LUCIDA

lucida, camera obscura and the kaleidoscope are examples; instruments serviceable for simultaneous vision with both eyes are termed binocular instruments; the stereoscope may be placed in this category; the optical action of the zoetrope, with its modern development the cinematograph, depends upon the physiological persistence of vision. meteorological optical phenomena comprise the corona, halo, mirage, rainbow, colour of sky and twilight, and also astronomical refraction (see refraction, astronomical); the complete theory of the corona involves diffraction, and atmospheric dust also plays a part in this group of phenomena. i. history § 1. there is reason to believe that the ancients were more familiar with optics than with any other branch of physics; and this may be due to the fact that for a knowledge of external things man is indebted to the sense of vision in a far greater degree than to other senses. that light travels in straight lines--or, in other words, that an object is seen in the direction in which it really lies--must have been realized in very remote times. the antiquity of mirrors points to some acquaintance with the phenomena of reflection, and layard's discovery of a convex lens of rock-crystal among the ruins of the palace of nimrud implies a knowledge of the burning and magnifying powers of this instrument. the greeks were acquainted with the fundamental law of reflection, viz. the equality of the angles of incidence and reflection; and it was hero of alexandria who proved that the path of the ray is the least possible. the lens, as an instrument for magnifying objects or for concentrating rays to effect combustion, was also known. aristophanes, in the _clouds_ (c. 424 b.c.), mentions the use of the burning-glass to destroy the writing on a waxed tablet; much later, pliny describes such glasses as solid balls of rock-crystal or glass, or hollow glass balls filled with water, and seneca mentions their use by engravers. a treatise on optics ([greek: katoptrika]), assigned to euclid by proclus and marinus, shows that the greeks were acquainted with the production of images by plane, cylindrical and concave and convex spherical mirrors, but it is doubtful whether euclid was the author, since neither this work nor the [greek: optika], a work treating of vision and also assigned to him by proclus and marinus, is mentioned by pappus, and more particularly since the demonstrations do not exhibit the precision of his other writings. reflection, or catoptrics, was the key-note of their explanations of optical phenomena; it is to the reflection of solar rays by the air that aristotle ascribed twilight, and from his observation of the colours formed by light falling on spray, he attributes the rainbow to reflection from drops of rain. although certain elementary phenomena of refraction had also been noted--such as the apparent bending of an oar at the point where it met the water, and the apparent elevation of a coin in a basin by filling the basin with water--the quantitative law of refraction was unknown; in fact, it was not formulated until the beginning of the 17th century. the analysis of white light into the continuous spectrum of rainbow colours by transmission through a prism was observed by seneca, who regarded the colours as fictitious, placing them in the same category as the iridescent appearance of the feathers on a pigeon's neck. § 2. the aversion of the greek thinkers to detailed experimental inquiry stultified the progress of the science; instead of acquiring facts necessary for formulating scientific laws and correcting hypotheses, the greeks devoted their intellectual energies to philosophizing on the nature of light itself. in their search for a theory the greeks were mainly concerned with vision--in other words, they sought to determine how an object was seen, and to what its colour was due. emission theories, involving the conception that light was a stream of concrete particles, were formulated. the pythagoreans assumed that vision and colour were caused by the bombardment of the eye by minute particles projected from the surface of the object seen. the platonists subsequently introduced three elements--a stream of particles emitted by the eye (their "divine fire"), which united with the solar rays, and, after the combination had met a stream from the object, returned to the eye and excited vision. in some form or other the emission theory--that light was a longitudinal propulsion of material particles--dominated optical thought until the beginning of the 19th century. the authority of the platonists was strong enough to overcome aristotle's theory that light was an activity ([greek: energeia]) of a medium which he termed the _pellucid_ ([greek: diaphanes]); about two thousand years later newton's exposition of his corpuscular theory overcame the undulatory hypotheses of descartes and huygens; and it was only after the acquisition of new experimental facts that the labours of thomas young and augustin fresnel indubitably established the wave-theory. § 3. the experimental study of refraction, which had been almost entirely neglected by the early greeks, received more attention during the opening centuries of the christian era. cleomedes, in his _cyclical theory of meteors_, c. a.d. 50, alludes to the apparent bending of a stick partially immersed in water, and to the rendering visible of coins in basins by filling up with water; and also remarks that the air may refract the sun's rays so as to render that luminary visible, although actually it may be below the horizon. the most celebrated of the early writers on optics is the alexandrian ptolemy (2nd century). his writings on light are believed to be preserved in two imperfect latin manuscripts, themselves translations from the arabic. the subjects discussed include the nature of light and colour; the formation of images by various types of mirrors, refractions at the surface of glass and of water, with tables of the angle of refraction corresponding to given angles of incidence for rays passing from air to glass and from air to water; and also astronomical refractions, i.e. the apparent displacement of a heavenly body due to the refraction of light in its passage through the atmosphere. the authenticity of these manuscripts has been contested: the _almagest_ contains no mention of the _optics_, nor is the subject of astronomical refractions noticed, but the strongest objection, according to a. de morgan, is the fact that their author was a poor geometer. § 4. one of the results of the decadence of the roman empire was the suppression of the academies, and few additions were made to scientific knowledge on european soil until the 13th century. extinguished in the west, the spirit of research was kindled in the east. the accession of the arabs to power and territory in the 7th century was followed by the acquisition of the literary stores of greece, and during the following five centuries the arabs, both by their preservation of existing works and by their original discoveries (which, however, were but few), took a permanent place in the history of science. pre-eminent among arabian scientists is alhazen, who flourished in the 11th century. primarily a mathematician and astronomer, he also investigated a wide range of optical phenomena. he examined the anatomy of the eye, and the functions of its several parts in promoting vision; and explained how it is that we see one object with two eyes, and then not by a single ray or beam as had been previously held, but by two cones of rays proceeding from the object, one to each eye. he attributed vision to emanations from the body seen; and on his authority the platonic theory fell into disrepute. he also discussed the magnifying powers of lenses; and it may be that his writings on this subject inspired the subsequent invention of spectacles. astronomical observations led to the investigation of refraction by the atmosphere, in particular, astronomical refraction; he explained the phenomenon of twilight, and showed a connexion between its duration and the height of the atmosphere. he also treated _optical deceptions_, both in direct vision and in vision by reflected and refracted light, including the phenomenon known as the _horizontal moon_, i.e. the apparent increase in the diameter of the sun or moon when near the horizon. this appearance had been explained by ptolemy on the supposition that the diameter was actually increased by refraction, and his commentator theon endeavoured to explain why an object appears larger when viewed under water. but actual experiment showed that the diameter did not increase. alhazen gave the correct explanation, which, however, friar bacon attributes to ptolemy. we judge of distance by comparing the angle under which an object is seen with its supposed distance, so that if two objects be seen under nearly equal angles and one be supposed to be more distant than the other, then the former will be supposed to be the larger. when near the horizon the sun or moon, conceived as very distant, are intuitively compared with terrestrial objects, and therefore they appear larger than when viewed at elevations. § 5. while the arabs were acting as the custodians of scientific knowledge, the institutions and civilizations of europe were gradually crystallizing. attacked by the mongols and by the crusaders, the bagdad caliphate disappeared in the 13th century. at that period the arabic commentaries, which had already been brought to europe, were beginning to exert great influence on scientific thought; and it is probable that their rarity and the increasing demand for the originals and translations led to those forgeries which are of frequent occurrence in the literature of the middle ages. the first treatise on optics written in europe was admitted by its author vitello or vitellio, a native of poland, to be based on the works of ptolemy and alhazen. it was written in about 1270, and first published in 1572, with a latin translation of alhazen's treatise, by f. risner, under the title _thesaurus opticae_. its tables of refraction are more accurate than ptolemy's; the author follows alhazen in his investigation of lenses, but his determinations of the foci and magnifying powers of spheres are inaccurate. he attributed the twinkling of stars to refraction by moving air, and observed that the scintillation was increased by viewing through water in gentle motion; he also recognized that both reflection and refraction were instrumental in producing the rainbow, but he gave no explanation of the colours. the _perspectiva communis_ of john peckham, archbishop of canterbury, being no more than a collection of elementary propositions containing nothing new, we have next to consider the voluminous works of vitellio's illustrious contemporary, roger bacon. his writings on light, _perspectiva_ and _specula mathematica_, are included in his _opus majus_. it is conceivable that he was acquainted with the nature of the images formed by light traversing a small orifice--a phenomenon noticed by aristotle, and applied at a later date to the construction of the camera obscura. the invention of the magic lantern has been ascribed to bacon, and his statements concerning spectacles, the telescope, and the microscope, if not based on an experimental realization of these instruments, must be regarded as masterly conceptions of the applications of lenses. as to the nature of light, bacon adhered to the theory that objects are rendered visible by emanations from the eye. the history of science, and more particularly the history of inventions, constantly confronts us with the problem presented by such writings as friar bacon's. rarely has it been given to one man to promote an entirely new theory or to devise an original instrument; it is more generally the case that, in the evolution of a single idea, there comes some stage which arrests our attention, and to which we assign the dignity of an "invention." furthermore, the obscurity that surrounds the early history of spectacles, the magic lantern, the telescope and the microscope, may find a partial solution in the spirit of the middle ages. the natural philosopher who was bold enough to present to a prince a pair of spectacles or a telescope would be in imminent danger of being regarded in the eyes of the church as a powerful and dangerous magician; and it is conceivable that the maker of such an instrument would jealously guard the secret of its actual construction, however much he might advertise its potentialities.[3] § 6. the awakening of europe, which first manifested itself in italy, england and france, was followed in the 16th century by a period of increasing intellectual activity. the need for experimental inquiry was realized, and a tendency to dispute the dogmatism of the church and to question the theories of the established schools of philosophy became apparent. in the science of optics, italy led the van, the foremost pioneers being franciscus maurolycus (1494-1575) of messina, and giambattista della porta (1538-1615) of naples. a treatise by maurolycus entitled _photismi de lumine et umbra prospectivum radiorum incidentium facientes_ (1575), contains a discussion of the measurement of the intensity of light--an early essay in photometry; the formation of circular patches of light by small holes of any shape, with a correct explanation of the phenomenon; and the optical relations of the parts of the eye, maintaining that the crystalline humour acts as a lens which focuses images on the retina, explaining short- and long-sight (myopia and hyper-metropia), with the suggestion that the former may be corrected by concave, and the latter by convex, lenses. he observed the spherical aberration due to elements beyond the axis of a lens, and also the caustics of refraction (diacaustics) by a sphere (seen as the bright boundaries of the luminous patches formed by receiving the transmitted light on a screen), which he correctly regarded as determined by the intersections of the refracted rays. his researches on refraction were less fruitful; he assumed the angles of incidence and refraction to be in the constant ratio of 8 to 5, and the rainbow, in which he recognized four colours, orange, green, blue and purple, to be formed by rays reflected in the drops along the sides of an octagon. porta's fame rests chiefly on his _magia naturalis sive de miraculis rerum naturalium_, of which four books were published in 1558, the complete work of twenty books appearing in 1589. it attained great popularity, perhaps by reason of its astonishing medley of subjects--pyrotechnics and perfumery, animal reproduction and hunting, alchemy and optics,--and it was several times reprinted, and translated into english (with the title _natural magick_, 1658), german, french, spanish, hebrew and arabic. the work contains an account of the camera obscura, with the invention of which the author has sometimes been credited; but, whoever the inventor, porta was undoubtedly responsible for improving and popularizing that instrument, and also the magic lantern. in the same work practical applications of lenses are suggested, combinations comparable with telescopes are vaguely treated and spectacles are discussed. his _de refractione, optices parte_ (1593) contains an account of binocular vision, in which are found indications of the principle of the stereoscope. § 7. the empirical study of lenses led, in the opening decade of the 17th century, to the emergence of the telescope from its former obscurity. the first form, known as the dutch or galileo telescope, consisted of a convex and a concave lens, a combination which gave erect images; the later form, now known as the "keplerian" or "astronomical" telescope (in contrast with the earlier or "terrestrial" telescope) consisted of two convex lenses, which gave inverted images. with the microscope, too, advances were made, and it seems probable that the compound type came into common use about this time. these single instruments were followed by the invention of binoculars, i.e. instruments which permitted simultaneous vision with both eyes. there is little doubt that the experimental realization of the telescope, opening up as it did such immense fields for astronomical research, stimulated the study of lenses and optical systems. the investigations of maurolycus were insufficient to explain the theory of the telescope, and it was kepler who first determined the principle of the galilean telescope in his _dioptrice_ (1611), which also contains the first description of the astronomical or keplerian telescope, and the demonstration that rays parallel to the axis of a plano-convex lens come to a focus at a point on the axis distant twice the radius of the curved surface of the lens, and, in the case of an equally convex lens, at an axial point distant only once the radius. he failed, however, to determine accurately the case for unequally convex lenses, a problem which was solved by bonaventura cavalieri, a pupil of galileo. early in the 17th century great efforts were made to determine the law of refraction. kepler, in his _prolegomena ad vitellionem_ (1604), assiduously, but unsuccessfully, searched for the law, and can only be credited with twenty-seven empirical rules, really of the nature of approximations, which he employed in his theory of lenses. the true law--that the ratio of the sines of the angles of incidence and refraction is constant--was discovered in 1621 by willebrord snell (1591-1626); but was published for the first time after his death, and with no mention of his name, by descartes. whereas in snell's manuscript the law was stated in the form of the ratio of certain lines, trigonometrically interpretable as a ratio of cosecants, descartes expressed the law in its modern trigonometrical form, viz. as the ratio of the sines. it may be observed that the modern form was independently obtained by james gregory and published in his _optica promota_ (1663). armed with the law of refraction, descartes determined the geometrical theory of the primary and secondary rainbows, but did not mention how far he was indebted to the explanation of the primary bow by antonio de dominis in 1611; and, similarly, in his additions to the knowledge of the telescope the influence of galileo is not recorded. § 8. in his metaphysical speculations on the system of nature, descartes formulated a theory of light at variance with the generally accepted emission theory and showing some resemblance to the earlier views of aristotle, and, in a smaller measure, to the modern undulatory theory. he imagined light to be a pressure transmitted by an infinitely elastic medium which pervades space, and colour to be due to rotatory motions of the particles of this medium. he attempted a mechanical explanation of the law of refraction, and came to the conclusion that light passed more readily through a more highly refractive medium. this view was combated by pierre de fermat (1601-1665), who, from the principle known as the "law of least time," deduced the converse to be the case, i.e. that the velocity varied inversely with the refractive index. in brief, fermat's argument was as follows: since nature performs her operations by the most direct routes or shortest paths, then the path of a ray of light between any two points must be such that the time occupied in the passage is a minimum. the rectilinear propagation and the law of reflection obviously agree with this principle, and it remained to be proved whether the law of refraction tallied. although fermat's premiss is useless, his inference is invaluable, and the most notable application of it was made in about 1824 by sir william rowan hamilton, who merged it into his conception of the "characteristic function," by the help of which all optical problems, whether on the corpuscular or on the undulator theory, are solved by one common process. hamilton was in possession of the germs of this grand theory some years before 1824, but it was first communicated to the royal irish academy in that year, and published in imperfect instalments some years later. the following is his own description of it. it is of interest as exhibiting the origin of fermat's deduction, its relation to contemporary and subsequent knowledge, and its connexion with other analytical principles. moreover, it is important as showing hamilton's views on a very singular part of the more modern history of the science to which he contributed so much. "those who have meditated on the beauty and utility, in theoretical mechanics, of the general method of lagrange, who have felt the power and dignity of that central dynamical theorem which he deduced, in the _mecanique analytique_ ..., must feel that mathematical optics can only then attain a coordinate rank with mathematical mechanics ..., when it shall possess an appropriate method, and become the unfolding of a central idea.... it appears that if a general method in deductive optics can be attained at all, it must flow from some law or principle, itself of the highest generality, and among the highest results of induction.... [this] must be the principle, or law, called usually the law of least action; suggested by questionable views, but established on the widest induction, and embracing every known combination of media, and every straight, or bent, or curved line, ordinary or extraordinary, along which light (whatever light may be) extends its influence successively in space and time: namely, that this linear path of light, from one point to another, is always found to be such that, if it be compared with the other infinitely various lines by which in thought and in geometry the same two points might be connected, a certain integral or sum, called often _action_, and depending by fixed rules on the length, and shape, and position of the path, and on the media which are traversed by it, is less than all the similar integrals for the other neighbouring lines, or, at least, possesses, with respect to them, a certain _stationary_ property. from this law, then, which may, perhaps, be named the law of stationary action, it seems that we may most fitly and with best hope set out, in the synthetic or deductive process and in the search of a mathematical method. "accordingly, from this known law of least or stationary action i deduced (long since) another connected and coextensive principle, which may be called by analogy the law of varying action, and which seems to offer naturally a method such as we are seeking; the one law being as it were the last step in the ascending scale of induction, respecting linear paths of light, while the other law may usefully be made the first in the descending and deductive way. "the former of these two laws was discovered in the following manner. the elementary principle of straight rays showed that light, under the most simple and usual circumstances, employs the direct, and therefore the shortest, course to pass from one point to another. again, it was a very early discovery (attributed by laplace to ptolemy), that, in the case of a plane mirror, the bent line formed by the incident and reflected rays is shorter than any other bent line having the same extremities, and having its point of bending on the mirror. these facts were thought by some to be instances and results of the simplicity and economy of nature; and fermat, whose researches on maxima and minima are claimed by the continental mathematicians as the germ of the differential calculus, sought anxiously to trace some similar economy in the more complex case of refraction. he believed that by a metaphysical or cosmological necessity, arising from the simplicity of the universe, light always takes the course which it can traverse in the shortest time. to reconcile this metaphysical opinion with the law of refraction, discovered experimentally by snellius, fermat was led to suppose that the two lengths, or _indices_, which snellius had measured on the incident ray prolonged and on the refracted ray, and had observed to have one common projection on a refracting plane, are inversely proportional to the two successive velocities of the light before and after refraction, and therefore that the velocity of light is diminished on entering those denser media in which it is observed to approach the perpendicular; for fermat believed that the time of propagation of light along a line bent by refraction was represented by the sum of the two products, of the incident portion multiplied by the index of the first medium and of the refracted portion multiplied by the index of the second medium; because he found, by his mathematical method, that this sum was less, in the case of a plane refractor, than if light went by any other than its actual path from one given point to another, and because he perceived that the supposition of a velocity inversely as the index reconciled his mathematical discovery of the minimum of the foregoing sum with his cosmological principle of least time. descartes attacked fermat's opinions respecting light, but leibnitz zealously defended them; and huygens was led, by reasonings of a very different kind, to adopt fermat's conclusions of a velocity inversely as the index, and of a _minimum time_ of propagation of light, in passing from one given point to another through an ordinary refracting plane. newton, however, by his theory of emission and attraction, was led to conclude that the velocity of light was _directly_, not _inversely_, as the index, and that it was _increased_ instead of being _diminished_ on entering a denser medium; a result incompatible with the theorem of the shortest time in refraction. this theorem of shortest time was accordingly abandoned by many, and among the rest by maupertuis, who, however, proposed in its stead, as a new cosmological principle, that _celebrated law of least action_ which has since acquired so high a rank in mathematical physics, by the improvements of euler and lagrange." § 9. the second half of the 17th century witnessed developments in the practice and theory of optics which equal in importance the mathematical, chemical and astronomical acquisitions of the period. original observations were made which led to the discovery, in an embryonic form, of new properties of light, and the development of mathematical analysis facilitated the quantitative and theoretical investigation of these properties. indeed, mathematical and physical optics may justly be dated from this time. the phenomenon of _diffraction_, so named by grimaldi, and by newton _inflection_, which may be described briefly as the spreading out, or deviation, from the strictly rectilinear path of light passing through a small aperture or beyond the edge of an opaque object, was discovered by the italian jesuit, francis maria grimaldi (1619-1663), and published in his _physico-mathesis de lumine_ (1665); at about the same time newton made his classical investigation of the spectrum or the band of colours formed when light is transmitted through a prism,[4] and studied _interference_ phenomena in the form of the colours of thin and thick plates, and in the form now termed _newton's rings_; _double refraction_, in the form of the dual images of a single object formed by a rhomb of iceland spar, was discovered by bartholinus in 1670; huygens's examination of the transmitted beams led to the discovery of an absence of symmetry now called _polarization_; and the finite velocity of light was deduced in 1676 by ole roemer from the comparison of the observed and computed times of the eclipses of the moons of jupiter. these discoveries had a far-reaching influence upon the theoretical views which had been previously held: for instance, newton's recombination of the spectrum by means of a second (inverted) prism caused the rejection of the earlier view that the prism actually manufactured the colours, and led to the acceptance of the theory that the colours were physically present in the white light, the function of the prism being merely to separate the physical mixture; and roemer's discovery of the finite velocity of light introduced the necessity of considering the momentum of the particles which, on the accepted emission theory, composed the light. of greater moment was the controversy concerning the emission or corpuscular theory championed by newton and the undulatory theory presented by huygens (see section ii. of this article). in order to explain the colours of thin plates newton was forced to abandon some of the original simplicity of his theory; and we may observe that by postulating certain motions for the newtonian corpuscles all the phenomena of light can be explained, these motions aggregating to a transverse displacement, translated longitudinally, and the corpuscles, at the same time, becoming otiose and being replaced by a medium in which the vibration is transmitted. in this way the newtonian theory may be merged into the undulatory theory. newton's results are collected in his _opticks_, the first edition of which appeared in 1704. huygens published his theory in his _traite de lumiere_ (1690), where he explained reflection, refraction and double refraction, but did not elucidate the formation of shadows (which was readily explicable on the newtonian hypothesis) or polarization; and it was this inability to explain polarization which led to newton's rejection of the wave theory. the authority of newton and his masterly exposition of the corpuscular theory sustained that theory until the beginning of the 19th century, when it succumbed to the assiduous skill of young and fresnel. § 10. simultaneously with this remarkable development of theoretical and experimental optics, notable progress was made in the construction of optical instruments. the increased demand for telescopes, occasioned by the interest in observational astronomy, led to improvements in the grinding of lenses (the primary aim being to obtain forms in which spherical aberration was a minimum), and also to the study of achromatism, the principles of which followed from newton's analysis and synthesis of white light. kepler's supposition that lenses having the form of surfaces of revolution of the conic sections would bring rays to a focus without spherical aberration was investigated by descartes, and the success of the latter's demonstration led to the grinding of ellipsoidal and hyperboloidal lenses, but with disappointing results.[5] the grinding of spherical lenses was greatly improved by huygens, who also attempted to reduce chromatic aberration in the refracting telescope by introducing a stop (i.e. by restricting the aperture of the rays); to the same experimenter are due compound eye-pieces, the invention of which had been previously suggested by eustachio divini. the so-called huygenian eye-piece is composed of two plano-convex lenses with their plane faces towards the eye; the field-glass has a focal length three times that of the eye-glass, and the distance between them is twice the focal length of the eye-glass. huygens observed that spherical aberration was diminished by making the deviations of the rays at the two lenses equal, and ruggiero giuseppe boscovich subsequently pointed out that the combination was achromatic. the true development, however, of the achromatic refracting telescope, which followed from the introduction of compound object-glasses giving no dispersion, dates from about the middle of the 18th century. the difficulty of obtaining lens systems in which aberrations were minimized, and the theory of newton that colour production invariably attended refraction, led to the manufacture of improved specula which permitted the introduction of reflecting telescopes. the idea of this type of instrument had apparently occurred to marin mersenne in about 1640, but the first reflector of note was described in 1663 by james gregory in his _optica promota_; a second type was invented by newton, and a third in 1672 by cassegrain. slight improvements were made in the microscope, although the achromatic type did not appear until about 1820, some sixty years after john dollond had determined the principle of the achromatic telescope (see aberration, telescope, microscope, binocular instrument). § 11. passing over the discovery by ehrenfried walther tschirnhausen (1651-1708) of the caustics produced by reflection ("catacaustics") and his experiments with large reflectors and refractors (for the manufacture of which he established glass-works in italy); james bradley's discovery in 1728 of the "aberration of light," with the subsequent derivation of the velocity of light, the value agreeing fairly well with roemer's estimate; the foundation of scientific photometry by pierre bouguer in an essay published in 1729 and expanded in 1760 into his _traite d'optique sur la graduation de la lumiere_; the publication of john henry lambert's treatise on the same subject, entitled _photometria, sive de mensura et gradibus luminis, colorum et umbrae_ (1760); and the development of the telescope and other optical instruments, we arrive at the closing decades of the 18th century. during the forty years 1780 to 1820 the history of optics is especially marked by the names of thomas young and augustin fresnel, and in a lesser degree by arago, malus, sir william herschel, fraunhofer, wollaston, biot and brewster. although the corpuscular theory had been disputed by benjamin franklin, leonhard euler and others, the authority of newton retained for it an almost general acceptance until the beginning of the 19th century, when young and fresnel instituted their destructive criticism. basing his views on the earlier undulatory theories and diffraction phenomena of grimaldi and hooke, young accepted the huygenian theory, assuming, from a false analogy with sound waves, that the wave-disturbance was longitudinal, and ignoring the suggestion made by hooke in 1672 that the direction of the vibration might be transverse, i.e. at right angles to the direction of the rays. as with huygens, young was unable to explain diffraction correctly, or polarization. but the assumption enabled him to establish the principle of interference,[6] one of the most fertile in the science of physical optics. the undulatory theory was also accepted by fresnel who, perceiving the inadequacy of the researches of huygens and young, showed in 1818 by an analysis which, however, is not quite free from objection, that, by assuming that every element of a wave-surface could act as a source of secondary waves or wavelets, the diffraction bands were due to the interference of the secondary waves formed by each element of a primary wave falling upon the edge of an obstacle or aperture. one consequence of fresnel's theory was that the bands were independent of the nature of the diffracting edge--a fact confirmed by experiment and therefore invalidating young's theory that the bands were produced by the interference between the primary wave and the wave reflected from the edge of the obstacle. another consequence, which was first mathematically deduced by poisson and subsequently confirmed by experiment, is the paradoxical phenomenon that a small circular disk illuminated by a point source casts a shadow having a bright centre. § 12. the undulatory theory reached its zenith when fresnel explained the complex phenomena of polarization, by adopting the conception of hooke that the vibrations were transverse, and not longitudinal.[7] polarization by double refraction had been investigated by huygens, and the researches of wollaston and, more especially, of young, gave such an impetus to the study that the institute of france made double refraction the subject of a prize essay in 1812. e. l. malus (1775-1812) discovered the phenomenon of polarization by reflection about 1808 and investigated metallic reflection; arago discovered circular polarization in quartz in 1811, and, with fresnel, made many experimental investigations, which aided the establishment of the fresnel-arago laws of the interference of polarized beams; biot introduced a reflecting polariscope, investigated the colours of crystalline plates and made many careful researches on the rotation of the plane of polarization; sir david brewster made investigations over a wide range, and formulated the law connecting the angle of polarization with the refractive index of the reflecting medium. fresnel's theory was developed in a strikingly original manner by sir william rowan hamilton, who interpreted from fresnel's analytical determination of the geometrical form of the wave-surface in biaxal crystals the existence of two hitherto unrecorded phenomena. at hamilton's instigation humphrey lloyd undertook the experimental search, and brought to light the phenomena of external and internal conical refraction. the undulatory vibration postulated by fresnel having been generally accepted as explaining most optical phenomena, it became necessary to determine the mechanical properties of the aether which transmits this motion. fresnel, neumann, cauchy, maccullagh, and, especially, green and stokes, developed the "elastic-solid theory." by applying the theory of elasticity they endeavoured to determine the constants of a medium which could transmit waves of the nature of light. many different allocations were suggested (of which one of the most recent is lord kelvin's "contractile aether," which, however, was afterwards discarded by its author), and the theory as left by green and stokes has merits other than purely historical. at a later date theories involving an action between the aether and material atoms were proposed, the first of any moment being j. boussinesq's (1867). c. christiansen's investigation of anomalous dispersion in 1870, and the failure of cauchy's formula (founded on the elastic-solid theory) to explain this phenomenon, led to the theories of w. sellmeier (1872), h. von helmholtz (1875), e. ketteler (1878), e. lommel (1878) and w. voigt (1883). a third class of theory, to which the present-day theory belongs, followed from clerk maxwell's analytical investigations in electromagnetics. of the greatest exponents of this theory we may mention h. a. lorentz, p. drude and j. larmor, while lord rayleigh has, with conspicuous brilliancy, explained several phenomena (e.g. the colour of the sky) on this hypothesis. for a critical examination of these theories see section ii. of this article; reference may also be made to the _british association reports_: "on physical optics," by humphrey lloyd (1834), p. 35; "on double refraction," by sir g. g. stokes (1862), p. 253; "on optical theories," by r. t. glazebrook (1885), p. 157. § 13. _recent developments._--the determination of the velocity of light (see section iii. of this article) may be regarded as definitely settled, a result contributed to by a. h. l. fizeau (1849), j. b. l. foucault (1850, 1862), a. cornu (1874), a. a. michelson (1880), james young and george forbes (1882), simon newcomb (1880-1882) and cornu (1900). the velocity in moving media was investigated theoretically by fresnel; and fizeau (1859), and michelson and morley (1886) showed experimentally that the velocity was increased in running water by an amount agreeing with fresnel's formula, which was based on the hypothesis of a stationary aether. the optics of moving media have also been investigated by lord rayleigh, and more especially by h. a. lorentz, who also assumed a stationary aether. the relative motion of the earth and the aether has an important connexion with the phenomenon of the aberration of light, and has been treated with masterly skill by joseph larmor and others (see aether). the relation of the earth's motion to the intensities of terrestrial sources of light was investigated theoretically by fizeau, but no experimental inquiry was made until 1903, when nordmeyer obtained negative results, which were confirmed by the theoretical investigations of a. a. bucherer and h. a. lorentz. experimental photometry has been greatly developed since the pioneer work of bouguer and lambert and the subsequent introduction of the photometers of ritchie, rumford, bunsen and wheatstone, followed by swan's in 1859, and o. r. lummer and e. brodhun's instrument (essentially the same as swan's) in 1889. this expansion may largely be attributed to the increase in the number of artificial illuminants--especially the many types of filament- and arc-electric lights, and the incandescent gas light. colour photometry has also been notably developed, especially since the enunciation of the "purkinje phenomenon" in 1825. sir william abney has contributed much to this subject, and a. m. meyer has designed a photometer in which advantage is taken of the phenomenon of contrast colours. "flicker photometry" may be dated from o. n. rood's investigations in 1893, and the same principle has been applied by haycraft and whitman. these questions--colour and flicker photometry--have important affinities to colour perception and the persistence of vision (see vision). the spectrophotometer, devised by de witt bristol brace in 1899, which permits the comparison of similarly coloured portions of the spectra from two different sources, has done much valuable work in the determination of absorptive powers and extinction coefficients. much attention has also been given to the preparation of a standard of intensity, and many different sources have been introduced (see photometry). stellar photometry, which was first investigated instrumentally with success by sir john herschel, was greatly improved by the introduction of zollner's photometer, e. c. pickering's meridian photometer and c. pritchard's wedge photometer. other methods of research in this field are by photography--photographic photometry--and radiometric method (see photometry, celestial). the earlier methods for the experimental determination of refractive indices by measuring the deviation through a solid prism of the substance in question or, in the case of liquids, through a hollow prism containing the liquid, have been replaced in most accurate work by other methods. the method of total reflection, due originally to wollaston, has been put into a very convenient form, applicable to both solids and liquids, in the pulfrich refractometer (see refraction). still more accurate methods, based on interference phenomena, have been devised. jamin's interference refractometer is one of the earlier forms of such apparatus; and michelson's interferometer is one of the best of later types (see interference). the variation of refractive index with density has been the subject of much experimental and theoretical inquiry. the empirical rule of gladstone and dale was often at variance with experiment, and the mathematical investigations of h. a. lorentz of leiden and l. lorenz of copenhagen on the electromagnetic theory led to a more consistent formula. the experimental work has been chiefly associated with the names of h. h. landolt and j. w. bruhl, whose results, in addition to verifying the lorenz-lorentz formula, have established that this function of the refractive index and density is a colligative property of the molecule, i.e. it is calculable additively from the values of this function for the component atoms, allowance being made for the mode in which they are mutually combined (see