By 1700 several important facts about light were known. White light was known to consist of a mixture of colors. Light was known to be deflected upon passing from one medium to another (refraction), the amount of deflection depending on the color (dispersion). The speed of light in empty space was known to be the same for all colors (otherwise a moon of Jupiter would appear one color upon first appearance from behind Jupiter, later other colors, or white). Light was known to travel in straight lines in a uniform medium and to experience a slight deflection in passing an obstacle (diffraction). It was known to carry energy. And a peculiar phenomenon called double refraction was known: Upon entering some crystals, light undergoes not one deflection but two at once, splitting into two separate beams.
In spite of this knowledge, and more accumulated during the eighteenth century, the nature of light remained a mystery for another hundred years. The fundamental question to be decided was: Does light consist of particles or is it a wave phenomenon? When the wave theory triumphed early in the nineteenth century, the defeated adherents of the particle theory could scarcely have imagined that after another hundred years light would turn out to consist of particles after all, leading to the modern resolution of the argument: Light is both wave and particle. (Or light is made of particles with wave properties.)
Given the knowledge that light travels at a fixed speed in straight lines through empty space, carrying energy from one place to another, a quite natural first guess is that light must consist of a stream of particles. This is the view commonly believed to have been championed by Newton, although, in fact, Newton recognized that the evidence was inadequate to decide one way or the other about the nature of light. The idea of light particles raised two problems in particular. (1) Why does an object giving off light apparently lose no weight, and an object absorbing light gain no weight? No one had yet imagined massless particles. (2) Why is the speed of light invariable? One might suppose that the particles of different colors of light should travel at different speeds, or that a more intense source of light should give off faster particles of light.
The wave theory, whose early champion was Newton’s contemporary Christian Huygens, accounted nicely for these two difficulties. A wave can transmit energy without conducting mass from one place to another. And it is a common feature of waves to have a fixed speed, independent of their strength and of their wavelength. The speed of sound, for instance, does not depend on the intensity or the pitch (what a cacophony would otherwise assault your ears in the second balcony at an orchestra concert). Both wave and particle theories can give an account of refraction, but with an important difference. The wave theory requires that light move more slowly in the denser medium, the particle theory that it move more quickly in the denser medium. When, in the mid-nineteenth century, experiment finally decided in favor of the slower speed, the wave theory was already rather firmly established.
One difficulty with the wave idea seemed to be that it required an all-pervasive substance filling space that could transmit the light vibrations. Something must do the vibrating. The ether, invented for this purpose, had to be indeed a very ethereal substance, for, unlike water and air, it had to be totally transparent and frictionless, offering no impediment to the passage of material objects through it. Otherwise, Earth would be slowed down and would spiral into the Sun. In spite of these unlikely properties, the ether was acceptable to most scientists. The idea of action at a distance with no transmitting agent seemed more repugnant to most scientists than did the idea of a mysterious ether.
Quite independent of arguments and speculation about the ether, a series of experiments in the first two decades of the nineteenth century so strongly supported the wave idea that there could no longer be any doubt that light is a wave motion. It is true that the diehard exponents of light particles offered some tortured and implausible explanations of these phenomena, but the experimental results were so simply and beautifully explained with light waves that there could be little doubt that the wave nature of light offered the “right” explanation. It is important to note at this point that these experiments, which led to the triumph of the wave theory, are as valid today as they were 200 years ago. In spite of our deeper knowledge, which leads us now to say that light does, after all, consist of particles—photons—the old experiments cannot be rejected. They may be repeated today with the same results and with the same interpretation in terms of waves. We must accept the new evidence that light is particle-like, but we must retain the old evidence that light is wavelike. Fortunately, the theory of quantum mechanics has come along to explain how photons can exhibit both properties, and how all other particles can do so too.
The conclusive evidence for the wave nature of light came through the phenomena of diffraction and interference. A wave passing an obstacle does not leave a precise sharp shadow, but is deflected a little into the dark region, giving the shadow a slightly fuzzy edge. This is diffraction. Two waves arriving at the same point may strengthen each other if they are crest to crest and trough to trough, or they may cancel each other out if the crest of one coincides with the trough of the other. This is interference. A little thought will show that each of these phenomena would be rather difficult to explain in terms of light particles. The wave theory, of course, did more than give a qualitative explanation of the existence of these phenomena. It provided a quantitative theory of diffraction and interference that accorded perfectly with the experimental facts. One can, for example, calculate the exact way in which the light intensity varies smoothly through the region of the fuzzy shadow edge, and also the pattern of interference resulting from light passing through a pair of slits.
The same phenomena that proved the existence of light waves provided a tool for measuring wavelength, and scientists soon learned that different colors are distinguished by different wavelengths. Visible light spans about one octave (that is, a factor of two) in wavelength, from short-wave violet, 350 nm, to long-wave red, 700 nm. (Here nm stands for nanometer, 10–9 m). Although small, these wavelengths are still several thousand times larger than the size of an atom, which is about 0.1 nm.
Besides wavelength, a wave can be characterized by its frequency, or number of vibrations per second. Light waves vibrate extremely rapidly, more than 1014 Hz. The highest pitched sound audible to the human ear is about 104 Hz. Radio waves vibrate at about 106 Hz in the AM band on up to and beyond 109 Hz in what is called the UHF, or ultra high frequency, band. In round numbers, vibrations of light are about one million times more rapid than UHF vibrations, and the wavelengths, correspondingly, a million times shorter.
Frequency and wavelength are related by a very simple equation,
λf = v,
where λ is the wavelength (for example, in meters), f is the frequency (for example, in vibrations per second, or hertz—measured as inverse time) , and v is the speed of the wave (for example, in meters per second). The formula can be used for any wave at all. Thus, for the standard musical A, f = 440 Hz. The wavelength in air of this standard tone is its speed in air, typically about 330 m/s, divided by its frequency, 440 Hz, or about 0.75 m. The same equation applies to light. For example, green light of wavelength 5 x 10–7 m, has a frequency equal to the speed of light, 3 x 108 m/s divided by this wavelength, or 6 x 1014 Hz. This little exercise, arriving at a such an enormous frequency, is a reminder of the power of simple physics to reach out far beyond the range of direct human perception.
The equation tying together wavelength, frequency, and wave speed is easy to derive. Imagine yourself in a boat at anchor watching an evenly spaced series of wave crests roll by. If the wave speed is v and the wavelength crest-to-crest distance is λ, how much time elapses between successive crests? This time (let us call it T) is the time required for the wave to move ahead a distance λ, and is equal to the distance divided by the speed:
This time, T, the period of the wave, is the inverse of the frequency: T = 1/f. This means that one can write the foregoing equation as
1/f = λ/v,
equivalent to the earlier equation linking these three quantities. The all-important equation governing wave propagation, λ f = v, is in fact nothing more than a restatement of the basic equation of constant-speed motion, x = vt: distance equals speed multiplied by time.
By 1820, scientists knew that light consisted of waves; they had explained the phenomena of interference and diffraction mathematically; they had measured the wavelength of light, at least approximately; and they had explained the phenomenon of double refraction in terms of the transverse vibration of light waves. Thomas Young in England was the first to propose a wave explanation for interference, in 1801. He went on to design specific experiments to reveal interference fringes. Subjected to ridicule by the then dominant adherents of the particle theory of light, Young abandoned his researches after a few years, returning to them only after 1815 when Augustin Fresnel rediscovered optical interference effects and received a more sympathetic hearing for his wave ideas in France than Young had received in England. In the years 1815-1820, Fresnel and Dominique Arago in France and Young in England carried out a series of experiments and mathematical analyses that won over most scientists to the wave theory. By 1821 Joseph von Fraunhofer in Bavaria had invented the diffraction grating and measured some wavelengths of light to high precision.
The riddle of double refraction was first correctly solved in 1817 when Young suggested that the vibrating motion in light waves might be transverse to the direction of propagation of the wave. A water wave is a simple example of a transverse vibration. The motion of the water is mostly up and down, transverse to the horizontal motion of the wave. A swimmer is lifted up and down as a wave passes by. But sound waves or shock waves that pass through a medium rather than over its surface are longitudinal—the material vibrates in the direction in which the wave is proceeding. A person struck by a shock wave from an explosion is first pushed away from the explosion, then sucked back toward it. The person is caused to vibrate (uncomfortably) along the direction of the wave motion. It was quite natural to think of light passing through the ether as analogous to sound passing through air, vibrating along its direction of motion. Indeed, from the time of Christian Huygens’ pioneering work on waves in the seventeenth century, it had been assumed that light, if it is a wave, is a longitudinal wave. Nevertheless, Young’s contrary suggestion was not long in finding acceptance. Two important puzzles were ripe for solution, and the hypothesis of transversality of light waves nicely accounted for both.
The first of these puzzles was the phenomenon of double refraction, which had gone unexplained since its discovery by Erasmus Bartholinus in 1669. It was necessary only to assume that the speed of light in the crystal depends on the orientation of the direction of vibration. Light vibrating in one direction will then be refracted differently from light vibrating in another direction. For a longitudinal wave there is only one possible direction for the vibration; hence there is no basis for explaining double refraction.
It would seem that a transverse wave should have infinitely many different possible directions of vibration. Indeed it does. However, it has only two independent directions, perpendicular to each other and to the direction of propagation. Any intermediate direction of vibration can be resolved into the two independent directions, just as any direction on Earth can be resolved into a north-south component and an east-west component. For this reason, crystals are at most doubly refracting, not triply or multiply refracting.
Apart from double refraction, light was known to have a dual character in general. In 1808 Etienne Malus discovered that light reflected from glass and many other substances had some properties different from the unreflected light. This was called polarization. Eight years later Arago and Fresnel learned to their surprise that light beams with different polarization could not be made to cancel each other through interference. This was the second important puzzle that was quickly clarified by Young’s suggestion of transverse vibration. No matter how arranged, two beams whose electric field vectors are not parallel cannot cancel one another by destructively interfering.
To summarize: Between 1800 and 1820, understanding of the nature of light took giant strides forward. Scientists established the wave nature of light beyond reasonable doubt, and measured the wavelengths and frequencies of visible light. The transversality of light waves explained polarization phenomena. One other discovery of importance, not so far mentioned, was also made in this period. It was the discovery of radiation with wavelengths shorter and longer than those of visible light. Ultraviolet and infrared, as these radiations were called, gave the first hint of the vast electromagnetic spectrum that we know today.
Even after these advances, there remained deep mysteries of light that required another century to plumb. Why does light travel at the speed it does, and why is its speed independent of its wavelength? What is doing the vibrating? What is the mechanism of emission and absorption of light? Why is light polarized by reflection and refraction? What is the connection between light and thermal radiation? What is the connection between light and electricity and magnetism? In 1820 not all of these questions had been asked, much less answered. Eventually all of them proved important, and all found answers.