Revival of the Wave Theory of Light in the Early Nineteenth Century

Overview

The nature of light is a very old issue in the history of science, dating back at least to Greek times. The prevalent belief among eighteenth-century natural philosophers was that light was made up of particles, not waves. The revival of the wave theory of light in the early nineteenth century is largely a tale of two cities, with Thomas Young (1773-1829)discovering the law of interference in London followed by the development of the mathematical wave theory by Augustin Fresnel (1788-1827) in Paris. The rise of the wave theory during the first three decades of the century is often regarded as a revolution in science. It exemplified a new style of scientific reasoning, with abstract mathematical models taking precedence over intuitive mechanical analogies for light. The ensuing debate on the validity of the new theory led to a closer examination of the standards and goals of scientific research. The domain of optics was redefined during this time, with the study of the physical aspects of light coming to be recognized as important for its own sake, apart from its relevance for theology or vision.

Background

Light and vision were intimately connected to the ancient Greeks and Arabs. The tactile theory, which held that our vision was initiated by our eyes reaching out to "touch" or feel something at a distance, gradually lost ground to the emission theory, which postulated that vision resulted from illuminated objects emitting energy that was sensed by our eyes. The nature of the emitted light occupied Renaissance thinkers in Europe, with early views envisioning light as a stream of particles, perhaps supported by the ether, an invisible medium thought to permeate empty space and all transparent materials.

Using the principle that light rays take the path that minimize their travel time, Pierre de Fermat (1601-1665)accounted for the phenomenon of refraction, the bending of light at the boundary between two transparent media such as air and water. An analogous principle for light waves was introduced by Christiaan Huygens (1629-1695), who considered spherical pulses of light propagating through an elastic ether. Huygens's principle would form the basis of the wave theory developed by Fresnel a century and a half later.

The void in the wave theory during the interim period is usually attributed to the influential legacy of Sir Isaac Newton (1642-1727), who preferred to think of light as made up of corpuscles, or particles, that were governed by the laws of motion that carry his name. Newton observed concentric fringe patterns in the reflection of light from a spherical glass surface—known as Newton's rings—but he failed to recognize the signature of wave interference in this phenomenon. His bias against the wave theory was grounded in the belief that light traveled in straight lines, forming geometrical shadows of sharp objects. Observations to the contrary, in which light diffracted around an object to form complex patterns near the edge of the shadow, were known to Newton but failed to convince him of the wave hypothesis.

Most eighteenth-century natural philosophers concerned with the nature of light thought, as Newton did, that light was composed of individual particles subject to mechanical forces and inertia. A less rigorous view held it to be more like a fluid of particles, subject to collective motion in the ether, with analogies drawn to heat and fire, sometimes with Biblical connotations. The wave theory of light was largely ignored during this century, with some exceptions. The mathematician Leonhard Euler (1707-1783), for instance, advocated a vibration theory based on a comparison of light and sound. Just as sound travels by vibrations in the air that are longitudinal, or parallel to its motion, Euler conceived of light as longitudinal vibrations of an ethereal medium.

Young himself believed in the vibration theory at the turn of the nineteenth century. Trained as a physician, his early research on human vision and acoustics led him to consider the physical nature of light and sound. He devised several experiments to test his views on light, the most famous of which is the double-slit experiment that carries his name. He considered light from an aperture incident on two evenly placed slits on an otherwise opaque screen. The light emerging from the two slits formed fringes of alternating bright and dark bands on an observation screen. Young identified this periodic pattern with wave interference, the light waves from the two slits superposing to annul or enhance each other, much like two overlapping ripples in a water tank. He measured the fringe spacing for different colors, affirming Euler's conjecture that the color of light is connected with the frequency of the ethereal vibrations. Young also recognized the role of interference in the formation of Newton's rings.

Despite Young's successes with the vibration theory, he was unable to tame the phenomenon of double refraction, long known to be an embarrassment to both particle and wave views of light. This was the tendency of a beam of light to refract into two distinct beams upon entering certain crystals, such as Iceland spar (calcite), with the relative intensities of the two beams depending on the angle of entry into the crystal. Neither particle nor vibration theory could explain how light could be "sided" like this, preferring one angle to another, as neither particles nor sound waves shared this property. This property of the polarization, or sided-ness, of light was shown by Étienne Malus (1775-1812) in 1810 to be associated with reflection as well, as differently polarized beams reflected by different amounts from a mirror based on their angle of incidence, a phenomenon known as partial reflection. Polarization provided the bridge between the vibration theory of Young and the true wave theory developed by Fresnel in the second decade of the century.

Fresnel began investigating diffraction phenomena in 1814, leaning toward a wave theory of light and advancing the notion that the high frequency of the wave oscillations perhaps accounted for the near-straight-line motion of light. Being mathematically inclined, Fresnel sought to construct a theory of diffraction based on Huygens's principle, allowing for each point on the wave front to be a source of spherical waves that interfered with one another. This marked the true beginnings of a mathematical theory of wave propagation. Fresnel used the principle in its generality, with a continuum of points on each wave front generating secondary wavelets that interfered over a full range of phases, not just two. Using analytical calculus, Fresnel was able to derive formulae for several diffracting geometries, including diffraction through a narrow slit and around an opaque disc, winning him a prize from the Paris Académie in 1819.

As early as 1817 Young suggested to Fresnel that perhaps the polarization of light could also be explained if one considered transverse waves, where the ether oscillated perpendicular to the direction of travel. Transversality would give light a two-sidedness, since there are two independent directions along which a wave could oscillate perpendicular to its motion. This was suggested by an experiment that Fresnel did in 1819, along with Dominique-François Arago (1786-1853), in which it was found that differently polarized beams of light did not interfere with one another. By 1822 Fresnel was able to incorporate transverse waves into his theory and produce convincing explanations for double refraction and partial reflection, with the two beams of light corresponding to the two transverse polarizations of the wave. The wave theory quickly gained in reputation after this period.

Impact

When Young first spoke in support of an analogy between light and sound waves before the Royal Society of London in 1800, his implicit rejection of Newton's views on light did not go over well with his English audience. His later expositions on interference in the double-slit experiment met with disbelief. The idea that a screen uniformly illuminated by a single aperture could develop dark fringes with the introduction of a second aperture—that the addition of more light could result in less illumination—was hard to accept, especially for those not used to thinking about light as a wave. A similar difficulty arose with Fresnel's theory of diffraction, with one of the judges on his 1819 prize committee, Siméon-Denis Poisson (1781-1840), highlighting the seemingly absurd fact that his theory implied a bright spot at the center of the shadow of an illuminated opaque disc, something that Arago immediately verified.

The situation changed dramatically in the 1820s with an increasing number of scientists adopting the wave theory of light. Fresnel's wave theory won support more readily than the vibration theories of Euler and Young, for several reasons. The replacement of longitudinal waves with transverse waves allowed polarization to be incorporated into a wave description. The theory gave concrete numerical predictions that could be tested readily, including phenomena like diffraction and double refraction that were hard to reconcile with the particle view. Also significant was the fact that the wave theory was an axiomatic theory founded essentially on Huygens's principle, rather than a set of ad hoc hypotheses characteristic of the particle theories, and this found increasing resonance among the scientists of the 1830s, especially the younger generation.

Analogies between light and other phenomena played a less pivotal role in the new wave theory. Particle theories compared light to material bodies, subject to mechanical forces, or else envisioned light as a fluid akin to heat and electricity, also modeled as fluids at the time. The vibration theory was based on the analogy with sound, invoking material properties in the ether like density and elasticity to explain the vibrations. By contrast, Fresnel's wave theory emphasized methodology, working out the mathematical consequences of an analytic principle. While its proponents continued to invoke the ether to interpret the theory and facilitate its assumptions, the formalism of the theory did not stand or fall with a particular interpretation. Indeed, the formalism was not restricted to light waves but could be used to explain all wave phenomena.

Although the wave theory dominated optical science after 1830, there remained a few critics who could not embrace its premises and who continued to seek explanations in terms of particles and rays. The dispute was on the nature of scientific laws and their relation to empirical facts, centering on the wave theory. Physical optics in the early nineteenth century was essentially an inductive science, like thermodynamics or chemistry, consisting of a collection of disparate observations in need of a unifying theoretical description. Although the wave theory provided a coherent description that could be tested, it relied on abstract hypotheses like Huygens's principle and transversality that were themselves not immediately testable, much less the properties of the ether that sustained them. This bothered those who thought that scientific hypotheses or laws should be both necessary and sufficient in explaining all relevant phenomena. Scottish physicist David Brewster (1781-1868), for instance, saw the abstract premises of the wave theory as superfluous and unwarranted and preferred a simpler induction from known facts. The wave theorists, on the other hand, put more stock in the unifying power of their theory, allowing it to gradually gain confidence by new experiments, implying a subtle shift in methodology. The transversality of the light wave, for instance, would eventually gain more physical significance in the work of James Clerk Maxwell (1831-1879), with associations to electricity and magnetism.

Optics had a different connotation for both scientists and their lay audience by the end of the wave revolution. Whereas eighteenth-century treatises and lectures in optics might include sections on theology and vision in their discussion of light, the nineteenth-century textbooks tended to treat the physical aspects of light exclusively, with increasing use of mathematics for the wave theory. Gradually, the empirical and theoretical aspects of light started to take center stage, with less concern for its sociological or physiological ramifications. The upshot was a specialization of the field, with less participation by the lay audience in scientific discourses and a more mathematically trained scientific elite.

It is often remarked that the modern discipline of theoretical physics became distinct from natural philosophy in the early nineteenth century, with increasing emphasis on the use of advanced mathematics to describe physical theories. A larger revolution was indeed happening in physical science at the time, with fields becoming increasingly specialized and autonomous, new scientific methods being expounded, and changes in the training and career patterns of the scientists. Many of these changes were integral to the rise of the wave theory of light.

ASHOK MUTHUKRISHNAN

THE INVENTION OF THE KALEIDOSCOPE

Akaleidoscope is an optical instrument containing mirrors placed at special angles to form multiple, symmetrical reflections of light. Colored glass or plastic, or liquid mixtures of oil and water are sometimes used to create changing, colorful patterns. Meaning "a beautiful form to see" in Greek, the kaleidoscope has offered inspiration to generations of artists, designers, and musicians. It was invented in 1816 by Scottish physicist David Brewster, who wrote: "If it be true that there are harmonic colors which inspire more pleasure by their combination than others; that dull and gloomy masses, moving slowly before the eye, excite feelings of sadness and distress; and that the aerial tracery of light and evanescent forms, enriched with lively colors, are capable of inspiring us with cheerfulness and gaiety; then it is unquestionable, that, by a skillful combination of these passing visions, the mind may derive a degree of pleasure far superior to that which arises from the immediate impression which they make upon the organ of vision." Nearly 200,000 kaleidoscopes were sold in Paris and London within three months, but Sir Brewster was unable to profit from the sales, as he was unsuccessful in enforcing his patent on the instrument.