Optics

OPTICS. - This name originally denoted that part of physics which deals with the modes of luminous phenomena. By light is meant a something which, coming — directly or not — from the surrounding bodies, makes them visible to our eyes. With respect to light, bodies are distinguished into luminous and dark. Luminous, or sources of light, are the bodies from which it emanates directly: every body becomes luminous when its temperature is raised considerably (gas lamp, electric lamp, etc.). The others, dark, are distinguished into opaque or transparent according as the light is stopped by them or not.

The vision of dark bodies is brought about inasmuch as the light that strikes them is thrown back by them to a greater or lesser degree in all directions. This is the phenomenon of the diffusion of light, which occurs when the surface of the body struck by the light is rough. In the opposite case, that is, when a beam of light reaches a flat and smooth surface (e.g., a metal plate), it is thrown back in a single direction or, as is usually said, reflected. The direction of the reflected beam of light depends on that of the incident light according to a physical law known by the name of the law of reflection.

If the smooth surface of the body on which the light arrives is not opaque but transparent, as, for example, the free surface of water, the luminous beam divides into two parts, one of which is reflected in the manner mentioned above, while the other penetrates into the interior of the body, following however a direction generally different from that of the incident beam of light. In this case the light is said to have undergone a refraction. The laws that govern the phenomenon of refraction are two; demonstrated experimentally by Snell in 1615, they were rediscovered theoretically in 1637 by Descartes, so that they are generally known by the name of Descartes' laws.

In the laws of reflection and refraction and in the two principles of the rectilinear propagation of light and of the dependence of luminous rays are substantially summed up the basic conceptions acquired over the many centuries of investigation into the nature of light and the modes of the phenomena pertaining to it. Such investigations begin with the brilliant and somewhat fanciful intuitions of the Greek thinkers from Pythagoras and Democritus to Plato and Aristotle; they continue with the O. of Euclid (a mere treatise on the geometry of vision and of reflection, linked to Pythagorean conceptions), the Catoptrics of Archimedes, the O. of Hero of Alexandria (in which the principle of the rectilinear propagation of light and the law of reflection are enunciated) and finally with the O. of Ptolemy (which contains the first systematic experimental studies on refraction) and arrive at the O. of Alhazen (al-Hasan), an Arab researcher who lived around the year 1000. An inquiring, independent and original spirit, Alhazen gathered in his work, which nevertheless retains a distinctly geometric character, numerous experimental data, acute observations on the mechanism of vision, the study of refraction in a sphere, from which his commentator Kāmil ad-dīn al-Fārīsī deduced the interpretation of the rainbow, etc.

That light propagates in a straight line is a datum of daily observation: this also occurs over distances far greater than terrestrial ones: the existence of eclipses bears witness to it.

The principle of the rectilinear propagation of light does not hold rigorously, but only as a first approximation. The light emitted by a point source, which passes through a hole made in an opaque screen, gives an image exactly aligned with them: this is proof of the rectilinear propagation of light. But if one is able to diminish gradually the dimensions of the hole, one sees that, when they are quite reduced (less than a millimeter), the image of the hole widens and appears surrounded by rings, alternately dark and light (the latter iridescent if the light emitted by the source is white). The image is therefore no longer aligned with the small hole: this means that the light coming from it does not propagate in a straight line, but scatters in every direction. Every time that the light emitted by sources of small dimensions passes through very narrow apertures, whatever their shape, this phenomenon occurs, known by the name of diffraction of light. It also appears when obstacles of tiny dimensions (wires, etc.) are interposed in the path of the light, or at the edges of very sharp obstacles.

From daily observation it is also inferred that two or more beams of light can cross without the path and the intensity of each of them appearing influenced by the other. In this consists the principle of the independence of luminous paths, which is susceptible to a criticism analogous to that exercised with regard to the principle of the rectilinear propagation of light. It is in fact possible to establish particular conditions that give rise to the phenomenon of luminous interference. As early as the 17th century Francesco M. Grimaldi (to whom belongs the merit of the discovery of diffraction), collecting on a screen the cones of light that departed from two nearby small holes, made in the shutter of a window, would have observed the appearance of alternations of light and shadow. But only at the beginning of the 19th century, after the interference phenomena had been reproduced and observed in numerous and disparate experiments (among which that of Newton's rings has remained famous) without any plausible explanation having been given for them, Thomas Young performed in an exact manner the interference experiment intuited by Fr. Grimaldi, at the same time providing its correct interpretation. The modification made by Young to Grimaldi's experiment consisted in illuminating the two small holes with light not coming directly from the sun, but made to pass beforehand through a first hole, so as to experiment with two luminous beams emitted from a single point source, the hole illuminated by the sun. Under these conditions, on the screen that collects the two luminous beams and precisely in the zone in which these, widened by diffraction, come to overlap, there appears an alternation of dark and light bands (the latter iridescent), the so-called interference fringes: the principle of the independence of luminous rays is no longer satisfied.

The fundamental problem of o. is that concerning the nature of light. The various hypotheses formulated since antiquity on the nature of light converged into two main currents. One of them, whose origin is to be traced in the atomistic conceptions of Democritus, identified light with an effluvium of particularly tenuous atoms which, emitted by luminous bodies along rectilinear trajectories, reach the eye, provoking vision. Among the supporters of this "corpuscular" theory are to be remembered Gassendi, Descartes and above all Newton.

Already more than a century earlier, taking up again the Aristotelian conception, which attributed vision to the disturbances produced by the color of a body or by fire or by other agents in an indeterminate medium filling all spaces, Leonardo da Vinci had asked himself whether the propagation of light might not occur in a manner analogous to that in which the disturbances excited in liquids propagate, as, for example, when a stone falls into stagnant water, that is, by waves; so that, as he himself admirably expresses it with regard to water, "the motion of the impression is accompanied only by the impetus and not by the motion of the water itself." The true initiator of the wave theory, however, is Christiaan Huygens: according to the great Dutch physicist, light is nothing other than a movement "by waves and spherical surfaces" of a certain matter interpenetrating all space, to which he gives the name ether, just as sound consists in an analogous movement of the air. Such waves move "with a successive movement" without transport of the "ethereal matter": from every single ethereal particle the movement is communicated to the contiguous particles in such a way that each of them becomes the center of a secondary wave whose propagation is independent of that of the others.

The envelope of all the secondary waves generated by one and the same wave constitutes the wave successive to it. In this consists Huygens' principle (1658), from which he deduced in a simple and immediate manner the interpretation of the phenomena of reflection and refraction, without realizing that by means of it he could have explained with equal ease the diffraction experiments carried out by Grimaldi.

Nevertheless, more than a century had to pass before the substantial clarification brought about by this principle was understood in all its importance.

The corpuscular theory had as its supporter Isaac Newton, whose authority was such that the wave hypothesis was practically abandoned at the beginning of the 18th century. From this epoch onward, research in optics was entirely founded on Newtonian conceptions and was practically directed toward overcoming the enormous obstacles encountered in the attempt to interpret on such bases the phenomena of diffraction, interference and dispersion. For although from the corpuscular theory one manages to deduce a more or less valid and persuasive interpretation of the experimental laws of reflection and refraction (admitting, as for example Gassendi did, that reflection occurs with a mechanism analogous to the rebound of an elastic ball against a wall, and that refraction is to be attributed to the oblique impact of the atoms of light against the refracting medium), unless one has recourse to particularly cumbersome and muddled mechanisms, which one might almost call absurd, one does not arrive with the same theory at an explanation of the deviations from the principle of rectilinear propagation and from the principle of the independence of light rays, nor of the phenomenon of dispersion.

This latter phenomenon was observed for the first time by Newton, who, sending onto a glass prism a narrow beam of solar light coming from a thin slit, observed on the screen that collected the light at the exit of the prism not the image of the slit, but rather a luminous strip or spectrum, in which the colors of the rainbow followed one another without interruption. Newton succeeded, inversely, in achieving the synthesis of the colors in solar light and understood that the latter is formed by the mixture of differently colored lights. Dispersion, that is, the decomposition of light into its individual components, is performed by the prism with a mechanism of which the English physicist, misled by his conceptions about the corpuscular nature of light, was unable to give an account.

Only at the beginning of the 19th century was the wave theory taken up again by Young, who, having supposed that the ethereal particles oscillate about their position of rest in the direction of propagation of light, succeeded in interpreting the experiment he set up along the lines of Grimaldi's as a phenomenon of reinforcement and cancellation of the wave motion, and also succeeded in explaining the chromatic phenomena in thin films and the coloration of striated surfaces.

The result of Young's research was not received favorably by his contemporaries. Meanwhile a great fervor of experimental investigations on light was spreading everywhere: Herschel and Ritter observed that the luminous spectrum extended beyond the red and respectively beyond the violet; Young himself became aware of the fact that radiant heat differed from light only by a greater wavelength; Malus, finally, demonstrated experimentally that light, after having undergone a reflection or a refraction, or after having passed through certain particular crystals, acquires some characteristics that vary with the azimuth relative to the direction of propagation. This latter phenomenon was called by Malus himself, who attempted to explain it on the basis of corpuscular conceptions, polarization of light.

So rich a harvest of experimental data, together with Young's considerations, was gathered by Augustin Fresnel, who between 1814 and 1816 developed a mathematical theory that came to form, so to speak, the skeleton of the wave hypothesis, while at the same time he devised and carried out (alone or in collaboration with F. Arago) a series of experiments to confirm and consolidate this theory. Taking as his starting point Huygens' principle and confirming Young's interference conceptions, he arrived at an explanation of the phenomena of diffraction, dispersion, and polarization, in the form in which they are still interpreted today.

The essential conceptions about the nature of light and its propagation, which constitute the principal result of Fresnel's scientific work, may be summarized as follows: a) the mechanism of propagation of light consists in a wave motion of an elastic medium, the ether, which occupies all space: this movement occurs according to the modalities established by Huygens' principle. It follows that the wave character of luminous propagation is revealed only when light encounters on its path obstacles whose dimensions are comparable with its wavelength (diffraction). b) The wavelength of visible luminous radiations is between 4 and 8 x 10⁻³ cm. The diversity of wavelength of a radiation appears to our visual sense as a difference of color, so that every color is characterized by a well-determined value of wavelength. Solar light and, in general, all those luminous radiations that are commonly called white, are the result of the superposition of radiations of all wavelengths, that is, of all colors. The dispersion of light performed by the prism is due to the fact that the magnitude of the refraction of a monochromatic light wave depends on the wavelength, that is, on its color. c) The movement of the ethereal particles at a point is the resultant of the movements that would be produced there by the action of the individual luminous sources: from this follows the interpretation of interference phenomena according to Young's conceptions. d) The oscillations of the ethereal particles occur perpendicularly to the direction of propagation of light.

This last assertion, in contrast with Young's hypothesis, which held that the luminous oscillations occur along the direction of propagation, is the result of the studies conducted by Fresnel on the phenomenon of polarization, of which he gave a simple and convincing interpretation.

Fresnel's work gave a new impulse to research in optics and on the other hand aroused a luxuriant flowering of investigations into elasticity, inasmuch as the hypotheses concerning the mechanism of light propagation, on which Fresnel's theory was founded, proposed a series of new problems in the field of elasticity. The principal conquests, achieved around 1805 through the work of a great number of distinguished scholars (Poisson, Cauchy, Green and Lamé) may be summed up in the following affirmation, which was to carry very great weight in subsequent research: the ether behaves with respect to the propagation of light as a perfectly elastic and incompressible rigid solid; in it the propagation of light takes place by transverse waves.

The enormous difficulties encountered in the attempt to reconcile the concept of a rigid solid ether with the freedom of movement of bodies, especially celestial ones, are easily intuited. In particular, the inference was drawn from it that, as a consequence of the earth's rotation, the earth ought to be struck by an "ether wind" and at the same time would drag the ether along with it.

Everyday observation led the most ancient thinkers to hold the propagation of light to be instantaneous: but already Hero rejected the hypothesis of instantaneity, affirming that, on the contrary, the propagation of light must be immeasurably rapid. Galileo took up this problem again; he intuited that the velocity of light must be finite, and in proof of this he devised certain experiments (1638) without, however, succeeding in his aim because of the inadequacy of the experimental means. The attempt was renewed in 1663 by the Accademia del Cimento, without any result. In 1676 the Danish astronomer Römer reported a periodic irregularity in the appearance of the eclipses of the first Medicean satellite: Huyghens, who for his part was also convinced that the propagation of light took place at a finite velocity, attributed the periodic advances and delays discovered by Römer to the variations in the time taken by light to travel the Earth-Jupiter distance, as a consequence of the different positions occupied by Jupiter with respect to the earth.

On the basis of such considerations Huyghens calculated that the velocity of light must be around 212,000 km/sec.

About two centuries after the attempt of the Accademia del Cimento, that is in 1849, Fizeau devised, and successfully carried out, an experiment for the terrestrial measurement of the velocity of light. The following year, with a more elegant experimental device, Foucault demonstrated that the velocity diminishes in more refracting bodies; and thus definitively brought down the corpuscular theory. Between 1840 and 1850, M. Faraday, perhaps inspired by the new theory on light propagation, abandoned the conception then universally accepted, which attributed the electric and magnetic phenomena of action at a distance between electric charges (and, respectively, between magnetic poles) and suggested a new scheme on the basis of which the reciprocal actions between electric charges or between magnetic poles are transmitted by the intervening medium. On Faraday's hypothesis James C. Maxwell based himself in order to establish his theory of electromagnetism, a admirable synthesis, in which electrical phenomena are interpreted as elastic actions of the medium interposed between the electric charges or the magnetic poles. From the four famous equations by means of which Maxwell expressed the properties of the perturbation, or, as it is usually called, of the electromagnetic field, one derives the equations of propagation of an electromagnetic field in motion in a homogeneous medium, which is the seat neither of free electric charges nor of conduction currents.

The formal identity existing between such equations and the equations of propagation of elastic waves proves that the propagation of electromagnetic actions takes place by waves and is not instantaneous, but possesses a finite velocity.

These considerations led Maxwell to recognize in light waves a particular case of electromagnetic waves: the principal consequence of such a supposition is that the velocity of light should be equal to that of electromagnetic waves. Experience confirmed this hypothesis. The Maxwellian theory of electromagnetism, perfected by Heaviside, received its definitive seal from the discovery of Hertzian waves (1888). In the following years Hertz himself, A. Righi and others succeeded in establishing an optics of Hertzian waves, reproducing with them the principal phenomena already observed for light (reflection, refraction, polarization, etc.) in complete confirmation of the Maxwellian hypothesis on the basis of which one could foresee that electromagnetic waves, generated by means of oscillators, differ from luminous ones only in wavelength, varying from a few thousand m. to a few cm.

In 1912 Laue, using as diffraction gratings the periodic structures of crystallized matter, succeeded in proving that even with the radiation discovered about twenty years earlier by Röntgen, the so-called X-rays, one could obtain experiments of diffraction and interference. The further research of Bragg, Siegbahn and Larson, etc., confirmed that even these radiations, which are of electromagnetic nature and differ from light solely in the brevity of the wavelength (less than 10⁻⁸ cm.). Towards that same epoch, finally, the emission by radioactive elements of X-rays of even shorter wavelength (less than 10⁻¹¹ cm) was proved, to which the name of γ rays was given.

Thus light waves definitively came to form part of a much broader category, that of electromagnetic waves, whose wavelengths extend from the Hertzian ones up to the γ rays on a vast scale comprised between a few thousand m and 10⁻¹¹ cm. In it the zone of the "visible", that is of light, according to the definition given at the beginning, is represented by a narrow interval, comprised between 4 and 8 × 10⁻³ cm. It has been seen how the electromagnetic theory was expressed by Maxwell in terms drawn from the theory of elasticity. The analogy is purely formal, but neither Maxwell nor the scientists who subsequently interested themselves in these problems realized it. Consequently it continued to be admitted for a long time that the propagation of electromagnetic waves takes place through the cosmic ether. In reality such an affirmation is not a necessary support of the electromagnetic theory, since the concept of ether is essential only for the problems of electrodynamics of bodies in motion, inasmuch as it would come to constitute a privileged system of reference (v. RELATIVITÀ).

When Michelson's experiment had demonstrated the non-existence of such a system, the independence of the Maxwellian theory from any elastic model finally became manifest. Electromagnetic phenomena, optical ones included, were then framed in a logical scheme, founded exclusively on the concepts of electric and magnetic field, without any need to resort to the hypothesis of the ether as a medium of propagation. Thus one of the greatest obstacles fell, which, as has been seen previously, had been opposed to the affirmation of the wave theory in the form in which it had been expressed by Fresnel. In this scheme light may be considered as a particular action at a distance between the light source and the illuminated body, dependent on both, not transmitted by any hypothetical medium and delayed in time: in other words one may also say that "light is a transfer of energy delayed in time".

The fact remains that from experimental observation one deduces solely the existence of a light source, of an illuminated body, and of an action at a distance, delayed in time, to which a transfer of energy is connected, likewise delayed in time, without being able to ascertain anything of what happens along that transfer. The localization, or rather the "visualization," of light cannot be achieved except through processes of absorption by atoms, which substantially alter the phenomenon.

In other words, an experiment that would allow the revelation of the passage of a photon or of a wave without perturbing its path is conceptually impossible. According to Heisenberg's principle one must therefore admit that the concept of "propagation" is devoid of any meaning; just as the theory of relativity had taught us to do without the ether, this principle imposes the renunciation of the definition of the trajectory of a photon, inasmuch as it cannot be revealed by any experiment. It will therefore be legitimate to speak of photons, provided that, renouncing the tracking of each individual photon in its movement, one limits oneself to seeking the number of photons received by the retina, or by a screen or by a photographic plate. The only task that the theory is capable of fulfilling is that of teaching how to calculate this number on the basis of the position of the screen, of the source, and of all the optical instruments required for the realization of the experiment. These recent considerations offer an interpretation of the electromagnetic theory of light and explain its inability to account for the photoelectric effect and for other phenomena as well.

From the rigorous revision of the principles on which the quantum theory and the electromagnetic theory of light were founded, one has arrived, through the renunciation of every superfluous conception, at the overcoming of the contrast existing between the two theories, which thus come to form a single synthetic vision.

The possibility, indeed the necessity, of resorting to the two conceptions, quantum or electromagnetic, according to the type of phenomena examined, can find further clarification in the crisis that, in those same years, the conceptions relating to the nature of matter were undergoing, so to speak, in the opposite sense. At the end of the last century, while the wave nature of light was being definitively confirmed, no one any longer doubted the discontinuous character of matter (molecules, atoms, etc.). It has been seen, however, how in the following years the corpuscular conception of light became increasingly established. Through a critical procedure analogous to that followed in the investigations into the nature of light, L. De Broglie arrived at admitting the possibility of a wave character of matter (1924). Three years later De Broglie's hypothesis, developed and completed subsequently by Schrödinger, Heisenberg, Born and others, found its confirmation in the experiments of Davisson and Germer, who, following the methods adopted by Laue and by Bragg for the study of X-rays, succeeded in carrying out a diffraction experiment with a beam of electrons. Thus electron optics arose, which has offered to modern technology the electron microscope and other valuable instruments.

The experiment of Davisson and Germer was repeated with molecular beams in 1931 by Estermann, Frisch and Stern. Thus the possibility for matter, as for radiation, of presenting itself under the two aspects, wave and corpuscular, was definitively established.

Camilla Festa