NATURE ITSELF WAS THE FIRST PHYSICS LABORATORY, AND AMONG natural phenomena there are none that are more beautiful and spectacular than the rainbow. It cries out for an explanation, and long before science this took the form of myths, with the ancient Greeks imagining that the rainbow was the path made by the goddess Iris when Zeus sent her to earth with a message. Being Irish, I was told by my paternal grandfather Tomas that the leprechaun’s secret hiding place for his pot of gold is at the end of the rainbow, but he didn’t tell me which end.
Aristotle was the first to attempt a scientific explanation of the rainbow, and his work formed the basis for subsequent research in medieval Islam and Latin Europe. Robert Grosseteste’s work on the rainbow, though it was mistaken in some of its basic ideas, was the starting point for those who followed him in their study of optics, some of their experiments being designed to simulate the rainbow.
We usually see a rainbow in the morning or evening after a rain shower; standing with our back to the sun, it appears as an arc with the full spectrum of visible light ranging from red on the outside to violet on the inside. The center of the bow is exactly opposite the sun relative to the observer, and if you move forward or backward the rainbow moves with you, so the leprechaun’s pot of gold remains safe, or so Tomas told me. If you have a friend with you, he has his own rainbow that moves with him. The arc makes an angle of 40 to 42° with the direction opposite the sun.
This is the primary rainbow. There is often a fainter secondary rainbow visible outside the primary arc, making an angle of 50 to 53°. The spectrum of colors in the secondary rainbow is the reverse of that in the primary arc, with violet on the outside and red on the inside. The dark region between the primary and secondary rainbows is known as Alexander’s band.
As we shall see, during the thirteenth and early fourteenth centuries a succession of scholars beginning with Grosseteste did research on the rainbow, laying the foundations for the theory that Newton published early in the eighteenth century. There, as we learned, Newton explained the rainbow as being due to a combination of reflection, refraction, and dispersion, or the division of sunlight into its component colors, a continuous spectrum extending from red to violet. The rainbow is due to sunlight passing through individual droplets of rain remaining from a shower. In the primary rainbow the light is refracted when it enters the drop, reflected internally at its back surface, and then refracted again as it leaves. In the secondary rainbow the light undergoes two internal reflections, inverting the spectrum of colors.
Grosseteste’s work on the rainbow inspired some verses written about 1270 by the French poet Jean de Meun in his continuation of Guillaume de Lorris’s Romance of the Rose. These are in chapter 83, where Nature explains the influence of the heavens, telling of how the clouds, “to give solace to the earth”:
Are wont to bear, ready at hand, a bow
Or two or even three if they prefer,
The which celestial arcs are rainbows called,
Regarding which nobody can explain,
Unless he teaches optics at some school,
How they are varicolored by the sun,
How many and what sorts of hues they show,
Wherefore so many and such different kinds,
Or why they are displayed in such a form.
The first significant advance beyond what Grosseteste and Bacon had done was by the Polish scholar Witelo (c. 1230–c. 1275). What little is known of Witelo’s life comes from scattered references in his best-known work, the Perspectiva. There he refers to “our homeland, namely Poland,” and he mentions Wroclaw (Breslau) and towns in its vicinity, indicating that he was born and raised there. He seems to have done his undergraduate studies in Paris, as surmised from his description of a nocturnal student brawl there in 1253. These battles were frequent occurrences at medieval universities and often involved the townspeople as well, as in the town versus gown brawl at Oxford in 1209 that closed the university for five years.
A decade later he is referred to as “Witelo, student of canon law” in a treatise he wrote while doing graduate studies at the University of Padua. During the winter of 1268–1269 Witelo appeared in Viterbo, where he met William of Moerbeke, the famous translator of scientific works from Greek to Latin, to whom he dedicated his Perspectiva. A manuscript of the Perspectiva refers to the author as “Magister Witelo de Viconia,” which has led to the suggestion that he retired to the abbey of Vicogne in his later years.
The Perspectiva is based on the optical works of Robert Grosseteste and Roger Bacon as well as those of ibn al-Haytham, Ptolemy, and Hero of Alexandria. It would seem that the Perspectiva was not written before 1270, since it makes use of Hero’s Catoptrica, the translation of which was completed by William of Moerbeke on December 31, 1269. The Perspectiva is such an immense work, coming to more than five hundred pages in the three printed editions, that it probably took several years to write, and so it would seem as if Witelo lived on until at least the mid-1270s.
Witelo adopted the ideas of the “metaphysics of light” and the “multiplication of forms” directly from Grosseteste and Roger Bacon. He said in the preface to the Perspectiva, “Sensible light is the intermediary of corporeal influences”; “light is the corporeal form”; and “Light is the first of all sensible forms.” The latter remark implies that light is an intermediary in certain phenomena, a case of the multiplication of forms. David C. Lindberg remarked that “although light is only one instance of natural action, it is the instance accessible to the senses and most amenable to analysis; therefore it serves, for Witelo, as the paradigm for the investigation of all natural actions.”
Thus Witelo, in discussing refraction and the dispersion of light into a spectrum of colors in the Perspectiva, wrote, “These are the things that occur to lights and colors in their diffusion through transparent bodies and in the refraction that occurs in all of them.” And in the preface, discussing in general the action of one body on another, he noted that “the investigation properly proceeds by means of visible entities.”
In the preface to the Perspectiva, which he addressed to William of Moerbeke, Witelo wrote “of corporeal influences sensible light is the medium,” adding that “there is something wonderful in the way in which the influence of divine power flows in to things of the lower world passing through the powers of the higher world.”
Witelo disagreed with Grosseteste and Bacon where they say that light rays travel from the observer’s eye to the visible object, and instead followed the reverse theory of ibn al-Haytham’s Optics that the rays emanate from the luminous object to interact with the eye, which we now know to be correct.
The Perspectiva is in ten books, the first of which consists of definitions, postulates, and geometrical theorems, from which Witelo derived the mathematical principles needed for his optical demonstrations in the following nine books. These cover the whole of what we now call geometrical optics, including reflection by plane and curved mirrors and refraction at plane or spherical interfaces between two different media, along with the rainbow and other phenomena occurring in the atmosphere.
It also covers the physiology, psychology, and geometrical optics of vision, both monocular and binocular; visual perception of size, shape, distance, roughness, darkness, and even visual beauty; along with the nature of radiation, the propagation of light, white and colored, the formation of shadows, and the camera obscura, or pinhole camera. The latter, invented by ibn al-Haytham and introduced to Europe by Witelo, is the basis of the modern camera, one of the most important inventions of medieval science.
Witelo followed Hero of Alexandria in deriving the law of reflection from the principle that a ray of light, in being reflected, will follow the path of minimum length, saying that nature does nothing in vain and “always acts along the shortest lines.”
Geometric optics is based on the principle that light is propagated rectilinearly, changing direction only when reflected or refracted at an angle of incidence other than zero. Witelo drew a distinction between the one-dimensional Euclidian lines used in a geometrical demonstration of optical analysis and actual light rays, which have perceptible width. He wrote: “In the least light ray that can be supposed, there is some width.” Nevertheless, “in the middle of that [radial line] is an imaginary mathematical line, parallel to which are all the other mathematical lines in that mathematical line.” This is the first indication of the wavelike nature of light, which causes it to spread out as it propagates through space, an idea that was revived by Christiaan Huygens (1629–1695) and Newton. It led to a discussion about whether light was a wave or a particle, which was finally resolved by Louis de Broglie (1892–1987), who won the Nobel Prize in Physics in 1929 for his wave-particle duality theory, which states that any moving particle has an associated wave, the basis of modern wave mechanics.
The methodology of Witelo is distinguished by his use of experimentation with quantitative results subjected to mathematical analysis. A good example is his attempt to construct a burning mirror that would concentrate the sun’s rays at a single focal point. After discussing various possibilities, he describes a paraboloidal mirror that he claimed to have invented himself. This was a surface produced by the rotation of a parabola about its axis of symmetry, based on the properties of parabolas in the Conics of Apollonius. Crombie gave a summary of Witelo’s description of how he manufactured a paraboloidal mirror from a concave piece of metal:
Two equal parabolic sections were drawn on a rectangular sheet of good iron or steel, and cut out. The parabolic edge of one was sharpened for cutting and that of the other made like a file for polishing. These sections were then used, with some mechanism to rotate them about their axes, to cut and polish the concave surface of the piece of iron so that it formed a parabolic mirror.
Another important example of Witelo’s method is his work on refraction. Here he made most of his measurements by repeating, with some changes, experiments described by ibn al-Haytham, whose work was based on similar experiments by Ptolemy. Ibn al-Haytham corrected Ptolemy by showing that the angle of refraction was not simply proportional to the angle of incidence. He also appears to have been the first to state the “reciprocal law,” which says that a light ray crossing the interface between two media will, if reversed, follow the same path. Witelo, in making a statement about the refraction of light, recommends that anyone wishing to study this phenomenon should use the instrument described by ibn al-Haytham, noting that “proof of this proposition depends on experiments with instruments rather than on other types of demonstration.”
The instrument that Witelo describes comprised a cylindrical brass vessel with a metal rod passing through the center of its base and fixed to the sidewalls of a glass container parallel to its bottom. The wall of the cylindrical vessel was perforated by two holes at either end of the diameter of a circle marked off into 360° and further divided into minutes of arc. When used to study the refraction of light passing from air to water, the glass container was filled with water up to the rod that formed the central axis of the brass cylinder, which was rotated so that the diameter joining the two holes was perpendicular to the surface of the water, the upper hole acting as a sight. The rod was then rotated so that the sight made an angle with the perpendicular ranging from 10 to 80°, at intervals of 10°. Light from the sun or a candle was allowed to pass through the sight along the diameter of the graduated circle until it reached the surface of the water, where it was bent away from its original direction through refraction. The axis of the cylinder was then rotated until the lower hole lined up with the refracted ray, which could then be seen as a point of light. The angles of incidence and refraction, both measured with respect to the perpendicular, could then be measured off from the graduated circle.
Then, to measure the refraction of light passing from water to air, Witelo looked through the sight and moved a stylus around the graduated circle until it came into view. Thus he was observing the angle of incidence necessary for the rays coming from the stylus to pass through the sight when the latter was in a given position.
To study the refraction of light passing from air into glass, Witelo inserted a glass hemisphere into the lower half of the brass cylinder. Then, to measure the refraction of light passing from glass into air, he simply rotated the cylinder 180° so that the glass hemisphere was in the upper half rather than the lower.
He tabulated his data to show the angles of refraction for given angles of incidence for four different arrangements: light passing from air to water, water to air, air to glass, and glass to air. An analysis of his results for light passing between air and water has been made to compare them with the values found using the modern law of refraction. It is impossible to do the same for the other cases since Witelo did not identify the kind of glass he used, the index of refraction differing appreciably from one type to another.
For the case of light passing from air into water, the analysis shows reasonable agreement between the values for the angles of refraction found by Witelo and those obtained using the modern law of refraction. But this is not true for the case of light passing from water into air, where it seems as if Witelo did not actually make the observations he records but simply obtained the values by using the reciprocal law, which he did incorrectly. Also, the results he records for angles of incidence ranging from 50 to 80° are impossible, because above a critical angle no refraction takes place when light is passing from a denser medium to one that is less dense optically, a phenomenon known as total internal reflection, of which Witelo was apparently unaware.
Witelo tried to express his results in a number of mathematical generalizations, but his efforts represented little improvement on what had been done by his predecessors. He also used his instrument to show that light rays of different color travel in the same straight line as white light when passing through a single uniform medium. He did this by putting pieces of colored material in the path of rays of sunlight entering the sight, observing that they passed through the hole on the opposite side with deviation.
He went on to discuss the properties of convex and concave lenses, of which he appears to have had only a theoretical knowledge, his principal source being ibn al-Haytham. His analysis of refraction makes use of the concept later known as the principle of minimum path. He justified this by the metaphysical notion of economy, saying that “it would be futile for anything to take place by longer lines, when it could better and more certainly take place by shorter lines.” In his analysis Witelo resolves the oblique motion of light into components perpendicular and parallel to the refracting surface, a technique that had come into use in the study of both optics and the science of motion.
In applying his knowledge of refraction to the study of the rainbow, Witelo drew heavily on the work of Roger Bacon. He differed from Bacon mainly in his belief that both reflection and refraction of sunlight in the individual raindrops of a cloud were involved in the phenomenon. Two observations convinced him of this. The first was that the rays by which the rainbow is seen came to the eye at angles equal to those at which the incident rays struck the drops, showing that reflection was involved. Secondly, unlike a simply reflected image, when an observer approached or retreated from the rainbow, it retreated or followed after him, respectively, without changing in size, indicating that refraction was also involved. He concluded, “Therefore the rainbow is seen not only by reflection but by the refraction of light within the body from which it is reflected.” Crombie described Witelo’s theory of the rainbow and the demonstration that he gave to support it.
It was seen, in fact, as part of the circumference of a cone produced by the rays coming to the eye, which was on the axis of the cone. As the observer approached or retreated from the rainbow, or moved to the right or left, he placed his eye on the axis of a different cone, of which an infinite number were produced by the multitudinous rays of light reflected from water drops in the atmosphere. This theory he supported by a simple experiment in which a rainbow in an artificial spray was seen to change its position according to whether the observer closed one eye or the other.
Witelo formulated a model to show how the water drops in the cloud produced the rainbow through a combination of refraction by individual raindrops and then reflection by other drops. His model would not, in fact, produce the results that he expected, but it paved the way for subsequent attempts to formulate the correct theory of the rainbow.
His study of the rainbow led Witelo to perform a number of experiments involving the refraction of sunlight by crystals. He produced the colors of the spectrum by passing light through a hexagonal crystal, observing that the blue rays were refracted more than the red. He also produced an artificial rainbow by passing sunlight through a spherical flask filled with water, noting that the subject was unexplored and experiment was the guide: “For the color or visible form is carried to vision only by the nature of light which it contains; and to what has been said the careful inquirer will be able by experiment to add many things.”
According to Lindberg, Witelo described the eye “as a composition of three glacial humors—glacial or crystalline, vitreous, and albugineous (aqueous) and four tunics—uvea, cornea or retina.” Witelo’s description of these humors and tunics was predominately geometrical; all of them are spherical in form, and those behind the glacial humor are concentric so that a perpendicularly incident ray will pass through all of them without refraction. Furthermore, the glacial and vitreous humors have exactly the shapes and relative densities so that the rays will converge at the center of the eye. Sight occurs when there is a “union of the visible forms and the soul’s organ” on the surface of the vitreous humor, or crystalline lens. The forms then pass through the optic nerve to the anterior part of the brain, where the nerves from the two eyes intersect to form the “common nerve,” the site of the ultimum sentiens, or ultimate perception. Lindberg gives an interesting assessment of the immense influence of Witelo, whose works were linked with those of ibn al-Haytham and Witelo’s English contemporary John Pecham:
It is difficult to separate Witelo’s influence on the history of late medieval and early modern optics from that of ibn al-Haytham, particularly after their works were published in a single volume in 1572. One can affirm in general that their writings, along with John Pecham’s Perspectiva communis, served as the standard textbooks on optics until well into the seventeenth century. More specifically, it is possible to establish Witelo’s influence on Henry of Hesse, Blasius of Parma and Nicole Oresme in the fourteenth century; Lorenzo Ghiberti, Johannes Regiomontanus, and Leonardo da Vinci in the fifteenth century; Giambattista della Porta, Francesco Maurolyco, Giovanni Battista Benedetti, Tycho Brahe, William Gilbert, Simon Stevin, and Thomas Harriot in the sixteenth century; and Kepler, Galileo, Willebrord Snell, Descartes, and Francesco Grimaldi in the seventeenth century.
John Pecham (c. 1230–1292) was born in the vicinity of Lewes in Sussex, where he received his elementary education at the local priory. He later matriculated in the arts faculties at the universities of Oxford and Paris. He joined the Franciscan order in the 1250s and was sent to Paris to study theology, receiving a doctorate in 1269. During the years 1269–1271 he served as regent master in theology in Paris, after which he returned to Oxford to serve as lecturer in theology to the Franciscan school, a position he held until he was appointed provincial minister of the order in 1275. Two years later he went to Rome as master in theology to the papal curia; then in 1279 he was appointed archbishop of Canterbury, a post he held until his death on December 8, 1292.
Both Robert Grosseteste and Roger Bacon directly influenced Pecham’s work in optics. Pecham was personally acquainted with Bacon, and they resided together in the Franciscan priory in Paris during the period when Bacon was writing his principal scientific works. Pecham’s was also influenced by Aristotle, Euclid, Ptolemy, Augustine, al-Kindi, and ibn al-Haytham, whose Optics was the primary source for his work on the science of light.
Pecham’s first optical work was the Tractus de perspectiva, probably written for the Franciscan schools during his years as a teacher in Paris and Oxford, since he says in the introduction that he wrote it to discuss light and number “for the sake of my simpler brothers.” It has been dismissively described as “a rambling piece of continuous prose … filled with quotations from the Bible and patristic sources, especially Augustine, that give it a theological and devotional flavor.”
Perhaps Pecham’s most important optical work is the Perspectiva communis, probably written in the years 1277–1279. He wrote in the introduction that his objective in writing this work was to “compress into concise summaries the teachings of perspective, which [in existing treatises] are presented with great obscurity.” The Perspectiva is a clear and concise summary of the science of light at the time, based largely on ibn al-Haytham, Witelo, and Pseudo-Euclid’s De speculis. It was deeply influenced by Grosseteste and Roger Bacon, in that Pecham conceived of light as a form of “multiplication of species,” and regarded the study of optics as a way of introducing mathematical certainty into physics. There is nothing particularly original in the book, but it remained a popular text on optics until the seventeenth century, published in twelve printed editions between 1482 and 1665, used and cited by many medieval and Renaissance scholars, including Leonardo da Vinci and Kepler.
The Perspectiva begins with a description of several experiments illustrating the properties of light, as well as discussion topics such as the cause of reflection, the anatomy of the human eye, and the physiology of vision. It goes on to give a summary of the theory of concave mirrors, including a sophisticated analysis of image formation, followed by a summary of the theory of concave and convex lenses, concluding with a summary of current theories of the rainbow. Pecham’s discussion of the rainbow attempts to reconcile previous theories of the phenomenon, where he argues that the effect is due to the concurrence of rectilinear, reflected, and refracted rays.
Pecham’s other works on natural philosophy and mathematical science include Tractatus de sphera and Tractatus de numeris. The Tractatus de sphera gives an elementary discussion of cosmology, astronomy, and astrology, including such topics as the sphericity of the earth and the celestial bodies, the rotation of the heavens, the variation in the length of days, the climactic zones and the terrestrial sphere, and the causes of eclipses. The Tractatus de numeris deals with the elementary properties of number as well as their mystical significance, including an explanation of the Trinity.
The next advances in optics were made by Dietrich of Freiburg (c. 1250–c. 1311), who is sometimes called Theodoric. Dietrich, who is thought to be from Freiburg in Saxony, entered the Dominican order and probably taught in Germany before studying at the University of Paris in around 1275–1277. In 1304 he attended the general chapter of the Dominican order in Toulouse, where the master general, Aymeric de Plaisance, asked him to write up his researches on the rainbow. The result was his principal work, De iride et radialibus impressionibus, or On the Rainbow and Radiant Impressions, the latter term meaning phenomena produced in the upper atmosphere by radiation from the sun or any other celestial body.
The only Latin source cited by Dietrich is Albertus Magnus, but his treatise indicates that he was certainly aware of the work of ibn al-Haytham and Witelo, probably that of Roger Bacon, and perhaps that of Grosseteste. The Greek and Arabic sources that he cites are Aristotle’s Meteorologica and other works, Euclid’s Elements, the Sphaera of Theodosius, Ptolemy’s Almagest, and works by Avicenna and Averroës. He was deeply influenced by Grosseteste and his followers, particularly in his belief in the “metaphysics of light” and in his scientific method, combining experiment and geometry with the principles of falsification and economy. He begins his lesser work, De iride, with the statement that knowledge of the rainbow, a phenomenon of admirable beauty, was guaranteed “by the combination of various infallible experiments with the efficacy of reasoning, as is clear enough from what follows.”
De iride begins with an account of what Dietrich terms the three modes of visual apprehension, that is, through direct, reflected, and refracted rays. He then lists fifteen types of impressiones radiales with which he was familiar, including primary rainbows, secondary rainbows, white and colored halos around the sun, and colors in stars seen through a mist. He goes on to identify five types of optical phenomena involved in these effects: a single reflection, a single refraction, two refractions and a single internal reflection in a drop of water or a crystalline sphere, two refractions and two internal reflections in the drop or sphere, and total reflection at the boundary between two transparent media. He is the first to mention the phenomenon of total internal reflection, which occurs above a critical angle of incidence when light strikes the interface between two media, in the case where the optical density of the second medium is less than that of the first, such as from water to air. This is extremely important, for it is the principle that led to modern fiber optics, among other advances.
The remainder of De iride is devoted to the application of Dietrich’s theory to the primary rainbow, the secondary rainbow, and the halo and other types of impressiones radiales, respectively.
Dietrich was the first to realize that the rainbow is due to the individual drops of rain rather than the cloud as a whole. This led him to make observations with a glass bowl filled with water, which he used as a model raindrop, for he writes “that a globe of water can be thought of, not as a diminutive spherical cloud, but as a magnified raindrop.” He also did similar experiments with hexagonal crystals and spherical crystalline balls. His observations and geometrical analysis led him to conclude that light is refracted when it enters and leaves each raindrop, and that it is internally reflected once in creating the primary bow and twice for the secondary arc. In the primary rainbow the light enters the lower part of the drop and emerges at the upper, whereas in the secondary rainbow it is just the opposite. As a result the orders of the colors in the spectrum are reversed in the two bows, ranging from red in the outer arc to blue in the lower for the primary or lower rainbow, and from blue in the outer arc to red in the lower for the secondary or outer bow.
Dietrich drew a series of geometrical diagrams to show “the manner in which the colours which appear in the rainbow come to the eye, in the case of the lower rainbow.” He summarized the results of his experiments to show that the collection of drops in which the rainbow appeared had “the breadth of the whole rainbow and also of each of its separate colours,” and “that the place of incidence of the radiation into any drop” and the places of internal reflection and of emergence had “breadth according to the different parts of which breadth the different colors shine so that any one of such parts has a breadth corresponding to one of the colors.” Furthermore, “in proportion as the radiation is incident along an oblique line more removed from the perpendicular, so does it go forth to the eye along another oblique line more removed from the same perpendicular.”
He went on to explain the manner in which the component colors come to the eye from drops in different positions:
So all the colors do not come spontaneously to the eye when it is in one and the same position with respect to the drop, but different colors come to the eye according to the different positions in which it is put with respect to a particular drop. And so if all the colors are seen simultaneously, as happens in the rainbow, this must necessarily result from different drops which have different positions with respect to the eye and the eye to them.
Referring to the first of a series of geometrical drawings, he shows how the banded arcs of the different colors appear as they do in the primary or lower rainbow, in which light enters the lower side of the drops and, after a single internal reflection, leaves through the upper. Then in his summary he gives the order of the colors in the rainbow, beginning with the outermost arc.
And so all the colors of the rainbow are seen at the same time and the whole rainbow appears in the circle of altitude in different little spherical drops according to which they are more or less elevated to different parts of the arch, from which particular parts particular colors come to the eye in the manner described. But from the drops elevated in the circle of altitude above the said arc no incident radiation is sent to the eye. The drops depressed below the said arc send some radiation incident upon them to the eye, but not with the colors of the rainbow but with white light unmixed with color.… Therefore, for the reasons stated, the color red shines in the highest part of the circle of altitude, next to this yellow, thirdly green, and finally blue, it follows that the upper and outer circle is blue, the next below yellow, then follows green, and the lowest and inner circle is blue.
Dietrich referred to another drawing to explain the secondary rainbow, in which the light enters on the lower side of the drop and, after making two internal reflections, emerges on the upper side. He showed that the arc of the secondary rainbow had the same center as that of the primary bow, with the entire secondary rainbow 11° higher than the lower bow.
Dietrich erred in his assertion that when the sun was on the horizon the maximum altitude of the primary rainbow was only 22°, as compared to the correct value of 42°, as Roger Bacon and Witelo had written. Dietrich made a number of other errors in his analysis; nevertheless, his work on the rainbow was far superior to those of any of his predecessors, and it paved the way for researches by his successors, most notably Regiomontanus, Descartes, and Newton.
Dietrich’s theory of the rainbow is very similar to that of his Persian contemporary, Kamal al-Din al-Farisi. Dietrich does not cite the work of al-Farisi, but since it was never translated from Arabic into Latin, he was probably not aware of it. In any event, it seems that the emerging European science had by the beginning of the fourteenth century reached a level comparable to that of Arabic scientific research, at least in optics. But whereas the work of al-Farisi was the last great achievement of Arabic optics, Dietrich’s researches would be an important stage in the further development of European studies in the science of light, culminating in the first correct theories of the rainbow and other optical phenomena in the seventeenth century by Newton, the final solution of a problem that had almost been solved fourteen centuries earlier by Claudius Ptolemaeus of Alexandria.
The very complexity of the rainbow, its geometry as well as its physics, made it an ideal subject for medieval physics to cut its teeth on, and thus optics, the science of light, developed apace with dynamics, the science of motion. As Crombie pointed out, “The work undertaken to explain the rainbow became linked with other work on originally independent problems.” And as we have seen, research on the rainbow in the thirteenth and early fourteenth centuries involved a number of innovations: the use of magnifying lenses and the invention of spectacles; an attempt to derive the laws of reflection and refraction from the principle of minimum path; the use of conic sections in the theory of paraboloidal mirrors; Witelo’s application of his studies in refraction to the optics of the human eye, and his realization that light rays have a finite width, a discovery that would lead to modern wave mechanics; Dietrich’s researches on the dispersal of sunlight in water-filled glass spheres into its spectrum of colors, anticipating Newton’s discoveries with glass prisms, and his discovery of total internal reflection, with its modern application in fiber optics. As Crombie concluded from all this activity: “To the eventually accepted theory of the rainbow nearly all this work contributed. Each separate contributor saw as the goal of contemporary optics as a whole the building up of a general theory of light and color by means of which all the separate problems would be related in a single system.”
When Newton’s successful explanation of the rainbow finally appeared in the first edition of his Opticks in 1714, his theory was a direct result of the researches done in the thirteenth and fourteenth centuries. A little more than a century later John Keats reacted to Newton’s theory in these lines from his “Lamia”:
Do not all charms fly
At the mere touch of cold philosophy?
There was an awful rainbow once in heaven:
We knew her woof, her texture: she is given
In the dull catalogue of common things.
Philosophy will clip an Angel’s wings,
Conquer all mysteries by rule and line.
Empty the haunted air, and gnomed mine—
Unweave a rainbow.
One of the ironies of modern physics, I feel, is that the theory of the rainbow, one of the triumphs of medieval physics and a big step forward on the road to modern science, is no longer taught in elementary physics courses, and so most people today have no better understanding of it than my grandfather Tomas. And whereas Tomas never missed a rainbow, for he would be out fishing when they appeared, almost everyone I know today hardly ever sees one, and so they will never find the leprechaun’s pot of gold.