Fritjof Capra (32 page)

THE NATURE OF LIGHT RAYS

Leonardo’s studies of perspective and of light and shadow not only found artistic expression in his mastery of rendering subtle visual complexities, but also stimulated his scientific mind to investigate the very nature of the rays that carried light in pyramids from the objects to the eye. With his empirical method of systematic observation and with highly ingenious experiments that used only the most rudimentary instruments, he observed optical phenomena and formulated concepts about the nature of light that would take hundreds of years to be rediscovered.

His starting point was the accepted contemporary knowledge that light is emitted by luminous objects in straight lines. To test this assertion, Leonardo used the principle of the camera obscura, which had been known since antiquity. Here is how he describes his experiment:

If the front of a building, or any piazza or field, which is illuminated by the sun, has a dwelling opposite to it, and if in the front that does not face the sun you make a small round hole, all the illuminated objects will send their images through that little hole and will appear inside the dwelling on the opposite wall, which should be white. And there they will be, exactly and upside down…. If the bodies are of various colors and shapes, the rays forming the images will be of various colors and shapes, and of various colors and shapes will be the representations on the wall.
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Leonardo repeats this experiment many times with various combinations of objects and with several holes in the camera obscura, as clearly illustrated on a folio in the Windsor Collection.
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Having performed a series of tests, he then confirms the traditional knowledge: “The lines from…the sun, and other luminous rays passing through the air, are obliged to keep in a straight direction.”
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He also specifies that these lines are infinitely thin, like geometrical lines. He calls them “spiritual,” by which he means simply without material substance.
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And finally, Leonardo asserts that light rays are rays of power—or, as we would say today, of energy
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—which radiate from the center of a luminous body, such as the sun. “It will appear clear to the experimenters,” he writes, “that every luminous body has in itself a hidden center, from which and to which…arrive all the lines generated by the luminous surface.”
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Thus, in essence, Leonardo identifies three basic properties of light rays: They are rays of energy generated at the center of luminous bodies; they are infinitely thin and without material substance; and they always travel in straight lines. Before the discovery of the electromagnetic nature of light in the nineteenth century, nobody could have improved on Leonardo’s description, and even then contradictions concerning the nature of light waves persisted until they were resolved by Albert Einstein in the twentieth century.
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On the other hand, the view of light rays as straight geometrical lines is still considered an excellent approximation for understanding a broad range of optical phenomena and is taught to physics students in our colleges and universities as geometrical optics.

THE WAVE NATURE OF LIGHT

The idea that light rays emanate from luminous objects in straight lines in all directions was known to Leonardo from Alhazen’s treatise on optics before he tested it experimentally. Another idea that was popular in medieval optics, which he adopted from John Pecham (who, in turn, was influenced by Alhazen), was the concept of pyramids of light filling the air with images of solid objects:

The body of the air is full of infinite pyramids composed of radiating straight lines which emanate from the edges of the surfaces of the solid bodies placed in the air; and the further they are from their cause the more acute are the pyramids, and although their converging paths intersect and interweave, nevertheless they never blend but proliferate independently, infusing all the surrounding air.
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With this poetic description, Leonardo simply rephrased Alhazen’s original insight, but he added the significant observation that the pyramids of light “intersect and interweave” without interfering with each other. In a remarkable display of systemic thinking, Leonardo used this observation as a key argument to speculate about the wave nature of light. Here is how he proceeded.

First, he combines the fact that light is radiated equally in all directions, which he has tested repeatedly, with the image of visual pyramids. He draws a diagram that shows a spherical body radiating equal pyramids (represented by triangles) in different directions, and he notes in the accompanying text that their tips are enclosed by a circle: “The equidistant perimeter of converging rays of the pyramid will give to their objects angles of equal size.”
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In other words, if observers were placed at the tips of these pyramids around the circle, their visual angles would be the same (see Figure 8-6). In the same diagram, Leonardo extends one pyramid to show that the visual angle at its apex decreases as the pyramid becomes longer.

From this exercise, he concludes that light spreads in circles, and he immediately associates this circular pattern with the circular spread of ripples of water and the spread of sound in air: “Just as the stone thrown into the water becomes the center and cause of various circles, and the sound made in the air spreads out in circles, so every object placed within the luminous air diffuses itself in circles and fills the surroundings with an infinite number of images of itself.”
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Having linked the circular pattern of the spread of light to the similar spread of ripples in water, Leonardo then sets out to study the details of the phenomenon in a pond in order to learn something about the radiation of light. In doing so, he uses, at the very beginning of his scientific explorations, a technique that would become an integral part of the scientific method in subsequent centuries. Since he cannot actually see the circular (or, more correctly, spherical) propagation of light, he takes the similar pattern in water as a model, hoping that it will reveal to him something about the nature of light under close study. And he does indeed study it very closely.

In Manuscript A, the very same Notebook that contains his analysis of perspective and many of his optical diagrams, Leonardo records his detailed investigations of the circular spread of water waves:

If you throw two small stones at the same time onto a sheet of motionless water at some distance from one another, you will see that around those two percussions two separate sets of circles are caused, which will meet as they increase in size and then interpenetrate and intersect one another, while always maintaining as their centers the places struck by the stones.
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Figure 8-6: Visual pyramids radiated from a spherical body, Ms. Ashburnham II, folio 6v

Leonardo illustrates this phenomenon with a diagram (Fig. 8-7), and to understand its exact nature, he focuses on the precise movement of the water particles, making it easier for the eye to follow them by throwing small pieces of straw into the pond and watching their movements. Here is what he observes.

Although there seems to be some demonstration of movement, the water does not depart from its place, because the openings made by the stones are closed again immediately. And that motion, caused by the sudden opening and closing of the water, makes in it a certain shaking, which one could call a tremor rather than a movement.

And so that what I say may be more evident to you, pay attention to those blades of straw which, because of their lightness, float on the water and are not moved from their original position by the wave that rolls underneath them as the circles arrive.

Figure 8-7: Intersection of circular water waves, Ms. A, folio 61r

Throughout history, countless people have thrown pebbles into ponds and watched the circular ripples they caused, but very few would have been able to match the accuracy and fine details of Leonardo’s observations. He recognized the essence of wave motion—that the water particles do not move along with the wave but merely move up and down as the wave passes by.
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What is transported along the wave is the disturbance causing the wave phenomenon—the “tremor,” as Leonardo calls it—but not any material particles: “The water, though remaining in its position, can easily take this tremor from neighboring parts and pass it on to other adjacent parts, always diminishing its power until the end.” And this is the reason, he concludes correctly, why the circular waves intersect smoothly without disturbing each other:

Therefore, the disturbance of the water being a tremor rather than a movement, the circles cannot break one another as they meet, because, water being of the same quality in all its parts, it follows that these parts transmit the tremor from one to another without moving from their place.

This smooth intersection of water waves is the key property that suggests to Leonardo that light and sound, too, propagate in waves. He has noted that the pyramids of light “intersect and interweave” without interfering with each other,
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and he applies the same reasoning to sound: “Although the voices that penetrate the air spread in circular motion from their causes, nevertheless the circles moved from different origins meet without any impediment, penetrate and pass into one another, always keeping their causes at their centers, because in all cases of motion, there is great conformity between water and air.”
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In other words, just as the intersecting circular ripples in the pond retain their distinct identities, we can see the images of different objects, or hear the sounds of different voices, and still distinguish them clearly.

From these observations, Leonardo draws the momentous conclusion that both light and sound are waves. A few years later he extends his insight to elastic waves in the earth and concludes that wave motion, caused by initial vibrations (or “tremors”), is a universal form of propagation of physical effects. “The movement of earth against earth, crushing it,” he writes, “moves the affected parts only slightly. Water struck by water creates circles round the place where it is struck; the voice in the air goes further, [and the tremor] in fire further still.”
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The realization that wave motion is a universal phenomenon in all four elements—earth, water, air, and fire (or light)—was a revolutionary insight in Leonardo’s time. It took another two hundred years before the wave-nature of light was rediscovered by Christian Huygens; the wave-nature of sound was first clearly articulated by Marin Marsenne during the first half of the seventeenth century, and earthquakes were associated with elastic waves only in the eighteenth century.
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In spite of Leonardo’s impressive insights into the nature of wave motion and its widespread occurrence in nature, it would be an overstatement to say that he developed a wave theory of light similar to that presented by Huygens two hundred years later. To do so would have meant to understand the mathematical representation of a wave and relate its amplitude, frequency, and other characteristics to observed optical phenomena. These concepts were not used in science until the seventeenth century, when the mathematical theory of functions was developed.

Leonardo gave a correct description of transverse waves, in which the direction of energy transfer (the spreading of the circles) is at right angles to the direction of the vibration (the “tremor”), but he never considered longitudinal waves, in which the vibrations and energy transfer go in the same direction. In particular, he did not realize that sound waves are longitudinal. He appreciated that waves in different media (or “elements”) travel at different velocities, but believed erroneously that the wave velocity is proportional to the power of the percussion that sets it off.
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He marveled at the swift velocity of light: “Look at the light of the candle and consider its beauty,” he wrote. “Blink your eye and look at it again. What you see of it was not there before, and what was there before is not anymore.”
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But he also realized that, however fast light moves, its velocity is not infinite. He asserted that the speed of sound is greater than that of elastic waves in earth, and that light moves faster than sound, but that the mind moves even faster than light. “The mind jumps in an instant from the East to the West,” he noted, “and all the other immaterial things have velocities that are by a long way inferior.”
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