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Optics

OPTICS

OPTICS. The development of optics between 1450 and 1789 can be conveniently divided into two phases bridged by the optical work of Johannes Kepler (15761630) and distinguished by a radical change in analytic focus. During the first phase, that focus was primarily on sight, not light. During the second, it shifted completely from sight to light. Reflecting this shift, the following essay consists of three sections, the first dealing with pre-Keplerian optics, the second with the Keplerian transition, and the third with post-Keplerian developments.

PRE-KEPLERIAN OPTICS

By 1450 two ostensibly contradictory models of sight were available to European thinkers. The first and simpler of the two harks back to the visual-ray theory of Euclid (fl. c. 300 b.c.e.). Brought to maturity by Ptolemy (c. 170 C.E.), this theory assumes that a constant stream of visual flux emanates from the center of the eye through the pupil to form a cone. This cone can be conceived of as a bundle of individual rays, each reaching out to "feel" things visually and, on that basis, to locate and define them in space by reference to the vertex at the eye's center. But there is more to seeing than spatial perception. Color and luminosity, which are all but ignored by Euclid, seem not only integral but fundamental to sight. Recognizing this point, Ptolemy based his account of vision on color perception. Understood as a real and inherent quality of external objects, color, for Ptolemy, is what makes them visible. But, on its own, it cannot be seen; it needs the added power of light, which acts as a catalytic agent for vision. Seeing therefore begins with the primitive grasp of color by visual flux when it touches a properly illuminated object. Transmitted radially back through the cone of flux to the eye, the resulting color impression gives rise to the perception of spatial characteristics, such as size, shape, and distance, which in turn gives rise to a perception of the object as a whole. For Ptolemy, then, color perception is absolutely primal; all other perceptions are derivative.

The second model of vision harks back to Alhacen (9651040) and his Perspectivist disciples, Roger Bacon (fl. c. 1265), Witelo (fl. c. 1275), and John Pecham (fl. c. 1280). Rejecting visual rays as functionally pointless, these theorists raised light to primacy in the visual process, supposing it to be an intrinsic quality of self-luminous or illuminated bodies. Each point of light on the surface of such bodies is a source of radiation in its own right, spreading outward in all directions in a process of self-replication. The resulting sphere of propagation can be analytically resolved into individual rays, along which point forms of the original light are transmitted. Color, too, is an intrinsic property of bodies. Yet although they are ontologically distinct, light and color are functionally inseparable. Both must be present in objects if they are to be seen, so what actually radiates from them is luminous color. Thus, like Ptolemy, the Perspectivists viewed luminous color as primal for sight.

Unlike Ptolemy, the Perspectivists gave a detailed account of how the optic complex contributes to vision. The eye itself, they assumed, is a sphere. Toward its front lies the crystalline lens, whose anterior surface is concentric with the eye as a whole. The space behind it is filled with vitreous humor, which is optically denser than the glacial humor occupying the lens. At the very back, directly in line with the center of the pupil and the center of the eye, lies the hollow optic nerve, which reaches from the eye to the forefront of the brain. A conduit for visual spirit manufactured in the brain, this nerve transmits the spirit to the lens and thereby sensitizes it. The anterior surface of the lens, meanwhile, is bombarded from all directions by point forms of luminous color radiating from external objects. Because of its visual sensitivity, though, the lens feels only those color forms that strike it orthogonally and thus selects out a formal representation of the object in point-to-point correspondence with it. The composite of all the rays linking the object and its formal representation on the lens's surface creates a cone of radiation with its base in the object and its vertex at the center of the eye. Mathematically equivalent to Ptolemy's visual cone, this radiative cone serves much the same function as the basis for spatial perception.

The lens's ability to select coherent visual representations is also optically determined. As a refractive body, the lens allows only those rays that strike it orthogonally to pass straight through toward the center of the eye. Before they reach that point, they are refracted at the back surface of the lens so as to channel the visual representation in proper upright order into the hollow optic nerve. Conveyed by the spirit perfusing this nerve, the visual representation eventually reaches the brain, where it is subject to perceptual scrutiny. From this scrutiny arises a more abstract perceptual representation of the object according to all its visible attributes. More abstract yet is the ensuing conceptual representation, by means of which we perceive the object as a specific or general type. Each succeeding representation is a virtual likeness of its predecessor, much as a painting is a likeness of its subject. Hence, from start to finish, visual perception unfolds in a succession of virtual replications that ensures a fundamental correspondence between objective reality and our mind's-eye picture of it.

The Perspectivists were thus convinced that vision is veridical under the right conditionsadequate light, a healthy eye, and so forth. But under the wrong conditions, sight can err. Reflection and refraction offer two specific and egregious examples. In both cases there is a clear disparity between reality and appearance, insofar as things always appear displaced and often distorted in mirrors and refracting media. Accordingly, the Perspectivists were at pains to reconcile appearance with reality on the basis of ray geometry. The result was an elaborate analysis of image formation and distortion in mirrors and refracting media based on two principles: the law of equal angles for reflection and the cathetus rule of image location for reflection and refraction. According to this rule, the image of any point object seen in a mirror will lie at the intersection of the extended line of reflection, which constitutes the line of sight, and the perpendicular dropped from the object point to the surface of reflection. Neverthelessand this point is crucialthe ultimate goal of this analysis was not to understand how light interacts with reflecting and refracting surfaces. It was to understand how things are perceived or, rather, misperceived by means of such surfaces. Perspectivist optics, in short, was "subjective," not "objective," in its analytic focus.

Not all optical phenomena are subjective, though. Long before the Renaissance, it was known that spherical and parabolic concave mirrors can gather incoming light rays to a point or spot where tinder will ignite. By at least 1300, moreover, it was known that convex lenses can correct presbyopia. And while this could be explained away through refractive magnification, the correction of myopia by concave lenses (known by the mid-fifteenth century at latest) could not. Not only do such lenses not magnify what is seen through them; they actually reduce it. In addition, by the mid- to late-sixteenth century, it had become relatively common knowledge that concave mirrors, convex lenses, and pinhole openings (the camera obscura) can project images onto a screen. Lying not "in" the mirror or lens but outside it, such images make little or no sense according to Perspectivist theory, in which all images are virtual, or subjective.

Perhaps that is why such phenomena were essentially disregarded within academic circles, where Perspectivist theory predominated. Yet over the fifteenth and sixteenth centuries, those same phenomena captured the attention of artists, instrument makers, and leisured amateurs who, unlike their academic confreres, tended to be less theoretical than pragmatic, even instrumentalist, in their orientation. Growing interest in the focusing properties of lenses and mirrors over the sixteenth century bears directly on this point. An early example of this interest can be found in Francesco Maurolyco's study of the lenticular correction of presbyopia and myopia. Published posthumously in the Photismi de lumine (1611), but dating to the mid-sixteenth century, this study is noteworthy in two respects. First, its theoretical underpinnings are thoroughly Perspectivist. Although he felt free to adjust the model slightly by having the visual image selected from a particular sheaf of oblique rather than perpendicular rays, Maurolyco had no doubt that the selection itself occurred at the crystalline lens. Second, despite his reliance on Perspectivist principles, albeit somewhat modified, Maurolyco couched his explanation in terms not of light radiation but of its apparent antithesis, visual radiation. While such conflation may seem illogical to us, it was anything but for Maurlyco and his pragmatically oriented contemporaries. After all, light rays and visual rays are mathematically equivalent, so, as far as pure geometrical analysis is concerned, they are interchangeable. In many ways, in fact, the visual ray model is preferable, because it is both conceptually and mathematically simpler.

Maurolyco's pioneering study of lenses manifests a subtle but important change in attitude toward reflection and refraction during the later Renaissance. Before, within the Perspectivist framework, both had been regarded as sources of misperception. Now they were looked to as a means not of deluding sight but of rectifying or improving it. To this end, a succession of thinkers after Maurolyco, Giambattista della Porta (15351615) foremost among them, turned their attention to image magnification in convex lenses and concave mirrors in the hope of constructing an effective telescopic device. Although they failed in this, they at least succeeded in nudging the study of lenses and mirrorsas well as of their focusing propertiestoward the mainstream of optical analysis. It would be up to Kepler and Galileo to bring this study fully into the mainstream during the first few years of the 1600s.

THE KEPLERIAN TRANSITION

Early in his effort to determine the orbit of Mars, Kepler realized that in order to ensure the accuracy of his observational data, he had to address a variety of optical issues involving the camera obscura and atmospheric refraction. That in turn brought him to a close, critical scrutiny of Perspectivist theory, the results of which he published in 1604 in a wide-ranging critique entitled Ad Vitellionem paralipomena (Supplement to Witelo). Of particular interest is his account of retinal imaging in chapter five. Kepler began by supposing that the crystalline lens, like any other convex lens, is a refractive body and nothing more. Using a water-filled glass sphere to represent the lens, he examined how light passes through it to be brought to focus on the other side. He was thus led to conclude in the end that the eye acts like a camera, the pupil forming a diaphragm and the lens focusing all the rays passing through it from a given spot on the external object to a given spot on the retina. In this way, the light from all the spots on the surface of the object are projected to corresponding spots on the retina to form an inverted image, or "painting," of the object at the back of the eye.

At a superficial level, all Kepler did was displace the visual image from the front to the back of the eye, but at a deeper level he did far more than that. For a start, by doing away with the Perspectivist cone of radiation, Kepler did away with the center of sight as an essential reference point for optical analysis. Furthermore, being "real," not virtual, Kepler's image is publicit is there for anyone, not just the perceiver, to see. Worse, that image is inverted, not upright like its Perspectivist counterpart. Worse yet, it is too large to pass through the optic nerve to the brain for perceptual scrutiny. How, then, do such images give rise to visual perception? Kepler's response was to shunt the problem from optics to natural philosophy, arguing that the domain of optics extends no further than the retina. Opticians, in short, must restrict their study to the outward, physical manifestations of light alone. Its inward, perceptual manifestations are no longer their business.

Within six years of the publication of Kepler's account of retinal imaging, Galileo had fulfilled the hopes of earlier optical researchers by constructing a telescope that consisted of a convex objective and a concave eyepiece. Magnifying at least twenty times, this instrument had adequate resolution to allow a fairly distinct view of the four largest satellites of Jupiter. Published in the Sidereus Nuncius of 1610, news of this invention reached Kepler, who was eager to know precisely how it worked. His examination of the Galileian telescope led him to a rigorous geometrical analysis of lenses and lens combinations based solely on focal points. Among the results of that analysis, which appeared in the Dioptrice of 1611, was the design for a new kind of telescope whose objective and eyepiece were both convex. Technical details aside, Kepler accomplished two crucial things with this work. First, he brought refraction to the fore as a central concern for subsequent optical thinkers. Second, by stripping optics of its perceptual and epistemological entailments, he put the analytic focus squarely on light.

POST-KEPLERIAN DEVELOPMENTS

Having divorced the analysis of light from the analysis of sight, Kepler set the stage for a radical transformation of optics based on the mechanization of light. The key figure in this transformation was René Descartes, whose ideas about light and color took published form in the Dioptrique of 1637. According to Descartes, all light sources consist of infinitesimal particles clumped together so tightly as to form a virtual continuum. These clumps rotate swiftly, imparting a strong centrifugal tendency to the particles on their surface. But every light source is embedded in an ethereal medium composed of tiny spherical particles that are perfectly inelastic and contiguous. Instead, therefore, of flying off, the surface particles of the light source can only push against the unyielding ethereal envelope. The result is an outward impulse propagated instantaneously in all directions through it. This impulse is lightor, rather, what we perceive as lightand each individual line of impulse constitutes a "ray." What we perceive as transparency is nothing more than the capacity of ether particles to transmit light impulses. Color, for its part, is a function of spin imparted to the ethereal spheres by those impulses. The faster the spin, the more vivid the color as it verges from blue toward redor, rather, what we perceive as blue and red. The epistemological implications of this account are clear. Since physical light and its perceptual effect are absolutely different in kind, there is no meaningful way of linking them through virtual representation. "Red" and "bright" are therefore not objectively real. They are epiphenomenal, mere figments of our imagination.

Light many not actually be a projectile for Descartes, but it acts just like one. Accordingly, as a case of virtual motion along a virtual trajectory, light radiation must follow the laws of actual motion. This notion underlies Descartes's "proof" for the sine law of refraction, which is based on two fundamental principles: that, in rebounding from a reflective surface or penetrating a refractive medium, light loses none of its virtual motion, or "speed," along the horizontal, and that in penetrating a denser refractive medium, light gains virtual motion, or "speed," in proportion to the density. From this it follows that when light passes from one refractive medium to another, the ratio of the sines of the angle of incidence and the angle of refraction will be constant.

Descartes's account of light enjoyed a mixed reception. The "Schoolmen," who clung to medieval theory, rejected it outright. Among those who accepted it, some, like Robert Hooke, took it more or less at face value. Others accepted it on principle, realizing nonetheless that it was deeply flawed. The most glaring problem, of course, is the apparent contradiction in supposing that instantaneously transmitted light impulses can somehow vary in virtual motion or "speed." One obvious response to this problem is to assume that light radiation involves actual rather than virtual motion (an assumption that was eventually vindicated by Olaus Roemer's demonstration in 1679 that light takes time to travel). This is the tack Christiaan Huygens took in the 1670s. Assuming with Descartes that light consists of impulses transmitted through contiguous particles of ether, Huygens parted ways with him by making those particles elastic rather than inelastic. He proposed, therefore, that the impulse passed into the ether causes its constituent particles to contract and expand in succession, the result being a spherical wave front of condensations and rarefactions passing outward seriatim from the light source. To justify this longitudinal wave model of light, Huygens used it to good effect in explaining double refraction in Iceland spar, a phenomenon first brought to light by Erasmus Bartholin in 1669.

While Descartes, Hooke, and Huygens placed the motion, whether virtual or real, in the ethereal medium, others placed it the light itself. By 1662, for instance, Pierre de Fermat perfected his least-time proof of the sine law, which treats light as a particle shooting through space. Upon entering a denser refractive medium, this particle is impeded and slowed down commensurately, so that of all possible trajectories the particle could follow, the one dictated by the sine law takes the shortest time to traverse. The crucial turn in the evolution of a particle theory of light came with the publication of Newton's first paper on light and color in 1672. There Newton demonstrated experimentally that color is not a modification of white light, as Descartes would have it. On the contrary, being composed of all the colors in the prismatic spectrum, white light is a modification of color. Newton's eventual explanation of this fact rested on the supposition that each color is associated with a particle of a specific size. Building on this supposition in the Opticks of 1704, Newton developed a coherent analysis of light and color based on the interaction of color particles with gross matter as well as with exquisitely elastic ether particlesall such interactions being governed by attractive and repulsive forces. On this basis, Newton was able to explain an astonishing array of optical phenomena, ranging from simple reflection and refraction to double refraction, the formation of colored rings in thin glass plates ("Newton's Rings"), and even diffraction. With the appearance of Newton's Opticks, the theoretical lines were drawn for the rest of the eighteenth century. Huygens's longitudinal wave theory was not abandoned altogether, but because of its superior explanatory power, Newton's particle theory held sway until the early nineteenth century, when transverse waves became the wave of the future for optics.

Along with these theoretical developments, the seventeenth and eighteenth centuries witnessed a number of significant technical advances centering on telescopy and microscopy. The telescope, of course, found its first major publicists in Galileo and Kepler. Its close cousin the compound microscope found its key publicists somewhat later, first with the appearance of Robert Hooke's Micrographia in 1665 and subsequently with the observations of Jan Swammerdam and Antoni van Leeuwenhoek. For both instruments, however, resolution was a serious problem, and although it was mitigated somewhat as lenses with greater focal lengths were produced to give greater magnification, the resulting increase in telescope length narrowed the field of view.

The two main obstacles to proper resolution are spherical and chromatic aberration. The first of these stems from the fact that spherical lenses (as well as spherical concave mirrors) do not bring light to true focus. This problem inspired both Kepler and Descartes to seek the precise curvature that would bring parallel rays to focus at a single point, Descartes basing his analysis on the newly established sine law of refraction. As Descartes eventually proved, either a plano-hyperboloidal or spherico-ellipsoidal lens will suffice, hence the continuing effort during the middle decades of the seventeenth century to grind plano-hyperboloidal lenses. As promising as that expedient may have been in theory, it was far less so in practice, and the effort was eventually abandoned as hopeless. Chromatic aberration went unrecognized until Newton realized that lenses have a prismatic effect that disperses the light according to color, creating a sort of halo effect on telescopic images. To overcome this effect, he designed a reflecting telescope in which a concave spherical mirror serves as the objective. In fact, he constructed such a telescope and presented it to the Royal Society in 1671. But here, too, promise outstripped practicality, because it was all but impossible to keep the mirror from tarnishing or losing its proper shape.

The upshot was that over the later seventeenth and early eighteenth century, efforts were concentrated on improving the magnification of refracting telescopes and finding ways to widen the field of view in compensation. In addition, micrometers were added for greater observational precision, so that by the 1720s it was within around one second of arc. Eventually, however, the unwieldiness of such long telescopes coupled with improvements in the manufacture of concave mirrors led in the mid-eighteenth century to a renewed focus on reflecting telescopes. Steady improvements in such telescopes during the second half of the eighteenth century culminated with William Herschel's discovery of Uranus in 1781.

See also Astronomy ; Camera Obscura ; Descartes, René ; Galileo Galilei ; Hooke, Robert ; Huygens Family ; Kepler, Johannes ; Leeuwenhoek, Antoni van ; Newton, Isaac ; Scientific Instruments .

BIBLIOGRAPHY

Lindberg, David C. Theories of Vision from Al-Kindi to Kepler. Chicago, 1981.

Park, David. The Fire within the Eye. Princeton, 1997.

Ronchi, Vasco. Optics: The Science of Vision. Translated by Edward Rosen. New York, 1991.

Sabra, A. I. Theories of Light from Descartes to Newton. Cambridge, U.K., 1981.

Shapiro, Alan E. Fits, Passions, and Paroxysms: Physics, Method, and Chemistry and Newton's Theories of Colored Bodies and Fits of Easy Reflection. Cambridge, U.K., 1993.

Simon, Gérard. Archéologie de la vision. Paris, 2003.

Smith, A. Mark. "Alhacen's Theory of Visual Perception." Transactions of the American Philosophical Society 91 (1991): 45.

. "Descartes's Theory of Light and Refraction." Transactions of the American Philosophical Society, 77.3 (1987).

Van Helden, Albert. "The Invention of the Telescope." Transactions of the American Philosophical Society 67 (1977): 4.

Wolf-Devine, Celia. Descartes on Seeing. Carbondale, Ill. 1993.

A. Mark Smith

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optics

optics Branch of physics concerned with the study of light and its behaviour. Fundamental aspects are the physical nature of light, both as a wave phenomenon and as particles (photons), and the reflection, refraction (bending), and polarization (restricting vibrations to one direction) of light. Optics also involves the study of mirrors and lens systems and of optically active chemicals and crystals that polarize light. See also polarized light

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optics

optics, scientific study of light. Physical optics is concerned with the genesis, nature, and properties of light; physiological optics with the part light plays in vision; and geometrical optics with the reflection and refraction of light as encountered in the study of the mirror and the lens.

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optics

op·tics / ˈäptiks/ • pl. n. [usu. treated as sing.] the scientific study of sight and the behavior of light, or the properties of transmission and deflection of other forms of radiation.

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