specialized to a degree that was unique among Americans at the end of the 19th century. While serving at Annapolis, he hit upon a slight but vital modification to a method then being used to measure the speed of light. With his simple device, consisting essentially of two plane mirrors, one fixed and one revolving at the rate of about 130 turns per second from which light was to be reflected, Michelson succeeded in obtaining a measure closer than any that had been obtained to the presently accepted figure—186,508 miles per second.

Michelson performed his most famous experiment at Cleveland in collaboration with the chemist Edward W. Morley. Light waves were regarded as undulations of the ether which filled all space. If a light source were moving through the ether, the speed of the light would be different for each direction in which it was emitted. In the Michelson-Morley experiment two beams of light, sent out and reflected back at right angles to each other, took the same amount of time. Thus the notion of a stationary ether had to be discarded.

Even though his own work helped touch off a revolution in physics, Michelson never realized the fundamental nature of the change. Basically a brilliant experimenter, he saw the future development of physics only as one of further precision and newer instruments which would bring the accuracy of scientific measurements to the ultimate degree. He never understood the more mathematical and theoretical approach which came to dominate physics toward the end of his life.

Michelson's contributions were numerous. He developed, as a by-product of his interference experiments, the first spectroscope having sufficiently high resolution to disclose direct optical evidence of molecular motion; gave the scientific world a new fundamental standard of length when he calibrated the international meter in terms of wavelengths of cadmium; and, using a variation of his interferometer, became the first man to measure the diameter of a star. He received the Nobel Prize in 1907, the first American to be so honored. He died on May 9, 1931, while at work on a still more refined measurement of the velocity of light.

Further Reading

A good account of the major work of Michelson's life is in Bernard Jaffe, Michelson and the Speed of Light (1960). There is a useful biographical memoir of Michelson by Robert A. Millikan in National Academy of Sciences, Biographical Memoirs, vol. 19 (1938), and another profile of his life and work is in Royal Society of London, Obituary Notices of Fellows of the Royal Society, vol. 1 (1932-1935). The Nobel Foundation, Nobel Lectures: Physics, 1901-1921 (1964), has a biographical sketch. □

Michelson, Albert Abraham

views updated May 21 2018

MICHELSON, ALBERT ABRAHAM

MICHELSON, ALBERT ABRAHAM (1852–1931), U.S. physicist; the first American to be awarded a Nobel Prize for science. He was born in Strelno, Prussia, and was taken by his family to the United States at the age of two. Michelson graduated from the naval academy at Annapolis in 1873. However, after spending two years at sea he resigned to become an instructor in physics at the naval academy (1875–79). He spent a year in Washington and then two years studying in Germany. He returned to the U.S. in 1883 to become professor at the Case School of Applied Science in Cleveland until 1889. From 1889 to 1892 he was at Clark University and finally he was professor at the University of Chicago (1892–1929). He was awarded the Nobel Prize in physics in 1907. Michelson was a remarkable experimentalist able to secure astonishing accuracies with the simplest apparatus. His lifelong interest was the velocity of light, and this was the subject of his first experiment even in his mid-20s when he was an instructor at the U.S. naval academy at Annapolis. At that time physicists believed in the existence of an ether that filled all space, was at absolute rest, and through which light traveled in waves. There was then no way of measuring the motion of any body relative to the ether and leading scientists doubted whether this could be done. If it could be measured, two beams of light should show interference fringes denoting the difference. By measuring the width of the fringes it should be possible to show the earth's exact velocity when compared with the ether. Not only would the earth's absolute motion be determined, but also that of all bodies in the planetary system whose motions relative to the earth were known. For his experiment Michelson developed the interferometer, an instrument now used to measure wavelengths of light and other wavelengths of the radiation spectrum. He carried out his first experiments in Berlin in 1881 in Helmholtz' laboratory. In 1887, together with Edward Williams Morley, he performed one of the most important experiments in the history of science, which provided a new starting point for the great theoretical developments in 20th-century physics. The conclusion of the experiment indicated that light travels with the same velocity in any direction under any circumstances, and the implication was that the ether did not exist. This became one of the basic concepts which led *Einstein in 1905 to his special theory of relativity. The proving of this revolutionary theory of the absolute speed of light under any conditions has become the underlying principle of modern physics, astronomy, and cosmology and is considered to be, perhaps, the one absolute natural law in the universe. As a great experimentalist, Michelson established in 1892/93 the meter in terms of the wavelength of cadmium. He also determined the diameter of Jupiter's satellites and was the first person to measure the dimension of a star, Alpha Orion. Michelson wrote Velocity of Light (1902), Light Waves and Their Uses (1903), and Studies in Optics (1927).

bibliography:

B. Jaffe, Michelson and the Speed of Light (1961), incl. bibl.

[Maurice Goldsmith]

Michelson, Albert Abraham

views updated Jun 11 2018

Michelson, Albert Abraham (1852–1931) US physicist, b. Germany. In 1887, he conducted an experiment with Edward Morley to determine the velocity of the Earth through the ether, using an interferometer of his own design. The negative result prompted the development of the theory of relativity. In 1907, Michelson became the first US scientist to receive a Nobel Prize.

Albert Abraham Michelson

views updated May 17 2018

Albert Abraham Michelson

1852-1931

American physicist best known for inventing the interferometer (1881) and for his 1887 experiments with Edward Morley that failed to detect the motion of Earth relative to the ether—a hypothetical substance most nineteenth-century physicists believed necessary for light propagation. This "null-result" was later explained by Albert Einstein's special theory of relativity. Michelson was awarded the 1907 Nobel Prize for Physics for his high-precision optical instruments and measurements carried out with their aid.

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