History of optics

"In Roger Bacon's works we find a tolerably distinct explanation of the effect of a convex glass; and in the work of Vitellio... the effect of refraction at the two surfaces of a glass globe is clearly traced. ...Vitellio had obtained experimentally a number of measures of the refraction out of air into water and into glass. Out of these facts no rule had yet been collected, when, in 1604 Kepler published his "Supplement to Vitellio." ...Kepler attempted to reduce to law the astronomical observations of Tycho,—devising an almost endless variety of possible formulæ, tracing their consequences with undaunted industry, and relating with a vivacious garrulity, his disappointments and his hopes,— ...he proceeded in the same manner with regard to Vitellio's Tables of Observed Refractions. He tried a variety of constructions by triangles, conic sections, &c., without being able to satisfy himself, and he at last is obliged to content himself with an approximate rule, which makes the refraction partly proportional to the angle of incidence, and partly to the secant of that angle. In this way he satisfies the observed refractions within a difference of less than half a degree each way. When we consider how simple the law of refraction is, (that the ratio of the sines of the angles of incidence and refraction is constant for the same medium,) it appears strange that a person attempting to discover it, and drawing triangles for the purpose, should fail; but this lot of missing what afterwards seems to have been obvious, is a common one in the pursuit of truth."

"The person who did discover the Law of the Sines, was Willebrord Snell, about 1621; but the law was first published by Descartes who had seen Snell's papers. Descartes does not acknowledge this... and after his manner, instead of establishing its reality by reference to experiment, he pretends to prove à priori that it must be true, comparing, for this purpose, the particles of light, to balls striking a substance which accelerates them."

"Descartes... showed considerable skill in tracing the consequences of the principle when once adopted. In particular we must consider him as the genuine author of the explanation of the rainbow. It is true, that Fleischer and Kepler had previously ascribed this phenomenon to the rays of sunlight which, falling on drops of rain, are refracted into each drop, reflected at its inner surface, and refracted out again. Antonio de Dominis had found that a glass globe of water, when placed in a particular position with respect to the eye, exhibited bright colours; and had hence explained the circular form of the bow, which, indeed, Aristotle had done before. But none of these writers had shown why there was a narrow bright circle of a certain definite diameter; for the drops which send rays to the eye after two refractions and a reflection, occupy a much wider space in the heavens. Descartes assigned the reason for this in the most satisfactory manner, by showing that the rays which, after two refractions and a reflection, come to the eye at an angle of about forty-one degrees with their original direction, are far more dense than those in any other position. He showed, in the same manner, that the existence and position of the secondary bow resulted from the same laws."

"[I]n 1672 Newton gave the true explanation of the facts; namely, that light consists of rays of different colours and different refrangibility. ...[T]he impression which this discovery made, both upon Newton and upon his contemporaries, shows how remote it was from the then accepted opinions. There appears to have been a general persuasion that the coloration was produced, not by any peculiarity in the law of refraction itself, but by some collateral circumstance,—some dispersion or variation of density of the light, in addition to the refraction. Newton's discovery consisted in teaching distinctly that the law of refraction was to be applied, not to the beam of light in general, but to the colours in particular."

"When Newton produced a bright spot on the wall of his chamber, by admitting the sun's light through a small hole in his window-shutter, and making it pass through a prism, he expected the image to be round; which, of course, it would have been, if the colours had been produced by an equal dispersion in all directions, but to his surprise he saw the image, or spectrum, five times as long as broad. He found that no consideration of the different thickness of the glass, the possible unevenness of its surface, or the different angles of rays proceeding from the two sides of the sun, could be the cause of this shape .He found, also, that the rays did not go from the prism to the image in curves; he was then convinced that the different colours were refracted separately, and at different angles; and he confirmed this opinion by transmitting and refracting the rays of each colour separately. ...Newton's opinions were not long in obtaining general acceptance; but they met with enough of cavil and misapprehension to annoy extremely the discoverer... impatient alike of stupidity and of contentiousness."

"[Anthony] Lucas of Liege repeated Newton's experiments, and obtained Newton's result, except that he never could obtain a spectrum whose length was more than three and a half times its breadth. Newton... persisted in asserting that the image would be five times as long as broad... We now know that the dispersion, and consequently the length, of the spectrum, is very different for different kinds of glass, and it is very probable that the Dutch prism was really less dispersive than the English one. The erroneous assumption which Newton made in this instance, he held by to the last; and was thus prevented from making [another] discovery."

"Newton was attacked by... Hooke and Huyghens. These philosophers, however, did not object so much to the laws of refraction of different colours, as to some expressions used by Newton, which, they conceived conveyed false notions respecting the composition and nature of light. Newton had asserted that all the different colours are of distinct kinds, and that, by their composition they form white light. ...Hooke maintained that all natural colours are produced by various combinations of two primary ones, red and violet; and Huyghens held a similar doctrine, taking, however, yellow and blue for his basis. ...These writers also had both of them adopted an opinion that light consisted in vibrations; and objected to Newton... involving the hypothesis that light was a body. Newton appears to have had a horror of the word hypothesis, and protests against its being supposed that his "theory" rests on such a foundation."

"The doctrine of the unequal refrangibility of different rays is clearly exemplified in the effects of lenses, which produce images more or less bordered with colour, in consequence of this property. The improvement of telescopes was, in Newton's time, the great practical motive for aiming at the improvement of theoretical optics. Newton's theory showed why they were imperfect... The false opinion... that the dispersion must be the same when the refraction is the same led him to believe that the imperfection was insurmountable, and made him turn his attention to the construction of reflecting instead of refracting telescopes. But the rectification of Newton's error was a further confirmation of the general truth of his principles in other respects; and since that time, the soundness of the Newtonian law of refraction has hardly been questioned among physical philosophers."

"Göthe not only adopted and strenuously maintained the opinion that the Newtonian theory was false, but he framed a system of his own to explain the phenomena of colour. ...Göthe's views are, in fact, little different from those of Aristotle and Antonio de Dominis though more completely and systematically developed. ...it is not difficult to point out the peculiarities in Göthe's intellectual character which led to his singularly unphilosophical views on this subject. ...[H]e appears, like many persons in whom the poetical imagination is very active, to have been destitute of the talent and the habit of geometrical thought. In all probability, he never apprehended clearly and steadily those relations on which the Newtonian doctrine depends. ...[P]robably ...he had conceived the "composition" of colours in some way altogether different from that which Newton understands by composition. What Göthe expected to see, we cannot clearly collect; but we know... his intention of experimenting with a prism arose from his speculations on the rules of colouring in pictures; and we can easily see that any notion of the composition of colours which such researches would suggest, would require to be laid aside before he could understand Newton's theory of the composition of light."

"Sir David Brewster... contests Newton's opinion, that the coloured rays into which light is separated by refraction are altogether simple and homogeneous, and incapable of being further analysed or modified. For he finds that by passing such rays through coloured media, (as blue glass for instance,) they are not only absorbed and transmitted in very various degrees, but that some of them have their colour altered; which cannot be conceived otherwise than as a further analysis of them, one component colour being absorbed and the other transmitted. ...The whole subject of the colours, of objects both opake and transparent, is still in obscurity. Newton's conjectures concerning the causes of the colours of natural bodies, appear to help us little; and his opinions on that subject are to be separated altogether from the important step which he made in optical science, by the establishment of the true doctrine of refractive dispersion."

"The discovery that the laws of refractive dispersion of different substances were such as to allow of combinations which neutralized the dispersion without neutralising the refraction, is one which has hitherto been of more value to art than to science."

"Euler observed, that a combination of lenses which does not colour the image must be possible, since we have an example of such a combination in the human eye; and he investigated mathematically the conditions requi site for such a result. Klingenstierna... also showed that Newton's rule could not be universally true."

", in 1757, repeated Newton's experiment, and obtained an opposite result. He found that when an object was seen through two prisms, one of glass and one of water, of such angles that it did not appear displaced by refraction, it was coloured. Hence it followed that, without being coloured, the rays might be made to undergo refraction; and that thus, substituting lenses for prisms, a combination might be formed, which should produce an image without colouring it, and make the construction of an achromatic telescope possible."

"Euler at first hesitated to confide in Dollond's experiments; but he was assured of their correctness by Clairaut, who had throughout paid great attention to the subject; and those two great mathematicians, as well as D'Alembert, proceeded to investigate mathematical formulæ which might be useful in the application of the discovery. The remainder of the deductions, which were founded upon the laws of dispersion of various refractive substances, belongs rather to the history of art than of science. Dollond used at first, for his achromatic object-glass, a lens of crown-glass, and one of flint-glass; afterwards, two lenses of the former substance, including between them one of the latter. He also adjusted the curvatures of his lenses in such a way as to correct imperfections arising from the spherical form of the glasses, as well as the fault of colour. Afterwards Blair, and more recently Mr. Barlow, have used fluid media along with glass lenses, in order to produce improved object-glasses; and various mathematicians, as Sir J. Herschel and Professor Airy among ourselves, have simplified and extended the investigation of the formulæ which determine the best combinations of lenses in the object-glasses and eye-glasses of telescopes, both with reference to spherical and chromatic aberrations."

"The phenomena of ocular spectra and complementary colours... forms a curious chapter in the history of those illusions which take their origin in the eye... [A]fter looking fixedly at a bright light or a striking colour for a few moments the eye preserves an impression of the object for a certain time. A very light window looked at intently for several seconds will leave the impression of its cross bars on the retina for several minutes, the colour of the image changing at every movement of the eye. The same effect may be observed when looking at the setting sun, or a flaring gas light. If the light at which we look is coloured we shall see the complementary colour in the impression left on the retina. Sir David Brewster was one of the first to notice and experiment upon these very interesting facts."

"[T]he complementary of any colour is that which is necessary to make white light. ...The impression left by the setting sun is of this character. At first, while the eye is open, the image is black, then brownish red, with a light blue border; but if the eye be shut suddenly, it becomes green, with a red border, the brilliancy of colour being apparently in proportion to the strength of the impression. These spectra may be perceived for a long time, if the eye is gently rubbed with the finger now and then. Some eyes are more impressionable in this respect than others, and Beyle gives an instance of an individual who saw the spectrum of the sun for years, whenever he looked at a bright object. A modern instance of this occurred lately to an amateur astronomer who was looking at an eclipse of the sun. He unfortunately used a glass that was not sufficiently smoked and the image... remained on his retina for months after. This... afforded an instance of the necessity of attention in order to see any object, for after the first few days he only became sensible of [it] when his attention was called to it by some accidental circumstance. These facts were so inexplicable to Locke that he consulted Newton on the subject, and was surprised to learn that the great philosopher himself had suffered for several months from a sun-spectrum in the eye."

"We can say with every confidence that "the Providence which shapes our ends," knows our wants better than we do ourselves, and bestows on us the things we ought to have asked for instead of those we have asked for. We shall find a very simple proof of this in the history of the discovery of the velocity of light."

"A short time after the invention of the telescope and the consequent discovery of Jupiter's satellites, Römer... was engaged in a series of observations... to determine the time which one of these bodies took to revolve round its planet. The method employed by Römer was to observe the successive s of the satellite and to notice the interval that elapsed between each of them. But it at last happened that the interval between the two occultations, which was about forty five hours, became prolonged by periods of 8, 13, and 16 minutes, during that half of the year when the earth was receding from the planet, while it became proportionally cut short during [earth's approach]. Römer was struck by a happy idea he suspected instantly that... an interval of time sufficiently long [was required] to allow the light that had left the satellite immediately after its disappearance to reach the eye of the observer. ...[T]he farther off the earth was from the satellite the longer was the interval of time between its disappearance and that of the arrival of the last portions of its light upon the earth ...It was thus that Römer explained the difference between the calculated and observed time of the occultation and he saw that he was on the threshold of a great discovery. ...he saw that light propagated itself through space with a certain velocity and that the fact... just mentioned furnished the precise means of measuring it. Thus the occultation of the satellite was retarded one second for every 185,000 miles that the earth is distant from Jupiter; the reason being that a ray of light takes a second to travel this distance... because the velocity of light is... 185,000 miles per second."

"There are many persons... whom we should astonish, and possibly enrage, by asserting... that we could cause darkness by means of light, that silence could be produced by sound, or cold by heat. ...[B]y throwing a second stone into the water we form another series of undulations which are mutually destroyed when they encounter each other. It is the same with the peculiar fluid which, existing throughout space, is thrown in a state of undulation by incandescent bodies; by opposing one set of waves to another we obtain rest as a result. This fact was first observed by Grimaldi in 1665 and Dr. Thomas Young was the first to offer an explanation. Fresnel used it with great success at the beginning of the century to demonstrate the truth of the undulatory theory, by showing that it could not be explained by any other."

"All experiments in which the eye of the investigator is provided with good optical instruments are distinguished, as is well known, by a high degree of precision; and some of the most important discoveries could not have been made without these instruments. Up to the present time, in experiments on diffraction there has been no instrument, except a magnifying-glass, which could be used with profit; and this may perhaps be one of the reasons why in this field of physical optics we are so backward, and why we know so little of the laws of this modification of light. ...[I]t is most to be desired that these laws should be exactly known; and this is specially so because a knowledge of them makes the nature of light itself better known at the same time."

"If sunlight is admitted into a darkened room through a small opening and falls upon a dark screen some distance away, which has a narrow aperture, and if the light which passes through this slit is allowed to fall upon a white surface or a piece of ground-glass placed a short distance behind the screen, one sees... that the illuminated portion of the white surface is larger than the narrow slit in the screen, and that it has colored edges—in short, that the light through the slit is inflected or diffracted. The narrower the openings, so much the greater is the inflection. The shadow of every body which is placed in a beam of sunlight entering a darkened room through a small opening is bounded by fringes of color which are, moreover, for any given distance of the surface on which the shadow is received, of the same size for bodies of all kinds of matter. The shadow of a narrow object, such as a hair, has, in addition to the outer fringes, others within the shadow, which change with the thickness of the hair, but in other respects are similar to the outer ones. Since the colored fringes are very small, and since most of the light is lost through absorption at the surface on which the shadow is cast, no great accuracy could be expected with the methods which have been used up to this time to observe diffraction phenomena; and this is all the more true because by these methods it is impossible to measure the angles of inflection of the light which alone can make us acquainted with the laws of diffraction. Up to the present, these angles from which the path of the diffracted light can be learned have been calculated from the dimensions of the colored bands and their distance from the diffracting body; but assumptions have been made which... do not agree with the truth, and which, therefore, give false results."

"In order to receive in the eye all the light diffracted through a narrow opening, and to see the phenomena strongly magnified; still more in order to directly measure the inflection of the light, I placed in front of the objective of a -telescope a screen in which there was a narrow vertical opening which could be made wider or narrower by means of a screw. By means of a heliostat I threw sunlight into a darkened room through a narrow slit so that it fell upon this screen, through whose opening the light was therefore diffracted. I could then observe through the telescope the phenomena produced by the diffraction, magnified, and yet seen with sufficient brightness; and at the same time I could measure the angles of inflection of the light by means of the theodolite."

"Descartes's theory of light rapidly displaced the conceptions which had held sway in the Middle Ages. The validity of his explanation of was, however, called in question by his fellow-countryman Pierre de Fermat... and a controversy ensued which was kept up by the Cartesians long after the death of their master. Fermat eventually introduced a new fundamental law, from which he proposed to deduce the paths of rays of light. This was the celebrated Principle of Least Time, enunciated in the form, "Nature always acts by the shortest course." From it the law of reflection can readily be derived, since the path described by light between a point on the incident ray and a point on the reflected ray is the shortest possible consistent with the condition of meeting the reflecting surfaces. In order to obtain the law of refraction, Fermat assumed that "the resistance of the media is different," and applied his "method of maxima and minima" to find the paths which would be described in the least time from a point of one medium to a point of the other. In 1661 he arrived at the solution. "The result of my work," he writes, "has been the most extraordinary, the most unforeseen and the happiest, that ever was; for, after having performed all the equations, multiplications, antitheses and other operations of my method, and having finally finished the problem, I have found that my principle gives exactly and precisely the same proportion for the refractions which Monsieur Descartes has established." His surprise was all the greater, as he had supposed light to move more slowly in dense than in rare media, whereas Descartes had... been obliged to make the contrary supposition."

"Although Fermat's result was correct, and, indeed, of high permanent interest, the principles from which it was derived were metaphysical rather than physical in character, and consequently were of little use for the purpose of framing a mechanical explanation of light. Descartes' theory therefore held the field until the publication in 1667§ of the Micrographia of Robert Hooke..."

"Hooke, who was both an observer and a theorist, made two experimental discoveries which concern [us]... but in both of these, as it appeared, he had been anticipated. The first was the observation of the iridescent colours which are seen when light falls on a thin layer of air between two glass plates or lenses, or on a thin film of any transparent substance. These are generally known as the "colours of thin plates," or ""; they had been previously observed by Boyle. Hooke's second experimental discovery, made after... Micrographia, was that light in air is not propagated exactly in straight lines, but that there is some illumination within the geometrical shadow of an opaque body. This observation had been published in 1665 in a posthumous work of Francesco Maria Grimaldi... who had given to the phenomenon the name ."

"Hooke's theoretical investigations on light were of great importance, representing as they do the transition from the Cartesian system to the fully developed theory of undulations. He begins by attacking Descartes' proposition, that light is a tendency to motion rather than an actual motion. "There is," he observes, "no luminous Body but has the parts of it in motion more or less"; and this motion is "exceeding quick." Moreover, since some bodies (e.g. the diamond when rubbed or heated in the dark) shine for a considerable time without being wasted away, it follows that whatever is in motion is not permanently lost to the body, and therefore that the motion must be of a to-and-fro or vibratory character. The amplitude of the vibrations must be exceedingly small, since some luminous bodies (e.g. the diamond again) are very hard, and so cannot yield or bend to any sensible extent."

"(Ptolemy) left in his Optics, the earliest surviving table of angles of refraction from air to water. ...This table, quoted and requoted until modern times, has been admired... A closer glance at it, however, suggests that there was less experimentation involved in it than originally was thought, for the values of the angles of refraction form an arithmetic progression of second order... As in other portions of Greek Science, confidence in mathematics was here greater than that in the evidence of the senses, although the value corresponding to 60° agrees remarkably well with experience."

"Descartes maintained his confidence in the instantaneity of light. ...Yet in his derivation of the law of refraction, Descartes reasoned that light traveled faster in a dense medium than in one less dense. He seems to have had no qualms about comparing infinite magnitudes!"

"Fermat had recourse to the principle of the economy of nature. Heron and Olympiodorus had pointed out in antiquity that, in reflection, light followed the shortest possible path, thus accounting for the equality of angles. During the medieval period Alhazen and Grosseteste had suggested that in refraction some such principle was also operating, but they could not discover the law. Fermat, however, not only knew (through Descartes) the law of refraction, but he also invented a procedure—equivalent to the differential calculus—for maximizing and minimizing a function of a single variable. … Fermat applied his method … and discovered, to his delight, that the result led to precisely the law which Descartes had enunciated. But although the law is the same, it will be noted that the hypothesis contradicts that of Descartes. Fermat assumed that the speed of light in water to be less than that in air; Descartes' explanation implied the opposite."

"Regardless of the prophetic value of Dirac’s description [on interference] his was probably the first discussion... including a coherent beam of light. In other words, Dirac wrote the first chapter in laser optics."

"Feynman uses Dirac's notation to describe the quantum mechanics of stimulated emission... he applies that physics to... dye molecules... In this regard, Feynman could have predicted the existence of the tunable laser."

"The intimate relation between interference and has its origin in the interference equation itself."

"Multiple-prism arrays were first introduced by Newton (1704) in his book . In that visionary volume Newton reported on arrays of nearly isosceles prisms in additive and compensating configurations to control the propagation path and the dispersion of light. Further, he also illustrated slight beam expansion in a single isosceles prism."