LIGHT

By: Ray Shelton

Introduction.
Our knowledge of the external world comes through the senses, primarily sight. The first science, Astronomy, relied on sight alone. The first astronomers could only use observation of the heavens, not experiment, to determine the motion of the heavenly bodies. It is natural to ask, "How do we see?" In answering this question, the subject of light arose. We can only see what is in the light; if an object is in darkness, the absence of light, it cannot be seen. What is the nature of light and how is it related to sight?

Ancient Theories of Light.
Little is known about what ancient civilizations thought about light. In the Hebrew Bible the subject of light comes up in the story of creation. In the first chapter of Genesis it says,

"And God said, 'Let there be light;' and there was light.
And God saw that the was good,
and God separated the light from the darkness.
God called the light Day, and the darkness he called Night.
And there was evening and there was morning, one day."
(Gen. 1:3-5)
In the Christian New Testament in the Gospel of John, it says about the eternal Word of God,
"All things were made through him,
and without him was not anything made that was made.
In him was life, and the life was the light of man.
The light shines in darkness,
and the darkness does not overcome it.
There was a man sent from God, whose name was John.
He came for testimony, to bear witness to the light,
that all men might believe. He was not that light,
but came to bear witness to the light.
The true light that enlightens ever man
was coming into the world." (John 1:3-9)
Later in that gospel, Jesus says, "I am the light of the world, he who follows me will not walk in darkness, but will have the light of life." (John 8:12) The Apostle John writes in his first epistle,
"God is light, and in him is not darkness at all.
If we say we have fellowship with him while we walk in darkness,
we lie and do not do the truth.
But if we walk in the light as he is the light,
we have fellowship with one another,
and the blood of Jesus his Son cleanses us from all sin."
(I John 1:5-7)
Obviously from these passages of Scripture, the concept of light plays an important part in Christian teaching. But nowhere in the Scriptures is the nature of physical light discussed. But the ancient Greek philosophers did discuss and argued about the nature of physical light. They were the first to raise the question about the nature of light, and to formulate and dispute among themselves the proposed answers. One of the earliest theory of light was the "tentacular" theory of light. This theory was developed in the following manner. We see with our eyes. How? Is seeing like touching? Does the eye reach out and get something from the thing seen? Or is it like hearing, where the sound comes to the ear and is heard? If so, what is this something? Because this "something" could not identified, the tentacular theory was the early favorite, according to which the eye puts forth invisible tentacles, and sees like a blind man "sees" with his fingers, or with a stick. Euclid, who lived in Alexandria about 300 B.C. and wrote the classic textbook on the logical structure of geometry, entitled Elements of Geometry, also wrote another book, Optics, from which the subject derives its name, proposed that the sense of sight is similar to the sense of touch. But instead of putting forth invisible tentacles, the eyes emit a stream of particles, rays of light; these rays go out and "apprehend" the thing seen. This emission concept is believed to have originated with the Pythagoreans. The problem with this concept, among others, was why did the object have to be illuminated by the sun or by a fire to be seen? Plato struggles to answer this problem in his Timaeus. But in spite of its difficulties this concept dominated the thinking about light until the Renaissance.

Although this was the dominate concept of light, there were other concepts. The atomists put forth a particle theory of light. They held that all objects emit a stream of tiny particles in all directions, some of which hit the eye. There were difficulties with this theory; it could not explain how the image and color of the object were carried from the object to the eye. But these difficulties were not the real reason that it was rejected by other philosophers, such as Aristotle. The theory was part of the atomistic philosophy, that all matter was made up of tiny, indivisible particles called atoms. Aristotle, in particular, rejected atomism, because it required empty space between the atoms for their movement, and, according to Aristotle, empty space is impossible; nature abhors a vacuum. Vacuum is nothing, non-being; therefore, cannot be or exist. And furthermore, what could the tiny light particles be made of? Surely not one of the four terrestrial elements, earth, water, air, or fire, since light comes to us from the celestial bodies, the sun, moon, and stars. Aristotle also rejected the tentacular theory, that the eye puts forth invisible tentacles and touches the object seen, something like a blind man "sees" by touching with his fingers or a stick. He also rejected the emission theory; he argued that if the eyes emits rays of light, how is it that when we open our eyes we see things immediately? If one replied that the rays travel very fast, at an infinite speed, Aristotle would reply that that is impossible, since nothing that we know travels at such speeds. Rejecting these solutions to the nature of light, Aristotle put forth his own solution; he proposed that light is, not something, but some kind of disturbance in the medium that pervades all space. He writes,

"To say, as the ancients did, that colors are emissions and that is how we see, is absurd. First of all, they should have proved that all our perceptions are due to the sense of touch... Once for all, it is preferable to accept that perception arises from a movement, produced by the body we perceive in the interposed medium, rather than to consider it to be due to a direct contact or to an emission."
Thus Aristotle stated in a primitive form the wave theory of light, the concept that light is a disturbance propagated in a medium.

The Properties of Light.
The ancient thinkers did get right some of simple properties of light, even though their explanation of these facts were often wrong. First of all, they observed that light travels in straight lines. This is an important fact, especially to those, who were trying to explain astronomical observations. The straight lines that rays of light follow were physical examples of the straight lines of geometry. Euclid laid out the geometrical properties of light. That light travels in a straight line can be seen from the shadow that a stick throws on the ground. Why does light travel in a straight line? Aristotle tries to answer this question by his concept of natural place. Everything moves naturally to its own place depending what element it contains or predominates in it. A rock contain the element earth, so when it is dropped, it falls downward toward the earth, its natural place. So light travels in a straight line because it is trying get its natural place as quick as possible, which is the center of the universe.

Now the ancient thinkers observed other properties of light. When light interacts with matter, it no longer travels in a straight line only. This can be seen in two different light phenomena: reflection and refraction. Reflection is the bouncing of light off a smoothed, polished surface, like a mirror or the surface of calm water. The ray of light is bent at the point where it strikes the mirror surface, so that to the eye an object seen in the mirror is not where it appears to be. The quantitative of law of reflection was first formulated by Euclid. The angle of incidence is exactly equal to the angle of reflection. That is, the angle between the incoming light ray and the surface is precisely the same angle between the reflected ray and the surface. This simple, precise rule allowed Euclid to explain how mirrors form images.

The Greek thinkers also observed that light bent, or refracted, when the light rays passed from one transparent medium into another. For example, when a light ray passes through an air-water surface as when a looking at straight-edged object sticking out of a glass of water; it looks bent although it is not really bent. Another interesting example is that of a swimmer under water. The position of the sun observed under water is not the same as observed above the water. This is because the sun's rays are bent or refracted as they pass through the surface of the water. Is there a simple law for the angle of refraction as there was for the angle of reflection? Yes, there is a law but it is not as simple as the law of reflection. Consider a light ray falling on the surface; it is not bent but continues straight down. Now if the light strikes the surface at an angle, it is bent so the ray in the water make a smaller angle with the perpendicular to the surface than the angle of the ray makes to the perpendicular in the air. The angle that a ray of light makes in the air with an imaginary line perpendicular to the surface is called the "angle of incidence." In the water the angle to the perpendicular is called the "angle of refraction." Now the angle of refraction in the water is always smaller that the angle of incidence. This terminology applies only when the light is passing from the air and entering the water. But the light ray follows same path when passing from the water into the air.

Is there a quantitative law relating these angles? When a light ray strikes the surface of water at a certain angle of incidence, it is always bent at a particular angle of refraction. As the angle of incidence is increased, so does the angle of refraction increase, but the angle of refraction remains smaller than the angle of incidence. Up to 40 degrees, a reasonably good rule is that the angle of refraction is three-fourth the angle of incidence for water. For example, for water, if the angle of incidence is 20 degrees, the angle of refraction is 15 degrees. Many thought that this was the law, but careful measurements showed that it was not, and that it was a poor rule for large angles of incidence. The astronomer and geographer, Claudius Ptolemy, in the 2nd century A.D., described a careful experiment for measuring the angles of incidence and refraction, and wrote down a table of values. His numbers for the angles of refraction are accurate to within half a degree up to 70 degrees of incidence, above which they become very inaccurate. Ptolemy made such careful and accurate measurements that his star charts and maps of the world were used for centuries. And so were his optical tables for refraction.

Alhazen.
After the fall of Rome in 410 A.D., Greek science was lost to the West. But in the great Islamic centers of learning stretching from India through the Middle East and North Africa to Spain Greek science flourished. The Arabs made many advances in mathematics; "algebra" is from the Arabic and our decimal number system comes from them. But in physics and cosmology they were content to expand on Aristotle and Ptolemy. One of the important Arabic scholars was Abu Ali Mohammed Ibn Al Hasan Ibn Al Haytham (965-1039). He lived in the new capital of Cairo, not far from Ptolemy's Alexandria. Some of his works were translated into Latin in the twelfth century, being ascribed to "Alhazen," as he was known. He influenced later Europeans, by refuting the concept of light being emitted from the eye and established the view that light is external and objective, emitted by the object and perceived by the eye.

Alhazen began as an astronomer, and at one time he tried to make a mechanical model for the Ptolemy's view of the heavens, with mechanical linkages for the epicycles. But he ran into difficulties, and began to wonder if perhaps the heavens were not as they appeared, and that we are fooled by the way light propagates. Alhazen main experimental tool was a pinhole camera, or camera obscura (Latin for "dark room"). The camera was, not a small box, but a dark chamber with a hole in one wall, and a screen opposite the hole. The camera was used by the astronomers to study the sun, especially the eclipses of the sun, the sun being too bright to look at directly. But the image of the sun was up side down and inverted. Since light rays travel in straight line, a ray from the top of the object crosses a ray from the bottom of the object at the little hole, and arrives at the screen as the bottom of the image. In fact, all the rays that reach the screen cross at the little hole. Alhazen took this as proof that the eye has nothing to do with light, and that Euclid's emission theory was wrong. If the light from a bright object fell on the hole, an image of it appeared on the screen, upside down and inverted. Even more convincing was that the camera would show an inverted image of an object that was not a source of light, like from the sun or a candle; it could form an image of a brightly lit landscape as the surface of the moon. Clearly the formation of these inverted images was independent of the light source. Thus Alhazen restricted the study of optics to the propagation of the light. The study of the mechanism of vision was the province of physiology or psychology, not physics. Thus, he separated the problems of vision from the problems of the propagation of light. He established the objective nature of light apart from the subjective apprehension of it.

Kepler.
Johann Kepler (1571-1630), like Ptolemy and Alhazen, was led to the study of optics out of a concern for accuracy of astronomical observations. He asked, "To what extent is one deceived in measurements of heavenly bodies by the properties of light itself?" Kepler became first concerned with this problem by the attempts of the Danish astronomer, Tycho Brahe (1571-1630), to measure the variation in the moon's distance from the earth by measuring the apparent change of moon's diameter. The measurement is difficult because the change of diameter of moon is so small, only a few minutes of arc, close to the limit of Tycho's precision. In order to improve the accuracy of his measurement, Tycho tried Alhazen's method. During the partial eclipse of the sun, he observed in a camera obscura the dark side of moon. By moving the screen far from the hole, the image of the partial eclipse of sun could be made very large, and the apparent diameter of the moon could be measured quite accurately. But Kepler was troubled with these measurements, because they did not fit in with other measurements of the moon's orbit. Thus he began to examine the functioning of the camera obscura. Tycho thought the image on the screen was an accurate picture of the eclipse of the sun. Kepler pointed out that it was not, because the hole was not a point but had a certain size. The dark image of moon on the image of the sun on the screen, which Tycho took to represent accurately the moon, was smaller than the bright image of the moon, when observed apart from the eclipse. Thus during the eclipse the moon appeared smaller and, hence, was assumed to be farther away than it was really was. Kepler showed by careful tracing of the light rays that he could correct for the size of the hole and find accurately the apparent diameter of the moon. With the corrected diameter of the moon, the distance to the moon agreed with his astronomical calculations of where is should be.

Kepler next examined the optics of the human eye. The traditional view was that the light rays stimulated the surface of eye, probably the pupil of the eye. But human anatomy had made progress in the seventeenth century, especially through the anatomical observations of the artists such as Leonardo da Vinci, Michelagelo, Raphael, and others. Kepler knew that the eye was a small chamber and the pupil is a transparent opening. At the back of eye is the retina, and in the space between is filled with a transparent fluid. And nerves connect the eye to the brain. His conclusion was that the eye is a camera obscura, forming an image on the sensitive retina, just like the image was formed on the screen in Alhazen's camera; the nerves in the retina sensitive to intensity and color reports this information to the brain.

But this view of the eye as a camera obscura had one difficulty. If the eye was a camera obscura, and the camera distorts the size of objects seen, as Kepler had shown, then does not our eye give us a distorted view of reality? Kepler does not address this difficulty. But he did investigate a related problem: how do lens function? Over three-hundred years before, in the later thirteenth century, someone, somewhere, probably in Italy, made the an important discovery. When an old person, whose eyesight had deteriorated, would look through a piece of glass in the shape like a lentil bean, he can see as clearly as in their youth. This lentil shaped piece of glass, which was called in English "lens", from the word "lentil," was soon put in a frame and hung on the nose in front of the eyes. These spectacles were gradually improved on a trial and error basis. There is no discussion of eyeglasses in any scholastic texts of the time. As long as it was believed that vision was due to direct contact with the eye by the object, it was also believed that eyeglasses distort and interfere with our direct perception of reality. The Aristotelian empiricism, that stated that our knowledge of reality is based on direct perceptions of our senses, opposed the use of optical instruments. It was believed that the instruments distorted reality and could not be trusted to give reliable evidence. Galileo ran into this opposition when he tried to demonstrate his telescope; the Thomist-Aristotelian philosophers and theologians refused to look into it for this reason.

Galileo.
Galileo Galilei (1564-1642) published his astronomical observations in 1609 in his booklet entitled the Starry Messenger or the Messenger from the Stars. When Kepler received a copy of it, he read with astonishment about Galileo's construction of telescope with two lens that magnified and brightened the heavenly bodies and allowed him, Galileo, to make observations which Galileo claimed to confirm the Copernican view. Kepler, using a borrowed telescope, was able to confirm Galileo's observations. But Galileo's critics claimed that observations through the telescope, not being direct sense perceptions, were not valid sources of knowledge about the heavens. Up to this time no one, not even Galileo, was able to explain how the telescope worked. Kepler decided to investigate the functioning of lenses. He wrote a theoretical treatise, entitled Dioptrice, in which he founded a new science and coined a name for it, dioptrics, the science of refraction of light by lenses. In this work Kepler studied the law of refraction. From careful experiments, he concluded that Ptolemy's tables with definitely wrong, and that, the angle of refraction for the same angle of incidence was not the same for water and glass. Kepler could find no general law to give the correct angles, but he made a table of his own, correct up to the accuracy that he could make. Kepler then investigated lens. His explanation is still the accepted one. A typical lens is formed by two surfaces of a sphere. Let S be the point source of light, emitting rays in all directions. A ray striking the lens perpendicularly at the center will go straight through and do not bend. A ray striking the lens off center, will be bent as passes into the glass, and then be bent again as it passes again in the air. The light ray entering the glass will be bent back toward the center line so that it is parallel with the ray passing straight through the lens at the center. And as the light ray leaves the glass and enters the air again it is bent again toward the center line so that it intersects the center line of lens at some point I, a distance beyond the lens. All rays of light entering the lens will bent back toward the center line and will converge at the same point I on the center line some distance beyond the lens. On can find the exact location of this point I by carefully tracing the rays, using the table of angles of refraction. Now all rays originating from a point source off the central axis of lens will converge at a point beyond the lens, but not at point I. If source point is above the central axis of the lens, the image will be below the central axis. In this way the image of the object at the source will be formed beyond the lens. From all this, Kepler reached an important conclusion. The camera obscura with a lens in the opening, not a simple open hole, as in Alhazen or Tycho's camera, is the correct model for the eye. Inside the pupil is a lens, which in a person of good eyesight focuses the light sharply on the retina, where it is sensed by the ends of the optic nerve. Thus Kepler was able to explain the operation of the eye, and, using the law of refraction, he was able to develop a system of geometrical and instrumental optics, and to deduce from it the principles of the so-called Astronomical or Keplerian Telescope. Kepler also discovered the law of light intensity; that is, the intensity of light in inversely proportional to the distance from the eye; in other words, the apparent brightness of an object diminishes with the square of the distance from the eye. For example, a candle 10 feet away will appear to be four times as bright as the same candle 20 feet away. Or, four candles 20 feet away will appear as bright as one candle 10 feet away. This law is important in estimating the real brightness of distant stars.

Snell's Law.
In 1631, a general form of the law of refraction was discovered by a Dutchman, Willebord Snell (1591-1626). Snell's Law, as it is known, may be stated as follows:
Let a horizontal line represent the surface or boundary between the two media, air-water or air-glass, and let another line be perpendicular or normal to the surface line at point S. Now choose points A and B on the ray, so that A is on air side of the surface and B is on the water/glass side of surface, and the length of AS is equal to the length of BS, S being the point where the light ray crosses the surface or boundary between the two media. Now from the points A and B draw lines perpendicular to the normal line at M and N, respectively, forming two right triangles, AMS and BNS. The acute angle ASM is the angle of incidence and the acute angle BSN is the angle of refraction. Snell's Law says that the ratio of AM to BN is the same for all angles of incidence between the same two media. Snell's Law may be stated another way. Noting that the ratio of the sides AM to AS in the right triangle AMS is the sine of the angle of incidence, ASM; and the ratio of the sides BN to BS in the right triangle BNS is the sine of the angle of refraction, BSN. Snell's Law may also be stated as follows: the ratio of the sine of angle of incidence to the sine of the angle of refraction is constant for the same two media, the angles being on opposite sides of the normal and the refracted ray is in the same plane as the incident ray and the normal. This ratio is a property of any substance, and is called the index of refraction of that substance. For water the index of refraction of water is almost exactly 4/3.

Diffraction.
In 1665 a Jesuit professor of mathematics at Bologna, Italy, Francisco Grimaldi, published a challenge to an ancient assumption that light travels in straight line, except when it is reflected or refracted. Grimaldi wanted to add another exception: light travels in straight line, except for reflection, refraction, and diffraction. In his book Grimaldi presented his study of diffraction, the name he gave to the bending of light rays around sharp obstacles. In one experiment Grimaldi let sunlight pass through a small hole into a darkened room, where he placed a solid object in its path. The shadow on the wall was wider than it should have been, based on rectilinear propagation. Also peculiar dark and light lines appeared at the shadow boundary, and the edges were colored. In another experiment light is beamed perpendicular to a circular opening, with the diameter GH. The diameter JK of the disk light seen on a distance screen was larger than the diameter NO of the projected circular opening on the screen. According geometric optics the diameter JK of the disk of light on the screen should be the same as the diameter GH of the circular opening. Obviously the light bent as it passed through the circular opening. In Grimaldi's words, "Light propagated not only in straight line, reflected or refracted, but also in a certain other direction, diffracted." Why this was so, he could not explain.

Color.
Kepler and most of his predecessors thought that white sunlight was pure light, and that color was added to white light to make it colored. But in the 1660's and 1670's Isaac Newton (1642-1727) performed a series of experiments that change this concept of color, which he published in his Opticks in 1704. Newton became interested in color theory while he was an undergraduate at Cambridge, when he set out to construct an astronomical telescope. One of the disturbing problems in constructing such an instrument, which was called "chromatic aberration," was that the images of stars appeared blurred, with colored fringes. It was probably to understand this defect that Newton began his investigation of color. When he was at home at his mother's farm in the plague year of 1666, Newton purchased a set of glass prisms "to investigate the celebrated Phaenomenon of colours." A prism is a length of glass that have a triangular shaped cross section. It was long known that sunlight shown on a prism produced the colors of the rainbow, blue at one edge and red on the other. For a long time it had been believed that the prism added the colors to the light as it passed through it. Newton performed this well known experiment with the prism, but he noted that the colors arrived at different places on the screen. The cylindrical beam of light from the circular opening in window shade after passing through the prism appeared on the opposite wall as elongated, rather than circular, patch of colors, which was violet at one end and red at the other, with a continuous graduation of colors in between. For such a pattern Newton invented the name "spectrum." Why was the spectrum elongated and not circular? Seeking an explanation, Newton passed the light through different thicknesses of glass, changed the size of hole in the window shade, and even placed the prism outside the window. But he found that none of things made a difference. The prism did not seem to add the color. He performed an experiment to test this. He placed a screen between the prism and the wall and made a small hole in it at the point where the green color of the spectrum was and let it pass through the screen. Next he put the second prism in the green beam of light and the green beam was refracted at the correct angle for the green color. But it did not add any colors to the green beam of light. He tested the other colors of the spectrum by rotating the first prism. Newton showed that the same was true for the other colors. It occurred to Newton that light must be made up of a mixture of colors, which the prism separated into a band of colors, into its spectrum. This phenomena of light has come to be called the dispersion of light. Then Newton performed his crucial experiment to test this hypothesis. Newton arranged the two prisms so that first separated the white light into its color. The second prism was place so that that spectrum would be recombined into the white light. This proved that separate colors was not produced by first prism. His first prism just bent the rays of the different color light at their characteristic angle, but did not add anything to the white light. When the second prism bent them all back into the same direction, the white light appears.

Newton was able to explain why things appear to have different colors. White objects reflect all the light they receive. Under red light, they appear red, and under blue light they appear blue. Colored things, on the other hand, far from adding anything to the white light, as generally thought, absorbs all colors except the one that it reflects as its color. A red object, for example, absorbs the all colors except the red, which is reflected as its color. When red light is shined on blue object, the red light is absorbed and since there are no other colors, nothing is reflected and the object appears black.

Finally, Newton returns to the problem that started his investigation of color, the chromatic aberration of telescope lens. In a refracting telescope the different colors refracted by the lens by different amounts and are, therefore, focused at different places, causing the chromatic aberration. Since this an inherent characteristic of refracting lens, Newton despaired of ever improving refracting telescopes. So he constructed the first reflecting telescope, using in place of a large lens, a mirror, for which no chromatic aberration occurs, because it reflects all colors at the same angle; the law of reflection is the same for all colors. Nearly all the largest telescopes in use today are of this kind, called the reflecting or Newtonian telescope.

The Speed of Light.
The idea of that light has a speed, that one does not see things when they happen, was as controversial as it is ancient. Most ancients believed that light had an infinite velocity and that one sees things instantaneously as they happen. But Aristotle argued that light must travel at some finite speed, since an infinite speed is impossible. Kepler apparently assumed the speed of light is infinite. This is because, he argued, light is immaterial, offering no resistance to the force necessary to move it. In this way, reasoning like an Aristotelian, Kepler reached a conclusion that Aristotle would have considered impossible. Descartes argued that light was a kind of pressure instantaneously transmitted through the "aether" of space from the sun and fixed stars. He compared vision to the sense of pressure transmitted to one like a blind man using a cane to find the position of things. Descartes did not hold that the speed of light was infinite; he believed that the speed of light was independent of time, therefore, instantaneous, that is, requires no time to propagate. Galileo, in his Dialogue on the Two New Sciences, published in 1638, discusses the problem of the speed of light in a conversation between three fictitious persons named Salviati, Simplicio (the spokesman for the Aristotelians), and Sagredo (spokesman for Galileo). Here is part of the conversation.

Simplicio: "Everyday experience shows that the propagation of light is instantaneous; for when we see a piece of artillery fired, at a great distance, the flash reaches our eyes without lapse of time; but the sound reaches the ear only after a noticeable interval."

Sagredo: "Well, Simplicio, the only thing I am able to infer from this familiar experience is that sound in reaching our ear, travels more slowly than light; it does not inform me whether the coming of the light is instantaneous or whether, although extremely rapid, it still occupies time."

Galileo, instead of trying to determine the speed of light by philosophical reasoning, decided to try to determine it by experiment. Galileo, through his spokesman in the dialogue, describes a method to measure the speed of light. He and assistant stand facing each other some distant apart upon mountain tops at night. Each has a lantern with a shutter to turn the light off and on. Galileo starts the experiment by opening this shutter. When the assistant sees Galileo's light he opens his shutter. When Galileo see his assistance's light, he can measure how long it took for the light to travel from his lantern to his assistance and back. The method failed because of the human reaction time were too slow. He proposed a modification of the experiment. He proposed using a single lamp, shutter, and mirror to determine the speed of light. The mirror was positioned on a hill some considerable distance away from the lamp and shutter. By measuring the time interval between removal of the shutter from the lantern and the perception of the light reflected from the mirror to the eye of the observer, the speed of light could be determined. The experiment again failed to give the speed of light. Galileo concluded that the speed of light "if not instantaneous, it is extremely rapid." When the Italian scientists of one of the oldest scientific societies, founded during the time of the Medicis, performed Galileo's suggested experiment with as much care and precision as they could, they concluded that there was no reason to believe that light was not instantaneous.

In 1675 the Danish astronomer, Olaus Roemer (1644-1710), a contemporary of Isaac Newton's, published the results of his very careful measurements of the period of one of the moons of Jupiter, which was discovered about 50 years earlier by Galileo. Roemer had started out to verify Kepler's three Laws of Planetary motion by timing the orbits of the four moons of Jupiter, discovered by Galileo. Roemer found a roughly annual variation in the periods of the satellites. Io, the innermost moon of Jupiter, had a average period of about 42.5 hours.

He measured Io's period by observing the eclipse of Io as it passed behind the planet. (Note that the period of Jupiter is about 12 earth years, so that as the earth revolves half way around the sun, the planet Jupiter moves only through 15 degrees.) Observing the orbital motion of Io, one should expect that its period should be constant, over long periods of time. However, Roemer observed a systematic variation in Io's period during a year's time. He found that Io's periods were longer than the average when the earth receded from Jupiter and shorter than average when the approached the planet. This variation of period was contrary to Kepler's Laws which required that each period be identical. Roemer hardly considered the possibility that the Laws of Kepler were not correct, so he sought another explanation. He hit upon an explanation which is still accepted today. In a paper he read before the Paris Academy in 1675, he declared that the observed variation in the periods was caused by

  1. the motion of the earth at different times of the year either toward or away from the Jupiter and
  2. the finite velocity of light.
Roemer proposal was a bold hypothesis. Kepler's Laws were indeed correct for the moons of Jupiter and the delay was due to the finite speed of light. If one observes two successive eclipses of the moon Io and measures the exact time between them, then a third eclipse could be predicted. As time went on, Roemer found discrepancies in the predictions of the eclipses and that they depended in a regular way on the relative position of the earth, Jupiter and the sun. Precisely, if the original prediction were made by observing eclipses when Jupiter was in opposition (i.e., when the earth is nearest to Jupiter), then one-half year later, when the earth is on the opposite of its orbit and farthest from Jupiter, the eclipses were 16.5 minutes late. And six months later, when Jupiter was in opposition again, the eclipses were on time. This 16.5 minutes delay represents the extra time it took light from Jupiter's moon to get across the earth's orbit to the earth when it was farthest from Jupiter. The speed of light could immediately be computed.

Using his data, Roemer calculated the speed of light to be 200,000 kilometers per second. Using Roemer's data Huygens estimated that the lower limit of the speed of light to be 230,000 kilometers per second. This low figure is due to the low figure for the diameter of the earth's orbit. Today we know the radius of the earth's orbit to be about 93,000,000 miles, so its diameter is 2 × 93,000,000 miles or 186,000,000 miles. Sixteen and one half minutes is about 1000 seconds (16.5 minutes × 60 seconds per minute = 990 seconds). Thus the speed of light is 186,000,000 miles divided by 1000 seconds, which 186,000 miles per second. This is a constant and is designated traditionally in science by the little letter c (from the Latin, celeritas, speed). The speed of light ranks with the Newton's universal gravitation constant as two of the fundamental constants of nature; much effort has been spent on measuring it accurately.

The first measurement by Roemer's was not very accurate, because the dimensions of the solar system was not accurately known. In Roemer's day the diameter of the earth's orbit was thought to be 172,000,000 miles and Roemer's first measurement of delay for the light to travel across the diameter of the earth's orbit was 22 minutes, hence the speed of light was calculated to be 130,000 miles per second or 210,000 km/sec. Many of Roemer's contemporaries refused to believe that the speed of light could be so large. But other astronomical methods confirmed Roemer's hypothesis that the speed of light in space was finite. The English third Astronomer Royal, James Bradley (1692-1762), using a different astronomical method, in 1728, two years before Newton revised and published his final edition of Opticks, calculated it to be 304,000 km/sec or 189,000 mi/sec. Since that time, terrestrial methods have been devised that give very accurate measurement of the speed of light. The present (1976) accepted measurement by laser interferometry is (299,792.458) km/sec or 186,282.339 mi/sec. The importance of Roemer's work was not his value of the speed of light but that he showed that light had a finite speed, although very large. He ended centuries of philosophical speculation with this discovery.

The Nature of Light.
Isaac Newton apparently developed his theory of the nature of light very early. During the two years (1665-1666) of the Great Plague, when he was at home at his mother's farm and made so many of his discoveries, he developed a particle theory of the nature of light. After returning to Cambridge in 1667 and finishing his graduate work, he was appointed Lucasian Professor of Mathematics at the age of 26. Continuing his study of optics, he sent a telescope to the Royal Society, which he had designed and constructed. At their request he published in 1672 in the Transactions of the Royal Society a description and explanation of the telescope entitled "Theory about Light and Colors." The paper evoked a controversy about the nature of light, especially with Robert Hooke. This controversy was very distasteful to Newton and he decided not to publish again. Only reluctantly, upon the persuasion of his friend Edmund Halley, did he publish his Principa and, after the death of Robert Hooke in 1703, did Newton publish in 1704 his views on light in his Opticks.

Newton had considered the wave theory of light and finally rejected it. He says in his Opticks concerning waves motion:

"The Waves, Pulses or Vibrations of the Air, wherein Sounds consist, bend manifestly, though not as much as the Waves of Water. For a Bell or a Cannon may be heard beyond a Hill which intercepts the sight of the sounding Body, and Sounds are propagated as readily through crooked Pipes as through straight ones. But light is never known to follow crooked Passages nor to be bend into the Shadow."
In addition, since wave motion required a medium for the propagation of the disturbances of the wave, and the space between the sun, moon, planets and stars was empty space, there was no medium for the propagation of the wave disturbances. Nevertheless, the light comes to us from them through great distances of this emptiness. Therefore, light must not be wave motion. Material particles, on the other hand, do not require a medium for them to travel through. Indeed, Newton had developed his mechanics to describe the motion of these particles through a vacuum. When his theory of gravitation was developed and applied to the motion of the planets, no resisting medium was necessary to account for their motion. In fact, such a resisting medium would have slowed the planets down and they would spiral into the sun; since they did not or had not done this, there was no medium to resist their motion. Thus a particle theory of light was consistent with Newtonian mechanics. The particles of light are so small and travel at such a fantastic speed that gravity has little effect on their straight line motion and that their deflection from their straight line paths by gravity is too small to be observed. It was this straight line motion of light that was crucial in his acceptance of the particle theory. Light travels in straight lines and particle like all bodies also travel in straight lines.

But the law of reflection of light was even a stronger argument for the particle theory. Alhazen had already centuries ago noticed this similarity between the reflection of light and the way balls bounce off a hard surface. Newton applied his mechanics, particularly the third law of motion, to the collision of a perfectly elastic ball off a hard surface. When a light particle or a perfectly elastic ball strikes a smooth surface it exerts a force on the surface. According to Newton's third law of motion, the surface exerts back an equal force on the particle of light or ball, but in the opposite direction. So the particle or ball bounces off the surface. If the particle of light or ball strikes the surface perpendicular to the surface, it bounces back perpendicular to the surface. Thus no force is exerted on the rebounding particle parallel with the surface. If the ball or particle strikes the surface at an angle, there is still no force exerted on the rebounding particle parallel with the surface; the only force exerted back on the ball or particle is perpendicular to the surface. This means that of the horizontal and vertical components of the velocity only the vertical component has changed, and that only in direction, not speed. Since there is only change in the vertical component of its velocity in direction, the velocity of the ball or particle after the collision will make the same angle with the surface as the velocity before the collision made with the surface. Thus the angle incidence is equal to the angle of reflection; that is, since tangent of angle of incidence equals the tangent of reflection, then angle of incidence equals the angle of reflection.

Newton also showed that the particle theory explained the law of refraction (Snell's Law). He assumed that in a dense medium (water or glass) the speed of light was faster than in vacuum or air. He thought that maybe forces similar to gravity exerted by the atoms of the medium on the light particles, accelerating the light particles to higher speed. Newton again argued that the surface would exert no force on the light particles parallel to the surface. So the component of the velocity parallel to the surface inside and outside would be the same. Since the velocity is greater inside the surface, the vertical component of that velocity must increase, thus the ray of light is refracted toward the perpendicular. Quantitatively, it can be shown that the ratio of sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of speed of light inside the medium to the speed of light in air, and this is the index of refraction of the medium. Newton also performed many experiments on diffraction, but he was unable to provide a quantitative explanation of it. However, the phenomenon did not seem to contradict the particle theory of light. Newton thought that when the light particles passed very close to matter, they are apparently deflected from their straight line path by some force, perhaps the same one that change the speed of light in glass or water.

To explain color, Newton suggested that light of different color consisted of particles of slightly different masses. Different mass particles would accelerate differently on entering the medium and would, therefore, be refracted differently. Thus he was able to explain to his satisfaction the dispersion of white light into its spectrum.

Even though the particle theory of light was not able to provide a quantitative explanation of some properties of light, such as diffraction, Newton was able to provide mechanistic explanations of the nature of light and a quantitative explanation of the laws of refection and refraction. Newton did not completely exclude the wave theory. He found it necessary to conceive of a periodicity in his "Fits of Easy Reflection and Transmissions" which he introduced in Book II of his Opticks in order to deal with phenomena now ascribed to optical interference. Newton's corpuscular theory, therefore, did not render an aether unnecessary, nor did it dispense entirely with the concept aether vibrations. Obviously Newton was not satisfied with the completeness of his particle theory. Newton wrote in his Opticks, "Since I have not finish'd this part of my design, I shall conclude with proposing only some Queries, in order to farther search to be made by others." In those Queries he suggests that wave motion might be necessary to explain some optical phenomena, like what we now call interference. Even though Newton was careful to distinguish between his speculations and hypotheses, on the one hand, and what he clearly knew from experimentation and mathematical deduction, on the other hand, the eighteenth century attributed to Newton an authority that was comparable to Aristotle's authority in the Middle Ages. His speculations, like Aristotle's, became unquestioned dogma, especially in eighteenth century England.

The Wave Theory of Light.
This explanation of nature of light was worked out in detail by the Dutch astronomer and mathematician, Christian Huygens (1629-1695). Huygen was the only contemporary of whom Newton always mentioned with great respect. Newton referred to him as one of three "greatest geometers of our time." Huygens was born into a famous Dutch family on April 14, 1629 at The Hague. His father, Constantin Huygens, who was a distinguished Latinist, a musician, and mathematician, as well as a diplomat, educated his sons. Christian, who was his second son, was instructed in language, music, and drawing. At the age of thirteen he began the study of mathematics and mechanics, which became his chief interest. Christian studied law at Leyden and later in 1646 he transferred to Breds, where his father directed the new university, and two years later took a degree in law. All this time he continued his interest in mathematics, of which he published distinguished papers. He discovered and was the first to publish the law of centripetal acceleration. He also discovered the law of the pendulum and invented the pendulum clock. He built the most powerful telescope of his time, discovering one of the moons of Saturn and he was the first to see the rings of Saturn clearly. His reputation would have been greater if he had not lived at the same time and had not been overshadowed by Newton.

By the seventeenth century, it was accepted that sound is wave disturbances that travels at a finite and measurable speed. It was inevitable that light would be considered to be wave motion. Robert Hooke held to a wave theory of light, and his disagreement with Newton about the nature of light was the initial reason for the life-long controversy between Hooke and Newton. In 1678 Huygens presented before the Paris Academic his Treatise on Light, which he later published in 1690, and in which he presented his wave theory of light, showing with a brilliant mathematical analysis how reflection and refraction can be explained by the theory of light that light is composed of longitudinal vibrations similar to sound waves. The principal reason Huygens believed that light was wave motion was the fact that beams of light cross each other without any apparent interaction. If light were composed of a stream of particles traveling through space, then surely some of these particles would collide with one another and be deflected from their paths. (Newton did not answer this objection directly. Apparently he considered light particles to be so small that there was little chance of them colliding when a beams of them cross.) Huygens believed that the wave theory better explained this phenomena. Huygens cited Roemer's demonstration of the finite but extremely high speed of light as an argument against the hypothesis that light is composed of particles. The wave theory better accounts for the high speed of light, because it is the disturbance, a wave, of particles that travels, and not the particles themselves that move at that speed. Huygens had performed experiments and found that sound traveled at a speed in air of about 1000 feet per second or about 600 miles per hour. Clearly no air particles were traveling at that speed, only the disturbance. If the particles traveled at that speed, a strong wind would be experienced. Similarly, as light travels, no particles of light (or the aether) do travel at the speed of light, but only the disturbance of the aether particles.

In his treatise Huygens analyzes the geometry of wave propagation. We know, for example, that when a stone is dropped in a still pool of water, a circular wave crest spreads outward from the center. (In three dimensions, like sound, a disturbance creates a spherical wave crest.) The wave crest moves outward at some speed characteristic of the medium, here in our example, the water. The surface of the water simply rises and falls as the crest travels pass. Just as the stone starts the rise and fall of the water surface, each point on the wave crest can be considered a creating the next rise and fall of the surface. Each point on the wave crest creates a little secondary wavelet propagating outward from its center. Huygen showed mathematically that adding up all these secondary wavelets recreates the original primary wave. From this he showed that waves travel in straight lines, not necessarily parallel with each other, but radially outwardly from the original center. Huygen constructed a geometrical rule for finding the next wave crest or wavefront, known as Huygens' principle, which may be stated as follows: every point on a wavefront can be considered as a point source of secondary wavelets which spread out in all directions with the wave speed of its medium. The wavefront at any time is the envelope of these wavelets, that is, all the wavelets add up into another wavefront. A wavefront is an imaginary surface that join points where all of the waves are in the same phase of vibration or oscillation. Light from a point source spread outward in a succession of spherical wavefronts, and at large distance from the point the source the wave fronts in a specific direction can be considered as a succession of planes. Huygens' principle applies to the propagation of plane and spherical wavefronts in an uniform medium (all wavefronts travel at same speed). Despite the name Huygens' principle is not in the same category as the laws of conservation of momentum, mass-energy, and electric charge, but is rather a convenient rule for studying wave motion in a geometrical manner. The concept of a wavefront is an important idea in the analysis of wave propagation and is related to the concept of a ray. A light ray is an imaginary line in the direction in which the wavefront is moving, and as so, is perpendicular to the wavefronts. In many minds the concept of a light ray is a narrow pencil of light, which is perfectly legitimate. However, an approach based exclusively on rays thus conceived do not reveal the characteristics of wave motion such as diffraction (the bending of waves around an obstacle into the "shadow" regions). The concept of wavefronts allow us to conceive of light as spread out over a plane moving in space.

In the eighteenth century the mechanics introduced by Newton flourished and reached its culmination in the works of Pierre Simon de Laplace (1749-1827) (Celestial Mechanics, 1799-1825) and Joseph Louis Lagrange (1736-1813) (Analytical Mechanics, 1788), whose analysis of celestial and terrestrial motion of bodies formed what appeared to be a complete system. The influence of Newton was so great that his particle theory of light was widely accepted and the wave theory developed by Huygens was ignored in the understanding of light and optical phenomena. Any explanation that did not fit into Newtonian system of mechanics was rejected. This was so through most of eighteenth century. When Thomas Young (1773-1829), an English doctor, in 1802 published the results of his experiments on the interference of light, it aroused so much opposition and disbelief among the followers of Newton that he gave up temporarily the subject. Some brilliant French scientists, who pursued the subject, were able to revive his interest, but only with difficulty. Young was born in Somerset, England, into a Quaker banking family. He practiced medicine for a while but gave it up, finding he was more interested in linguistics and scientific problems. He was one of the most versatile scholars ever to turn his mind to science. He master seven languages by the age of fourteen; he had read the Bible twice by the age of four. He deciphered the Rossetta stone that opened the understanding of the Egyptian hieroglyphic language. This accomplishment alone would have guaranteed his fame, if he had done nothing in science. In 1801 he became a professor at the Royal Institution in London, where Faraday later carried out his life work. There, among other studies, he turned his attention to optics and the wave theory of light. It was his interest as a doctor in the physiological problems of sight and hearing that lead him to investigating light, optics and sound. The wave theory provided a satisfactory explanation of both sound and light. He was able to explain satisfactorily why light as wave motion appeared to move in straight lines. Because the wave length of light is so extremely short, light appears to travel in straight lines, not to bend around objects. Light does bend around objects, but it is difficult to observe because of the extremely short wave length of light the bending is so small. Young added this concept of wavelength to Huygen's original wave theory. Huygens's description of light as wave motion saw light as the motion of a single crest. Young saw light as a series of crests and troughs, regularly spaced, moving in the same direction with the same speed. The distance between two adjacent crests or troughs is called the wavelength of the wave, λ. The interval time between the passage of two successive crests or troughs by a particular point is called the period of the wave, T. That is, a particular crest travels the distance of one wavelength during one period of time. Hence, the speed of the wave traveling passed a point is equal to the wavelength divided by the period:
v = λ/T.
Now the frequency. f, of the wave motion is the number of waves crests or troughs pass a point per unit of time. And since the period of a wave is the time interval that it takes one wave from one crest to the next to pass a point, then the frequency of the wave is one wave divided by its period:
f = 1/T. (1)
Hence, the speed of the motion of waves is the product of the length of the waves and its frequency:
v = λ/T = λf. (2)
Now, suppose that two waves with the same wavelength and frequency arrive at the same place. What is the result? The result depends on the whether the crests of both arrive simultaneously, or not. Suppose that they arrive simultaneously, that is, the crests of the two waves at the same time at the same place, so that their crests and troughs match. In this case the two waves reinforce each other, and the result is a wave whose crests and troughs are twice a big as the crests and troughs of each the original waves. This effect is called constructive interference. On the other hand, suppose that the crest of one wave arrives at the same time and same place at the trough of the other wave. Then, the crests and troughs cancel; the result is no wave at all. This effect is called destructive interference. This interference phenomena is the fundamental difference between waves and particles. Waves can interfere, but particles cannot. Two streams of particles arriving at the same time at the same place can never cancel each other; they would deflect each other together or separately.

This phenomena of interference of wave motion is what Thomas Young demonstrated for light in his famous double-slit experiment, which he first published in 1802. Suppose that light is passed through a pin hole in an opaque barrier to a screen, the pattern on the screen will be a spot. If the pin hole is clean and smooth, there will be color fringes about that spot. Now suppose a second pin hole is made in the barrier next to the first and the first pin hole is covered up for a moment, the pattern on the screen will also be a spot. If a photographic plate is used at the screen to record the first spot by covering the second hole and then to record the second spot by covering the first hole, not uncovering both holes at the same time, the pattern recorded on the photographic plate will be two distinct spots on a dark background. But if the light passes through both holes at the same time, the pattern on the screen is a light spot with light and dark stripes on either side. It is as if the light knows whether or not one or both holes are uncovered. This pattern of light on the screen is the result of the interference of the two beams of light from the two separate pin holes in the barrier. The light spot and the light stripes are the result of constructive interference and the dark stripes between the light stripes is the result of destructive interference. If two thin slits closed together are used instead of the two pin holes, then the pattern on the screen would be a series of alternating light and dark bands with larger bright bands at the center. This gives a clearer pattern to interpret. Using monochromatic (single color) light Young discovered that many more interference fringes could be seen. Furthermore, the distance between the successive bright fringes changed with color; therefore, the wavelength of differently colored light was different. From his experiments Young was able to determine the wave length of monochromatic light. Young using the wave theory was able to explain the nature and degree of this pattern as the result of the interference of waves. The particle theory of light could not explain it. This experiment of Young's was the experimentam crucis; it was decisive experiment in the decision between the particle and wave theory.

But it took nearly twenty years before his view was understood and accepted. His contemporaries, who held Newton's particle theory, described his papers as

"... destitute of every species of merit.... We ... dismiss, for the present, the feeble lucubrations of this author, in which we have searched without success for some traces of learning, acuteness, and ingenuity, that might compensate his evident deficiency in the powers of solid thinking."
Such criticism marred Young's reputations for years. Then, in 1815, a young French engineer, Augustin Fresnel (1788-1827), independently discovered the same optical phenomena that Young had been studying, devised additional experiments, and interpreted all of this in a mathematical theory of wave motion. Fresnel formulated the wave theory with much greater mathematical refinement and clarity. Abandoning Huygens geometrical constructions, Fresnel developed a more powerful methods for calculating the pattern of intensity of the light behind slits or barriers of any shape.