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History of optics

study of the development of optics with lenses and theories of light and vision over time

History of Optics begins with the development of lenses by the ancient Egyptians and Mesopotamians, followed by theories on light and vision developed by ancient Greek philosophers, and the development of geometrical optics in the Greco-Roman world. The word optics is derived from the Greek term τα ὀπτικά meaning "appearance or look". Optics was significantly reformed by the developments in the medieval Islamic world, such as the beginnings of physical and physiological optics, and then significantly advanced in early modern Europe, with a serious investigation of diffraction. The term "modern optics" begins largely with 20th century research in physical optics and quantum optics. Earlier theories in optics are included under "classical optics."

Spectrum of sunlight

Quotes edit

  • The spectrum of the sun was first observed, in 1666, by Newton, who allowed light coming from a small round opening in a shutter to pass through a glass prism. This spectrum was most impure; and a pure spectrum was not obtained until, in 1802, Wollaston repeated Newton's experiment, replacing the round opening by a slit parallel to the edge of the prism. He observed several dark lines crossing the spectrum, which limited, as he thought, the different spectral colors.
  • It is manifest that everything in the world, whether it be substance or accident, produces rays in its own manner like a star... Everything that has actual existence in the world of the elements emits rays in every direction, which fill the whole world.
    • Al-Kindi, De Causis diuersitatum aspectus et dandis demonstrationibus geometricus super eas, also known as De Aspectibus (ca. 860) as quoted by David C. Lindberg, Theories of Vision from Al-kindi to Kepler (1976)
  • Mohammedan science made a great advance on that of the Greeks... [in] optics, and this was very largely a by-product of medicine. Optics comes much more in the doctor's province, especially in tropical and sub-tropical countries where there is a prevalence of eye diseases ...This goes right back to the Babylonians, who were doing ...cataract operations, between 2000 and 2500 BC. Therefore... they introduced into science something ...which the Greeks did not have ...the lens. The Greeks ...knew that the mirror could focus the rays—that was due to Archimedes—but they did not have any lenses.
  • Phenomena were accounted for by taking into consideration the frictional resistances that would interfere with rapid vibrations of the electrons. When these frictional resistances were weak, oscillatory disturbances, such as rays of light, could be propogated through the dielectric, which was then termed transparent (glass). When these frictional forces were considerable, the light ray was unable to set the electrons into vibration; its energy was consumed in the attempt, and as a result it could not proceed; the dielectric was then opaque (ebonite, sulphur).
  • Kepler's theory of vision introduced the concept of optical images that is the basis of modern geometrical optics.
    • Olivier Darrigol, A History of Optics from Greek Antiquity to the Nineteenth Century (2012)
  • The wave theory furnishes the simplest possible explanation of interference phenomena. On the other hand it has considerable difficulty in explaining the rectilinear propagation of light. In this respect the analogy between sound and light seems to break down, for sound does not travel in straight lines. ...This analogy between sound and light presents still further contradictions when polarization phenomena are under consideration. It was these contradictions which prevented for a long time the general recognition of the wave theory in spite of the simple explanation which it offers of interference. The difficulties were not removed until a too close analogy between sound and light was given up.
  • [T]he explanation of the rectilinear propagation of light from the standpoint of the wave theory presents difficulties. To overcome these difficulties Huygens made the supposition that every point P which is reached by a light-wave may be conceived as the source of elementary light-waves, but that these elementary waves produce an appreciable effect only upon the surface of their envelope. ...Fresnel replaced Huygens' arbitrary assumption that only the envelope of the elementary waves produces appreciable light effects by the principle that the elementary waves in their criss-crossing influence one another in accordance with the principle of interference. Light ought then to appear not only upon the enveloping surface, but everywhere where the elementary waves reinforce one another; on the other hand, there should be darkness wherever they destroy one another. ...[I]t is possible to deduce from this Fresnel-Huygens principle not only the laws of diffraction, but also those of straight-line propagation, reflection, and refraction.
  • The result of my work 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.
    • Pierre de Fermat, Epist. XLII, written at Toulouse (Jan. 1, 1662) and reprinted in Œvres de Fermat, ii, p. 457; i, pp. 170, 173, as quoted by E. T. Whittaker, A History of the Theories of Aether and Electricity from the Age of Descartes to the Close of the Nineteenth Century (1910) p. 10.
  • Newton's proof of the law of refraction is based on an erroneous notion that light travels faster in glass than in air, the same error that Descartes had made. This error stems from the fact that both of them thought that light was corpuscular in nature.
    • John Freely, Before Galileo, The Birth of Modern Science in Medieval Europe (2012)
  • To complete the theory of reflexion and refraction on the undulatory hypothesis, it will be necessary to show what becomes of those oblique portions of the secondary waves, diverging in all directions from every point of the reflecting or refracting surfaces... which do not conspire to form the principal wave. But to understand this, we must enter on the doctrine of the interference of the rays of light,—a doctrine we owe almost entirely to the ingenuity of Dr. Young, though some of its features may be pretty distinctly traced in the writings of Hooke, (the most ingenious man, perhaps, of his age,) and though Newton himself occasionally indulged in speculations bearing a certain relation to it. But the unpursued speculations of Newton, and the appercus of Hooke, however distinct, must not be put in competition, and, indeed, ought scarcely to be mentioned with the elegant, simple, and comprehensive theory of Young,—a theory which, if not founded in nature, is certainly one of the happiest fictions that the genius of man has yet invented to group together natural phenomena, as well as the most fortunate in the support it has unexpectedly received from whole classes of new phenomena, which at their first discovery seemed in irreconcileable opposition to it. It is, in fact, in all its applications and details one succession of felicities insomuch that we may almost be induced to say, if it be not true, it deserves to be so. The limits of this Essay, we fear, will hardly allow us to do it justice.
  • We must never forget that it is principles, not phenomena,—the interpretation, not the mere knowledge of facts,—which are the objects of enquiry to the natural philosopher. As truth is single, and consistent with itself, a principle may be as completely and as plainly elucidated by the most familiar and simple fact, as by the most imposing and uncommon phenomenon. The colours which glitter on a soap-bubble are the immediate consequence of a principle the most important from the variety of phenomena it explains, and the most beautiful, from its simplicity and compendious neatness, in the whole science of optics. If the nature of periodical colours can be made intelligible by the contemplation of such a trivial object, from that moment it becomes a noble instrument in the eye of correct judgment; and to blow a large, regular, and durable soap-bubble may become the serious and praise-worthy endeavour of a sage, while children stand round and scoff, or children of a larger growth hold up their hands in astonishment at such waste of time and trouble. To the natural philosopher there is no natural object unimportant or trifling. From the least of nature's works he may learn the greatest lessons.
    • John Herschel, Preliminary Discourse on the Study of Natural Philosophy (1831) taken from pp. 13-14 in the new (1851) edition.
  • Perhaps the most striking example of the services which have been rendered to Science by the contemplation of various models, many or all of which have ultimately been found to be inadequate for complete representation, is to be found in the history of Optics. The various forms of the corpuscular theory, and of the wave theory, of Light were all attempts to represent the phenomena by models, the value of which had to be estimated by developing their Mathematical consequences, and comparing these consequences with the results of experiments. The adynamical theory of Fresnel, the elastic solid theory of the ether developed by Navier, Cauchy, Poisson, and Green, the labile ether theory developed by Cauchy and Kelvin, and the rotational ether theory of MacCullagh were all efforts of the kind... indicated; they were all successful in some greater or less degree in the representation of the phenomena, and they all stimulated Physicists to further efforts to obtain more minute knowledge of those phenomena. Even such an inadequate theory as that of Fresnel led to the very interesting observation by Humphry Lloyd of the phenomenon of conical refraction in crystals, as the result of the prediction by Rowan Hamilton that the phenomenon was a necessary consequence of the Mathematical fact that Fresnel's wave surface in a biaxal crystal possesses four conical points.
  • There can be no doubt that light consists of the motion of a certain substance. For if we examine its production, we find that here on earth it is principally fire and flame which engender it, both of which contain beyond doubt bodies which are in rapid movement, since they dissolve and destroy many other bodies more solid than they: while if we regard its effects, we see that when light is accumulated, say by concave mirrors, it has the property of combustion just as fire has, that is to say, it disunites the parts of bodies, which is assuredly a proof of motion, at least in the true philosophy, in which the causes of all natural effects are conceived as mechanical causes. Which in my judgment must be accomplished or all hope of ever understanding physics is renounced.
    • Christiaan Huygens, Traite de la Lumière (1690) p. 2, as quoted by Ernst Mach, "On the Principle of the Conservation of Energy" in Popular Scientific Lectures (1895) pp. 155-156, Tr. Thomas J. McCormack.
  • Velocity of transverse undulations in our hypothetical medium, calculated from the electromagnetic experiments of 'MM'. Kohlrausch and Weber, agrees so exactly with the velocity of light calculated from the optical experiments of M. Fizeau, that we can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.
    • James Clerk Maxwell, Lecture at Kings College (1862) as quoted by F. V. Jones, "The Man Who Paved the Way for Wireless," New Scientist (Nov 1, 1979) p. 348 & Andrey Vyshedskiy, On The Origin Of The Human Mind 2nd edition
  • That light is not itself a substance may be proved from the phenomenon of interference. A beam of light from a single source is divided by certain optical methods into two parts, and these, after travelling by different paths, are made to reunite and fall upon a screen. If either half of the beam is stopped, the other falls on the screen and illuminates it, but if both are allowed to pass, the screen in certain places becomes dark, and thus shows that the two portions of light have destroyed each other. Now, we cannot suppose that two bodies when put together can annihilate each other; therefore light cannot be a substance. ... What we have proved is that one portion of light can be the exact opposite of another portion... Such quantities are the measures, not of substances, but always of processes taking place in a substance. We therefore conclude that light is... a process going on in a substance... so that when the two portions [of light] are combined no process goes on at all. ...the light is extinguished when the difference of the length of the paths is an odd multiple of... a half wave-length. ...we see on the screen a set of fringes consisting of dark lines at equal intervals, with bright bands of graduated intensity between them. ...if the two rays are polarized ...when the two planes of polarization are parallel the phenomena of interference appear as above ...As the plane turns ...light bands become less distinct ...at right angles ...illumination of the screen becomes uniform, and no trace of interference can be discovered. ...The process may, however, be an electromagnetic one ...the electric displacement and the magnetic disturbance are perpendicular to each other, either ...supposed to be in the plane of polarization.
  • Thomas Young... attained equal eminence by his discoveries in connection with the undulatory theory of light, in which he was the first to assert the principle of interference, and that of transverse vibrations... The remarkable fact that Young, of whom Helmholtz says that he came a generation too soon, remained scientifically unrecognised and popularly almost unknown to his countrymen, has been explained by his unfortunate manner of expression and the peculiar channels through which his labours were announced to the world. ...[S]everal great names contributed, by the authority they commanded, to oppose Young's claims to originality and renown. Lord Brougham, shielded by the powerful anonymity of the 'Edinburgh Review,' and ostentatiously parading the authority of Newton, submitted the views of Young to a ruthless and unfair criticism, the popular influence of which Young probably never overcame. The great authority on optics, Brewster, who has enriched that science by such a number of experiments and observations of the first importance, never really adopted the theories of Young and Fresnel.
  • [W]ith regard to light, that it consists of vibrations was almost proved by the phenomena of diffraction, while those of polarisation showed the excursions of the particles to be perpendicular to the line of propogation; but the phenomena of dispersion, etc., require additional hypotheses which may be very complicated. Thus, the further progress of molecular speculation appears quite uncertain. If hypotheses are to be tried haphazard, or simply because they will suit certain phenomena, it will occupy the mathematical physicists of the world say half a century on the average to bring each theory to the test, and since the number of possible theories may go up into the trillion, only one of which can be true, we have little prospect of making further solid additions to the subject in our time.
  • Contemporary with Vitellio and Peccam was... Roger Bacon, a man of almost universal genius, and who wrote on almost every branch of science. He frequently quotes Alhazen on the subject of optics, and seems to have carefully studied his writings, as well as those of other Arabians, which were the fountains of natural knowledge in those days, and which had been introduced into Europe by means of the Moors in Spain. Notwithstanding the pains this great man took with the subject of opticks, it does not appear that, with respect to theory, he made any considerable advance upon what Alhazen had done before him.
  • Descartes subscribed to the doctrine of instantaneous propagation, but with him something new emerged: for his was the first uncompromisingly mechanical theory that asserted the instantaneous propagation of light in a material medium... Indeed, mechanical analogies had been used to explain optical phenomena long before Descartes, but the Cartesian theory was the first clearly to assert that light itself was nothing but a mechanical property of the luminous object and of the transmitting medium. It is for this reason that we may regard Descartes' theory of light as legitimate starting point of modern physical optics.
    • A. I. Sabra, Theories of Light, from Descartes to Newton (1981)
  • One of the most distinguished and prolific mathematicians in the medieval tradition of Arabic Islamic science, al-Hasan ibn al-Haytham (Latinized as Alhacen or Alhazen) became known in Europe in the thirteenth century as the author of the monumental book on optics—the mathematical theory of vision. In his Kitâb al-Manâ zir (De aspectibus), the eleventh-century scholar offered a new solution to the problem of vision, combining experimental investigations of the behavior of light with inventive geometrical proofs and constant forays into the psychology of visual perception — all systematically tied together to form a coherent alternative to the Euclidean and Ptolemaic theories of "visual rays" issuing from the eye.
    • A. I. Sabra, “Ibn al-Haytham Brief life of an Arab mathematician," Harvard Magazine (September-October 2003)
  • [I]t was Ibn al-Haytham's early embrace of empiricism and trust in mathematical proof that underlay the revolutionary project of his mature magnum opus, the Optics, the book that pointed the science of vision in the direction later pursued in seventeenth-century Europe. It was wholly composed of systematically arranged experiments and geometrical proofs, all expressed in clear, consistent vocabulary and orderly exposition. The Latin translation influenced medieval European scientists and philosophers such as Roger Bacon and Witelo. But the book came into its own later, when it attracted the attention of mathematicians like Kepler, Descartes, and Huygens, thanks in part to Friedrich Risner's edition published in Basel in 1572.
    • A. I. Sabra, “Ibn al-Haytham Brief life of an Arab mathematician," Harvard Magazine (September-October 2003)
  • Of those who ascribe perception to something other than similarity, Alcmaeon states... the difference between men and animals. For man, he says, differs from other creatures "inasmuch as he alone has the power to understand. Other creatures perceive by sense but do not understand"; since to think and to perceive by sense are different processes and not, as Empedocles held, identical.
    not Empedocles held He next speaks of the senses severally. ...Eyes see through the water round about. And the eye obviously has fire within, for when one is struck <this fire> flashes out. Vision is due to the gleaming,—that is to say, the transparent character of that which [in the eye] reflects the object; and sight is the more perfect, the greater the purity of this substance.
  • Anaxagoras holds that sense perception comes to pass by means of opposites, for the like is unaffected by the like. He then essays to review each separately. Accordingly he maintains that seeing is due to the reflection in the pupil, but that nothing is reflected in what is of like hue, but only in what is of a different hue. Now with most <creatures> this contrast of hue <with that of the pupil> occurs by day, but with some by night, and this is why the latter are keen of vision by night. But, in general, night the rather is of the eye's own hue. Furthermore, there is reflection by day, he holds, because the light is a contributing cause of reflection, and because the stronger of two colours is regularly reflected better in the weaker.
  • [W]hen, in 1815, a young French military engineer, named Augustin Jean Fresnel, returning from the Napoleonic wars, became interested in the phenomena of light, and made some experiments concerning diffraction which seemed to him to controvert the accepted notions of the materiality of light, he was quite unaware that his experiments had been anticipated... He communicated his experiments and results to the French Institute, supposing them to be absolutely novel. That body referred them to a committee, of which... the dominating member was Dominique Francois Arago... [who] at once recognized the merit of Fresnel's work, and soon became a convert to the theory. He told Fresnel that Young had anticipated him as regards the general theory, but that much remained to be done, and he offered to associate himself with Fresnel in prosecuting the investigation. Fresnel was not a little dashed to learn that his original ideas had been worked out by another while he was a lad, but he... went ahead with unabated zeal. ...
    [A] bitter feud ensued, in which Arago was opposed by the "Jupiter Olympus of the Academy," Laplace, by the only less famous Poisson, and by the younger but hardly less able Biot. So bitterly raged the feud that a life-long friendship between Arago and Biot was ruptured forever. The opposition managed to delay the publication of Fresnel's papers, but Arago continued to fight with his customary enthusiasm and pertinacity, and at last, in 1823, the Academy yielded, and voted Fresnel into its ranks, thus implicitly admitting the value of his work.
    • Henry Smith Williams, A History of Science (1904) Vol. 3, Modern Development of the Physical Sciences
  • It was in May 1801 that I discovered, by reflecting on the beautiful experiments of Newton, a law which appears to me to account for a greater variety of interesting phenomena than any other optical principle that has yet been made known. I shall endeavour to explain this law by a comparison.
    Suppose a number of equal waves of water to move upon the surface of a stagnant lake, with a certain constant velocity, and to enter a narrow channel leading out of the lake. Suppose then another similar cause to have excited another equal series of waves, which arrive at the same channel, with the same velocity, and at the same time with the first. Neither series of waves will destroy the other, but their effects will be combined: if they enter the channel in such a manner that the elevations of one series coincide with those of the other, they must together produce a series of greater joint elevations; but if the elevations of one series are so situated as to correspond to the depressions of the other, they must exactly fill up those depressions, and the surface of the water must remain smooth; at least I can discover no alternative, either from theory or from experiment.
    Now, I maintain that similar effects take place whenever two portions of light are thus mixed; and this I call the general law of the interference of light. I have shown that this law agrees, most accurately, with the measures recorded in Newton's Optics, relative to the colours of transparent substances, observed under circumstances which had never before been subjected to calculation, and with a great diversity of other experiments never before explained. This, I assert, is a most powerful argument in favour of the theory which I had before revived: there was nothing that could have led to it in any author with whom I am acquainted, except some imperfect hints in those inexhaustible but neglected mines of nascent inventions, the works of the great Dr. Robert Hooke, which had never occurred to me at the time that I discovered the law; and except the Newtonian explanation of the combinations of tides in the Port of Batsha.
    • Thomas Young, "Reply to the Edinburgh Reviewers," (1804) in Miscellaneous Works of the Late Thomas Young Including his Scientific Memoirs, &c. (1855) Vol. 1, pp. 202-203.

Opticks (1704) edit

by Isaac Newton
  • The Angles of Refexion and Refraction, lie in one and the same Plane with the Angle of Incidence.
    • Axiom I.
  • The Angle of Reflexion is equal to the Angle of Incidence.
    • Axiom II.
  • If the reflected or refracted Ray be returned directly back to the Point of Incidence, it shall be refracted into the Line before described as the incident Ray.
    • Axiom III.
  • Refraction out of a rarer Medium into a denser, is made toward the Perpendicular; that is, so that the Angle of Refraction be less than the Angle of Incidence.
    • Axiom IV.
  • The Sine of Incidence is either accurately or very nearly in a given Ratio to the Sine of the Refraction.
    • Axiom V.
  • Do not Bodies act upon Light at a distance, and by their action bend its Rays; and is not this action (caeteris paribus [all else being equal]) strongest at the least distance?
    • Query 1
  • Do not the Rays which differ in Refrangibility differ also in Flexibility; and are they not by their different inflexions separated from one another, so as after separation to make the Colours in the three Fringes... ? And after what manner are they inflected to make those Fringes?
    • Query 2
  • Are not the Rays of Light in passing by the edges and sides of Bodies, bent several times backwards and forwards, with a motion like that of an Eel? And do not the three Fringes of colour'd Light... arise from three such bendings?
    • Query 3
  • Do not the Rays of Light which fall upon Bodies, and are reflected or refracted, begin to bend before they arrive at the Bodies; and are they not reflected, refracted, and inflected, by one and the same Principle, acting variously in various Circumstances?
    • Query 4
  • Do not Bodies and Light act mutually upon one another; that is to say, Bodies upon Light in emitting, reflecting, refracting and inflecting it, and Light upon Bodies for heating them, and putting their parts into a vibrating motion wherein heat consists?
    • Query 5
  • Do not several sorts of Rays make Vibrations of several bignesses, which according to their bigness excite Sensations of several Colours, much after the manner that the Vibrations of the Air, according to their several bignesses excite Sensations of several Sounds? And particularly do not the most refrangible Rays excite the shortest Vibrations for making a Sensation of deep violet, the least refrangible the largest form making a Sensation of deep red, and several intermediate sorts of Rays, Vibrations of several intermediate bignesses to make Sensations of several intemediate Colours?
    • Query 13
  • Is not the Heat of the warm Room convey'd through the Vacuum by the Vibrations of a much subtiler Medium than Air, which after the Air was drawn out remained in the Vacuum? And is not this Medium the same with that Medium by which Light is refracted and reflected and by whose Vibrations Light communicates Heat to Bodies, and is put into Fits of easy Reflexion and easy Transmission? ...And do not hot Bodies communicate their Heat to contiguous cold ones, by the Vibrations of this Medium propagated from them into the cold ones? And is not this Medium exceedingly more rare and subtile than the Air, and exceedingly more elastick and active? And doth it not readily pervade all Bodies? And is it not (by its elastick force) expanded through all the Heavens?
    • Query 18
  • Doth not this Æthereal Medium in passing out of Water, Glass, Crystal, and other compact and dense Bodies into empty Spaces, grow denser and denser by degrees, and by that means refract the Rays of Light not in a point, but by bending them gradually in curve Lines? And doth not the gradual condensation of this Medium extend to some distance from the Bodies, and thereby cause the Inflexions of the Rays of Light, which pass by the edges of dense Bodies, at some distance from the Bodies?
    • Query 20
  • Is not this Medium [æther] much rarer within the dense Bodies of the Sun, Stars, Planets, and Comets, than in the empty celestial Spaces between them? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great Bodies towards one another, and of their parts towards the Bodies; every Body endeavouring to go from the denser parts of the Medium towards the rarer? ...And though this Increase of density may at great distances be exceeding slow, yet if the elastick force of this Medium be exceeding great, it may suffice to impel Bodies from the denser parts of the Medium towards the rarer, with all that power which we call Gravity. And that the elastic force of this Medium is exceeding great, may be gather'd from the swiftness of its Vibrations.
    • Query 21
  • As Attraction is stronger in small Magnets than in great ones in proportion to their Bulk, and Gravity is greater in the Surfaces of small Planets than in those of great ones in proportion to their bulk, and small Bodies are agitated much more by electric attraction than great ones; so the smallness of the Rays of Light may contribute very much to the power of the Agent by which they are refracted.
    • Query 21
  • And so if any one would suppose that Æther (like our Air) may contain Particles which endeavour to recede from one another (for I do not know what this Æther is) and that its Particles are exceedingly smaller than those of Air, or even than those of Light: The exceeding smallness of its Particles may contribute to the greatness of the force by which those Particles may recede from one another, and thereby make that Medium exceedingly more rare and elastick than Air, and by consequence exceedingly less able to resist the motions of projectiles, and exceedingly more able to press upon gross Bodies, by endeavouring to expand it self.
    • Query 21
  • Are not all hypotheses erroneous, in which light is supposed to consist of a Pression or Motion, propagated through a fluid medium? ...If Light consisted only in Pression propagated without actual Motion, it would not be able to agitate and heat the Bodies which refract and reflect it. If it consisted in Motion propogated to all distances in an instant, it would require an infinite force every moment, in every shining Particle, to generate that Motion. And if it consisted in Pression or Motion, propogated either in an instant or in time, it would bend into the Shadow. For Pression or Motion cannot be propogated in a Fluid in right Lines, beyond an Obstacle which stops part of the Motion, but will bend and spread every way into the quiescent Medium which lies beyond the Obstacle. Gravity tends downwards, but the Pressure of Water arising from Gravity tends every way with equal Force, and is propogated as readily, with as much force sideways as downwards, and through crooked passages as through straight ones. The Waves on the Surface of stagnating Water, passing by the sides of a broad Obstacle which stops part of them, bend afterwards and dilate themselves gradually into the quiet Water behind the Obstacle. The Waves, Pulses or Vibrations of the Air, wherein Sounds consist, bend manifestly, though not so much as 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 propogated as readily through crooked Pipes as through straight ones. But light is never known to follow crooked Passages nor to bend into the Shadow. For the fix'd Stars by the Interposition of any Planets cease to be seen. And so do parts of the Sun by Interposition of the Moon, Mercury or Venus. The Rays which pass very near to the edges of any Body, are bent a little by the action of the Body, as we shew'd above; but this bending is not towards but from the Shadow, and is perform'd only in the passage of the Ray by the Body, and at a very small distance from it.
    • Query 28.

A Compleat System of Opticks (1738) edit

Robert Smith, A Compleat System of Opticks in Four Books, viz. A Popular, a Mathematical, a Mechanical, and a Philosophical Treatise. To which are added Remarks upon the Whole by Robert Smith LL.D. Professor of Astronomy and Experimental Philosophy at Cambridge, and Master of Mechanicks to his Majesty. Source.
  • Whoever has considered what a number of properties and effects of light are exactly similar to the properties and effects of bodies of a sensible bulk, will find it difficult to conceive that light is any thing else but very small and distinct particles of matter: which being incessantly thrown out from shining substances, and every way dispersed by reflection from all others, do impress upon our organs of seeing that peculiar motion, which is requisite to excite in our minds the sensation of light. But for the present purpose it is sufficient to observe that light consists of parts, both successive in the same lines and contemporary in several lines: because in the same place, you may stop that which comes one moment, and let pass that which comes presently after; and at the same time, you may stop it in one place, and let it pass in another. For that part of the light which is stopt cannot be the same with that which is let pass.
    • Book I, Ch. I.
  • The least light or part of light, which may be stopt alone, without the rest of the light, or propagated alone, or do or suffer any thing alone, which the rest of the light doth not or suffereth not, is called a Ray of light. That rays of light are straight, is evident enough from the shadows of bodies; or from the appearance of light passing through little holes into a dark room full of dust or smoke; or because bodies cannot be seen through the bore of a bended pipe; or because they cease to be seen by the interposition of other bodies, as the fixt stars by the interposition of the moon and planets; and the parts of the sun by the interposition of the Moon, Mercury or Venus. Rays of light may therefore be represented by straight lines, not Mathematical but Physical, which are described by the motion of the parts or particles of light: and the point which a ray possesses in falling upon any surface may be considered as a Physical Point.
    • Book I, Ch. I.
 
Robert Smith, Compleat System of Opticks in Four Books (1738) Fig. 1 & 2.
  • When a ray of light falls obliquely upon a smooth polished surface, it is turned out of its way either by reflection or refraction in the following manner. Imagine the paper upon which this figure is drawn to be perpendicular to the surface of stagnating water, and to cut it in the line RS, and that a ray of light, coming in the air along the line AC, falls upon RS at the point C. Then supposing the line PCQ... to be perpendicular to the surface of the water, if the ray be reflected, or turned back at C into the air again, it will describe a straight line CB, inclined to the perpendicular PC at an angle PCB exactly equal to the angle PCA.
    • Book I, Ch. I.
  • But if the ray that came along AC goes into the water at C, it will not proceed straight forward, but being refracted or bent at C, it will describe another straight line CE inclined to the perpendicular CQ at a lesser angle ECQ than the angle ACP; and the line CE will always be so situated, that when any circle, described about the center C, cuts the line CA in A and CE in E, the perpendiculars AD and EF, drawn from A and E to the line PQ shall always bear the same proportion to each other; whatever be the magnitude of the angle ACP. In water the line EF is always three quarters of AD. ...
    [T]he angle ACP [is] the Angle of Incidence, BCP the Angle of Reflection, ECQ the Angle of Refraction; the line AD the Sine of Incidence, that is, of the angle of incidence; and EF the Sine of Refraction, that is, of the angle of refraction.
    • Book I, Ch. I.
  • The foregoing properties of Reflection and Refraction being discovered and established by repeated experiments upon light and bodies of all sorts both fluid and solid, without any exception yet known; and being the principal foundation of the whole science of Opticks, are called the Laws of Reflection and Refraction; and are expressed by Sir Isaac Newton...
    • Book I, Ch. I.

History of the Inductive Sciences (1837) edit

by William Whewell
  • [T]he optical philosophers of antiquity had satisfied themselves that vision is performed in straight lines;— ...they had fixed their attention upon those straight lines, or rays, as the proper object of the science;—they had ascertained that rays reflected from a bright surface make the angle of reflection equal to the angle of incidence;—and they had drawn several consequences from these principles.
    We may add... the art of perspective, which is merely a corollary from the doctrine of rectilinear visual rays... The ancients practised this art, as we see in the pictures which remain to us; and we learn from Vitruvius, that they also wrote upon it. Agatharchus, who had been instructed by Eschylus... was the first author on this subject, and Anaxagoras, who was a pupil of Agatharchus, also wrote an Actinographia, or doctrine of drawing by rays... The moderns re-invented the art in the flourishing times of their painting... about the end of the fifteenth century; and... we have treatises on it.
    • Book IX, History of Optics, Formal and Physical, Formal Optics, Ch. 1 Primary Induction of Optics.—Rays of Light and Laws of Reflection.
  • Alhazen... asserted (lib. vii.), that "refraction takes place towards the perpendicular;" and reference is made to experiment for the proof. On the same ground he states that the quantities of refraction differ according to the magnitudes of the angles which the (primœ lineœ) directions of incidence make with the perpendicular to the surface; and moreover (which shows accuracy as well as distinctness,) that the angles of refraction do not follow the proportion of the angles of incidence.
    • Book IX, Ch. 2 Discovery of the Law of Refraction.
  • 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.
    • Book IX, Ch. 2.
  • 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.
    • Book IX, Ch. 2.
  • 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.
    • Book IX, Ch. 2.
  • [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.
    • Book IX, Ch. 3 Discovery of the Law of Disperion by Refraction.
  • 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.
    • Book IX, Ch. 3.
  • [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.
    • Book IX, Ch. 3.
  • 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.
    • Book IX, Ch. 3.
  • 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.
    • Book IX, Ch. 3.
  • 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.
    • Book IX, Ch. 3.
  • 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.
    • Book IX, Ch. 3.
  • 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.
    • Book IX, Ch. 4 Discovery of Achromatism.
  • 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.
    • Book IX, Ch. 4.
  • John Dollond, 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.
    • Book IX, Ch. 4.
  • 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.
    • Book IX, Ch. 4.

The Wonders of Optics (1871) edit

by Fulgence Marion, translated from French by Charles W. Quin, source.
  • 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 occultations 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.

Prismatic and Diffraction Spectra: Memoirs (1899) edit

Joseph von Fraunhofer, Tr. J. S. Ames, source.
  • 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.
    • New Modifications of Light by the Mutual Influence and the Diffraction of Rays, and the Laws of this Modification
  • 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.
    • New Modifications of Light by the Mutual Influence and the Diffraction of Rays, and the Laws of this Modification
  • 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 theodolite-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.
    • Prismatic and Diffraction Spectra

A History of the Theories of Aether and Electricity from the Age of Descartes to the Close of the Nineteenth Century (1910) edit

by E. T. Whittaker: source
  • Descartes's theory of light rapidly displaced the conceptions which had held sway in the Middle Ages. The validity of his explanation of refraction 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 "Newton's rings"; 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 diffraction.
  • 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.

The Rainbow: From Myth to Mathematics (1959) edit

by Carl B. Boyer
  • (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.

Tunable Laser Optics (2003) edit

by F. J. Duarte
  • 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.
    • "Introduction to Lasers"
  • 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.
    • "Introduction to Lasers"
  • The intimate relation between interference and diffraction has its origin in the interference equation itself.
    • "Dirac Optics"
  • Multiple-prism arrays were first introduced by Newton (1704) in his book Opticks. 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.
    • "The Physics of Multiple-Prism Optics"

See also edit

External links edit

 
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