S. I. Vavilov’s Book The Microstructure of Light *)

V. A. Fabrikant

With a bitter sense of fresh loss one takes up this small book, which unexpectedly became the final result of S. I. Vavilov’s work on the fundamental problems of optics.

We wish to emphasize that the book deals indeed with a number of fundamental problems of optics. The book shows the breadth and depth of S. I. Vavilov’s scientific interests. It reflects the image of S. I. Vavilov as a scientist, best characterized by the word natural philosopher.

S. I. Vavilov was never satisfied with a formal solution of a problem and always provided direct experimental confirmations of basic theoretical propositions. It is no accident that the end of the preface to the book is devoted to formalism, which still has a place in the solution of a number of problems of optics.

Alongside questions of luminescence, which constituted the leitmotif of S. I. Vavilov’s scientific work, the book sets forth important results obtained by him in other areas of optics. It is essential to note that the questions of luminescence themselves are treated from the standpoint of their general significance. The book clearly shows how incorrect is the generally accepted point of view that the study of complex objects by means of comparatively simple methods cannot yield clear and fundamental results. S. I. Vavilov showed that the study of the luminescence of complex molecules provides an effective path for elucidating the general properties of elementary radiators.

The purpose of the present article is to give a brief exposition of the main content of the book. The task is not an easy one, for the book itself already represents a very compressed survey and contains an enormous amount of material.

) S. I. Vavilov, The Microstructure of Light (Studies and Essays)*, Academy of Sciences of the USSR, Moscow, 1950, 198 pp.

In the preface S. I. explains the somewhat unusual title of the book and thereby defines the range of problems touched upon in it.

He writes: “... it is always tacitly assumed that any light source and any luminous flux can be fully characterized by three features: the energy of the radiation, the spectrum, and the state of polarization. In reality this is practically sufficient only for solving problems of macro-optics, the optics of considerable light powers, long observation times, and large dimensions of the radiation source. Behind macro-optics there lies micro-optics, differing from the former in certain respects just as the thermodynamic theory of matter differs from its molecular theory” (an obvious misprint—it should be the other way round.—V. F.).

Micro-optics includes: fluctuations of the luminous flux, the interference properties of very small radiators, manifestations of the lifetime of excited states of molecules and, finally, interactions of luminous molecules with the surrounding medium.

Accordingly, the contents of the book are divided into three parts. 1) experimental studies of light fluctuations by the visual method; 2) on the premises and some conclusions of the elementary theory of light interference; 3) properties of light emitted by an absorbing medium.

Let us pass to an exposition of the concrete contents of the individual parts of the book.

1. EXPERIMENTAL STUDIES OF LIGHT FLUCTUATIONS BY THE VISUAL METHOD

For observing light fluctuations it is naturally necessary to experiment with very weak light sources or luminous fluxes. It is interesting that “These two conditions are not equivalent for the classical (wave) and quantum consideration of the problem” (p. 9).

According to classical notions, “... light fluctuations must depend to a very great extent on the physical state of the light source...” (p. 10).

“The quantum nature of radiation radically changes the character of fluctuation phenomena. Even... when from the classical point of view light fluctuations may be absent, quantum fluctuations must manifest themselves fully, determined by the so-called ‘spontaneous’ independence of the acts of radiation of individual molecules” (p. 10).

For the particular case of absolutely black radiation, Einstein’s formula is valid (p. 10):

\[ \overline{(\Delta E_0)^2}=h\nu E_0+\frac{c^3}{8\pi\nu^2\Delta\nu}\cdot\frac{E_0^2}{v_0}, \tag{1} \]

where \(E_0\) is the radiation energy; \(\overline{(\Delta E_0)^2}\) is the mean square fluctuation; \(v\) is the volume of the black-body cavity, \(\nu\) is the frequency, \(\Delta \nu\) is the frequency interval under consideration. The first term on the right-hand side of (1) represents quantum fluctuations, and the second term “classical” fluctuations.

The first term can be obtained from the most elementary statistical considerations that take into account the quantum nature of radiation.

The second term begins to play a noticeable role only at temperatures on the order of \(30\,000^\circ\).

Quantum fluctuations should be observed independently of the state of the light source, provided there is sufficient resolution of the observed light flux.

The experimental investigation of light fluctuations is of great interest for two reasons: 1) the observation of quantum fluctuations is direct confirmation of the quantum nature of radiation; 2) the observation of “classical” fluctuations provides a new method for investigating the physical conditions existing in the light source (for equilibrium radiation, the determination of temperature, while for nonequilibrium cases it may yield results not at all described by formula (1)).

S. I. Vavilov proposed using observations of light fluctuations in both directions, but, unfortunately, he managed to complete only the first series of studies, devoted to quantum fluctuations.

The experimental method he used is remarkable for its simplicity.

Under proper conditions the human eye proves to be the best receiver for the study of light fluctuations in the visible part of the spectrum.

First of all, the minimum visually perceptible energy amounts to only 100–200 photons falling on our eye per second. A considerably smaller number of photons undoubtedly reaches the retina. An even smaller number of photons is absorbed by the retina. The number of absorbed photons is measured in a few tens.

Under such conditions the fluctuations of the absorbed energy must be very large.

“It is important to emphasize that visual observation and measurement (of fluctuations.—V. F.) is greatly facilitated by the presence of a sharp threshold of visual sensation. The visual effect in the region of the threshold changes continuously; it falls very rapidly to zero at some ‘threshold’ value of the light energy” (p. 14).

However, in order to make use of these advantages of the eye as a receiver of radiant energy, it is necessary to create the corresponding conditions.

Therefore S. I. Vavilov sharply criticizes Barnes and Czerny, who correctly predicted the possibility of visually observing light fluctuations, but who set up entirely erroneous experiments for realizing this possibility.

The fluctuations observed in these experiments were caused purely by physiological reasons (the absence of a fixation point).

S. I. Vavilov points out that: “...the observation of quantum fluctuations in a continuous light flux is impossible owing to the finite duration of the visual impression and the averaging of fluctuations that follows from this. Nor is the observation of fluctuations possible for large angular dimensions of the luminous surface. Furthermore, to observe quantum fluctuations it is necessary to fix the eye (in view of the unequal sensitivity of the individual points of the retina.—V. F.)” (p. 14).

Consequently, for the observation of physical fluctuations at threshold light fluxes, three conditions must be satisfied:

1) the flashes must be short-lived,
2) the image on the retina must be small, and
3) the eye must be fixed.

In addition, peripheral vision should be used, corresponding to the greatest sensitivity of the eye.

Owing to the presence of a sharp threshold, those flashes whose energy is less than a certain limiting value are not visible at all.

If by \(n_0\) we denote the number of photons corresponding to the threshold, then only flashes corresponding to a number of photons greater than \(n_0\) will be visible.

Fig. 1. Probability \(P\) as a function of
\[ \frac{1-x}{\sqrt{x}} . \]

If \(n\) is the average number of photons absorbed per unit time, then, as S. I. Vavilov showed, the probability of observing a flash can be determined by means of the approximate formula (formula (13), p. 17)

\[ P=\frac{1}{2}-\frac{1}{2}\sqrt{\frac{n_0}{2}\,\frac{(1-x)}{\sqrt{x}}}, \tag{2} \]

where

\[ x=\frac{n}{n_0}. \]

In Fig. 1 (Fig. 1, p. 17) the exact course of \(P\) is shown as a function of

\[ \frac{1-x}{\sqrt{x}} . \]

Formula (2) corresponds to the middle rectilinear part of the curve.

The slope of the rectilinear part of the curve makes it possible to determine \(\eta_0\) directly. It is important to note that even if \(\eta_0\) itself undergoes fluctuations, formula (2) is nevertheless suitable for determining the mean value of \(\eta_0\).

In constructing the experimental apparatus, all the requirements formulated above were taken into account.

The book contains an interesting photograph “from a bird’s-eye view” of the first experimental apparatus of 1933 for measuring visual quantum fluctuations.

In Fig. 2 (Fig. 3, p. 20) a diagram is shown of a later version of the experimental apparatus.

Fig. 2. Diagram of the second apparatus for measuring visual quantum fluctuations.

The light of lamp \(L\) was reflected from the mirror \(m\), passed through the diaphragm \(O\), covered with milk glass, and fell on a slowly rotating disk (1 revolution per second) with an aperture \(D\). The disk transmitted the light for 0.1 sec. and blocked it for 0.9 sec. A green filter selected the required portion of the spectrum. The light could be attenuated by means of a stack of glass plates \(P\) and a wedge \(K\). To fix the eye, so that the light from lamp \(L\) would fall continuously on one and the same point of the periphery of the retina, a second lamp \(S\) with a red filter was used. The angular distance between the red and green spots was usually equal to \(8^\circ\).

The revolutions of the disk were recorded by a chronograph on a tape. By pressing a key, the observer marked on the same tape the flashes visible to him. At high brightnesses of the green spot, naturally, the revolution marks coincided with the flash marks.

When the brightness was reduced, omissions began to appear in the observer’s counts. Processing of the tapes showed that a typical fluctuation pattern was observed.

In Fig. 3 (Fig. 6, p. 25) are presented the results of measurements by four observers, which are in good agreement with formula (2).

In general, a large number of observers were involved in these experiments, and an enormous amount of statistical material was collected.

Fig. 3. Results of fluctuation measurements by four observers.

The data obtained made it possible to determine \(n_0\). For different observers \(n_0\) ranges from 8 to 47. The number of photons \(N\) incident on the eye in this case ranges from 108 to 335. Thus, as a by-product, it proved possible to determine what fraction of the photons incident on the eye is actively absorbed by the retina. The ratios obtained agree fairly well with physiological data.

In 1941, G. Hecht and his collaborators repeated S. I. Vavilov’s experiments (though on a considerably smaller scale) and obtained approximately the same results.

In his first publication, G. Hecht kept silent about S. I. Vavilov’s priority. In a detailed article of 1942 he did so, however, in a form that provoked sharp and justified criticism from S. I. Vavilov (note on pp. 32–33).

“In 1944,” writes S. I. Vavilov, “the method of visual quantum fluctuations was once again ‘discovered’ in Utrecht by van der Velden” (p. 34). This author at first did not refer at all

...to his predecessors, and then began to refer only to the American works. The results obtained in the Dutch works sharply diverge from the results of other works and arouse strong doubts (\(n_0 = 2!\)). Finally, Baumgardt (Paris), in a book published in 1950, reports analogous measurements carried out in his laboratory and gives results that agree with the data of S. I. Vavilov.

If the principal fluctuation experiments were later repeated by other researchers, then a number of interesting data were obtained only by S. I. Vavilov and his collaborators.

These include the dependence of \(n_0\) on wavelength, the influence of raising the threshold, and, finally, observations of fluctuations of coherent beams, fluctuations of polarization, and fluctuations in the interference field.

In the experiments with fluctuations of coherent beams, the arrangement shown in Fig. 2 was used. Only a Fresnel biprism with a refracting edge positioned horizontally was placed between the disk and the eye. Thus, in the field of view two coherent spots are visible, symmetrically situated with respect to the red fixation point.

When the threshold brightness is reached, both points fluctuate quite distinctly relative to one another. The probability of the simultaneous observation of both spots is obviously equal to \(P^2\). In other words, the square root of this probability must satisfy formula (2).

The experimental results of these difficult measurements confirm this conclusion.

S. I. Vavilov writes: “This phenomenon of independent relative oscillations of coherent rays has a catastrophic significance for the wave theory...” (p. 48).

For observing polarization fluctuations, a Wollaston prism was used. In this case the two green spots were polarized in mutually perpendicular planes.

As in the preceding experiment, both spots fluctuated completely independently.

In Fig. 4 (Fig. 14, p. 49), along the ordinate axis is plotted \(\sqrt{p}\) (\(p\) is the probability of simultaneous observation of two spots) as a function of \(\dfrac{1-x}{\sqrt{x}}\). We see that the fundamental relation (2) is again excellently satisfied.

Fig. 4. Results of the experiment with polarized rays.

Observations of fluctuations in the interference field were carried out on the same apparatus as all the other experiments, but a Young double slit and a diaphragm with two apertures were placed in the path of the rays. One aperture was located opposite a bright interference fringe, and the other opposite a dark fringe. The fluctuations of the bright interference fringe were observed and quantitatively measured. The dark fringe remained dark throughout.

“Before the observer in this experiment there appears with particular vividness the corpuscular-wave duality of the light process” (p. 129).

The entire totality of S. I. Vavilov’s fluctuation experiments is striking for the skill with which the properties of such an “instrument” as the human eye are used.

The results of these experiments have not only important physical significance, but also provide new information about the eye itself.

It would be very interesting to develop the second line of fluctuation research (“classical” fluctuations) outlined by S. I. Vavilov.

2. ON THE PREMISES AND CERTAIN CONCLUSIONS OF THE ELEMENTARY THEORY OF THE INTERFERENCE OF LIGHT

In this part there is a distinctive and very successful combination of the exposition of the author’s original works with considerable didactic material. It would seem that it is already difficult to say anything new in so well-established a field of optics as interference.

However, S. I. Vavilov did so, and did so with genuine brilliance. In his hands the old tree of classical optics once again began to bear fruit.

It is enough to mention the establishment of a connection between wide-angle interference and the properties of elementary emitters, and the discovery of the Cherenkov effect.

The second part begins with a brief analysis of the advantages and shortcomings of interference as a method and as a principle. Characteristic of S. I. Vavilov is the reproduction of two pages from L. Euler’s New Theory of Light and Colors (1746), establishing his priority in creating the concept of light beams as sharply bounded channels within which light energy propagates in a wave-like manner; this concept, as is known, played a substantial role in the development of the theory of interference.

There follows an exposition of the results of S. I. Vavilov’s works concerning the verification of the limits of applicability in vacuum of the fundamental principle of optics—the principle of superposition. This is the question of the self-scattering of light, a phenomenon which Lomonosov called “interference in rays.” Experiments with a powerful spark (1928–1930), light

which converged inside an evacuated vessel, gave a negative result. Here, a comparison of two light sources with the same average power, but with a sharply different concentration of radiation density in time, was ingeniously used. The radiation density reached \(10^{11}\dfrac{\text{erg}}{\text{sec}\cdot\text{cm}^2}\).

From data on the brightness of the solar corona, an estimate was made of the greatest magnitude of light scattering, which does not exceed \(1.8\cdot 10^{-17}\) per one centimeter of the path of a light ray. In the case of a spark it follows from this that, to detect deviations from superposition, a receiver is needed that responds to a radiation power of less than \(1.8\cdot 10^{-12}\dfrac{\text{erg}}{\text{sec}}\).

When light propagates in an absorbing substance, the question of the limits of applicability of the principle of superposition is more complicated. Here the quantum properties of radiation and of the absorbing molecules can lead to a violation of the principle of superposition and thereby make the wave equation for light waves nonlinear.

In 1920 S. I. Vavilov published the results of experiments testing the independence of light absorption from brightness over wide limits. In these experiments, in measurements, the existence of the visual threshold was used for the first time.

The brightness of the source was changed by the incandescence of the lamp, and the difficulty associated with the change of the spectrum when the incandescence changed was elegantly avoided. Not the radiation of the lamp itself was used, but the rhodamine luminescence excited by it, which in this case preserved its spectral composition.

Gelatin films stained with rhodamine, aqueous solutions of rhodamine, fuchsin, and other dyes were investigated.

When the density of the light flux was varied from \(2.5\cdot 10^{-12}\) to \(2\cdot 10^{8}\dfrac{\text{erg}}{\text{sec}\cdot\text{cm}^2}\) (i.e., over twenty orders of magnitude!), the absorption proved constant to an accuracy of up to 5%.

S. I. Vavilov recalls that in those years Planck, in the second edition of his well-known book on thermal radiation, proposed a very peculiar variant of quantum theory.

According to this variant, molecules absorb light continuously, but emit it in quanta. S. I. Vavilov’s experiments were in sharp contradiction with this conception, for at the very lowest intensities the time required for the accumulation in a molecule of one quantum would have exceeded thirty million years! At the upper limit of intensities this time became of the order of \(10^{-5}\) sec.

In the first case, according to Planck’s hypothesis, the substance should be completely opaque, while in the second it should possess normal transparency.

In later experiments by S. I. Vavilov and V. L. Levshin, noticeable violations of linearity were discovered in measurements of the absorption of uranium glass. This is a purely quantum effect, connected with the finite lifetime of excited states, to which attention is rarely paid.

As a result of excitation, the number of absorbing centers may decrease appreciably when the lifetime of the excited states is sufficiently long, whereas the absorption coefficient of classical oscillators, of course, does not depend on the amplitude of their oscillations. In phosphors, large nonlinear effects of this type are observed. The nonlinearity of phosphors was even used to construct an original photometer without a comparison lamp. “However, physics has become so accustomed to the linearity of ordinary optics that even now there is still no formally rigorous mathematical apparatus for solving real ‘nonlinear’ problems” (p. 73).

Giving a very profound and lucid exposition of the foundations of the theory of interference, S. I. Vavilov shows the possibility of obtaining coherent, but noninterfering, light beams. Of great interest is the reduction of any interference to the interference of parallel and antiparallel beams (p. 87).

Along with this it is noted that coherent light may be obtained from two different particles of matter located at a distance measured by several particle diameters (p. 78).

Judging by the concreteness of the remarks, S. I. Vavilov had in mind the setting up of the corresponding experiments.

S. I. Vavilov introduces the term “Fresnel interference” for interference between different beams propagating from one and the same luminous point, and contrasts it with “Newton interference,” which arises when a single beam is split. He considers Fresnel interference in particular detail, as directly connected with the properties of radiation sources.

Here one should note the transparent analysis of the question of the resolving power of interferometers and the detailed examination of the role of the dimensions of the source. The latter is done as preparation for an exposition of S. I. Vavilov’s truly classical experiments on wide-angle interference.

The history of these experiments is interesting. In his report to the physics section of a conference at Moscow State University in 1944, S. I. Vavilov said (Priroda, 1945, No. 4): “In 1923 there appeared Schredinger’s experimental work. It was devoted precisely to the question of interference at large angles from a thin incandescent tungsten filament; moreover, at an angle of about 60° Schredinger did not notice any peculiarities of the interference pattern. The experiments were set up to solve a question then of current interest …”

about whether the so-called “needle radiation” (Nadel-Strahlung) exists, the possibility of which, from the quantum point of view, was pointed out by A. Einstein. What is curious here is that Schrödinger did not notice that the classical theory of radiation also leads to the necessity of unusual phenomena in the interference of rays at large angles.

In ordinary interference experiments we always deal with small angles. To observe wide-angle interference, light sources of exceptionally small dimensions, comparable with the wavelength of light, are necessary. This is the difficulty in observing wide-angle interference. But wide-angle interference provides a new method for studying the properties of elementary emitters. The model of a radiating atom or molecule in the form of a linear electric dipole, as is known, passed from classical physics into quantum physics. Quantum mechanics gives a method for calculating the radiation of such a dipole that leads to results agreeing with experiment. One of the most characteristic properties of a dipole is the directionality of its radiation, Fig. 5 (Fig. 29, p. 106). At the same time, in analyzing interference experiments we usually make use of a simplified conception of the elementary emitter. S. I. Vavilov writes: “The usual simplified conception of an isotropically luminous point must be assigned to the group of entirely abstract and erroneous images, since not one real elementary emitter can correspond to it” (p. 105). However, it is easy to see that when observing the interference of rays forming small angles, the directionality of the radiation of elementary emitters is practically immaterial; the intensities radiated by a dipole in two nearby directions are practically equal to one another.

Fig. 5. Plane diagrams of the spatial radiation of an electric dipole and a quadrupole.

The situation changes sharply when observing wide-angle interference, when the angle between the rays is large. It should be remembered that, in essence, waves emerging from one and the same emitter are coherent with one another. Consequently, the chaotic arrangement of the dipoles changes little, and one cannot speak of characteristics of the emitters averaged over directions. A ray emitted by some emitter “recognizes,” upon meeting, another ray emitted by the same emitter, and only with it will it interfere. Therefore, what is important is the ratio of the amplitudes of precisely these rays, emerging from a single elementary emitter in entirely different directions (we intentionally use the language of the elementary theory of interference).

In Fig. 6 (Fig. 32, p. 107) two arrangements of the radiating dipole \(O\) are shown for observing interference in the limiting case when the angle between the rays is \(180^\circ\). The mirrors \(S_1\) and \(S_2\) form angles of \(45^\circ\) with the direction of the rays and make them parallel. Next one should imagine an objective which brings both rays together in its focal plane, where the interference pattern arises. The vectors \(A\) and \(B\) depict the light vibrations. We see that in the first case there will be, as usual, a bright fringe at the center of the interference pattern, but in the second case a dark fringe will be obtained, despite the equality of the optical path lengths! With a chaotic arrangement of dipoles, each of them can be resolved into three components, one of which is directed along the line of observation and is insignificant, while the other two are mutually perpendicular and correspond to cases \(a\) and \(b\) of Fig. 6.

Fig. 6. A radiating dipole between mirrors turned by \(45^\circ\) to the axis connecting them:
\(a\)—the dipole is perpendicular to the plane \(S_1AS_2B\);
\(b\)—the dipole is parallel to the plane \(S_1AS_2B\).

It is clear that the simultaneous existence of two dipoles \(a\) and \(b\) will lead to the disappearance of the visibility of the interference pattern*) (the bright fringe of case \(a\) coincides with the dark fringe of case \(b\)), but it is not difficult to see that an interference field uniform in intensity will possess a striped polarization structure, owing to the fact that in some places horizontal vibrations will be annihilated (for example, at the center), and in others vertical ones. When observed through a Nicol prism, interference fringes should arise, shifting by one fringe when the Nicol is rotated by \(90^\circ\). S. I. Vavilov considered the general case when the angle between the rays is equal to \(\varphi\). Then the visibility of the interference pattern (without a Nicol) is equal to

\[ V=\frac{1+\cos\varphi}{2}. \]

For quadrupoles one obtains

\[ V=\frac{1+\cos\varphi}{2}-\sin^2\varphi. \]

Thus, by observing the dependence of the visibility of the interference on the angle, one can determine whether the elementary radiators are dipoles or quadrupoles.

) Schrödinger would have drawn the conclusion of the incoherence of the rays, i.e. of “needle radiation”! — V. F.*

In carrying out experiments on wide-angle interference, S. I. Vavilov and E. M. Brumberg used an ultramicroscopic setup. The microscope objective was covered with a diaphragm with two apertures. The angles between the rays were varied within the range from 10 to 130°. The light sources were the tiniest crystals of uranyl nitrate suspended in paraffin oil. Either the crystals’ own glow resulting from luminescence was observed, or the light scattered by the crystals. The results obtained agree brilliantly with the considerations set forth above. In particular, the disappearance of interference fringes was observed at a sufficiently large $\varphi$, and the appearance of fringes when a Nicol prism was introduced between the eyepiece and the eye. These experiments and their theory should enter physics courses as an excellent illustration of the fundamental properties of elementary emitters.

The book devotes attention to distinctive interference paradoxes that testify to the inadequacy of the usual description of the properties of natural light. “Let two different media be placed in the path of two parallel coherent quasi-monochromatic natural beams interfering with one another—one rotating the plane of polarization, the other inactive, ... with the optically active medium rotating the plane of polarization ... by 90°. Both beams, having passed respectively through the active and inactive media, remain natural, i.e., ... should remain experimentally indistinguishable from one another. In reality, under interference their difference must be revealed. Under the specified conditions (despite the coherence!—V. F.) the beams will not interfere... Such an interference experiment makes it possible to carry out a measurement that at first glance seems impossible and internally contradictory, namely: to determine the rotation of the plane of polarization of unpolarized light” (pp. 118–119). A similar experiment is possible with a plate in a half-wave. These experiments of S. I. Vavilov are new interference experiments of great fundamental significance.

Altogether five pages of the book are devoted to the remarkable Cherenkov effect, discovered under the direction and with the direct participation of S. I. Vavilov. In recent years the great importance of this effect for various areas of physics, and not only for optics in the narrow sense of the word, has become clear.

It is important to note that this effect is in essence a purely “classical” effect and follows directly from the most elementary interference considerations. S. I. Vavilov writes: “Here no general theory of the new phenomenon is reproduced; Cherenkov radiation is considered here because, at least in its elementary interpretation, it represents a very interesting and highly instructive example of the application of the interference method in optics” (p. 120).

As is known, Cherenkov radiation arises when electrons move in a medium with a velocity exceeding the phase velocity of light in that medium.

S. I. Vavilov gives an elementary and clear exposition of the theory of Cherenkov radiation, developed by I. M. Frank and I. E. Tamm, using throughout the method of Fresnel zones. As a result of the interference of coherent secondary waves emitted by the molecules of the medium, perturbed by the field of the passing electron, there arises a resultant wave propagating at an angle \(\theta\) to the direction of flight of the electrons. The angle \(\theta\) is determined by the simple formula (formula (68), p. 124)

\[ \cos \theta = \frac{c}{nv}, \tag{3} \]

where \(v\) is the velocity of motion of the electrons, and \(n\) is the refractive index of the medium. What is fundamental here is that, from the macroscopic point of view, Cherenkov radiation is not the result of accelerated motion of a charge, in contrast to all previously known types of radiation. This was not understood by the American researchers who repeated Cherenkov’s experiments.

S. I. Vavilov also gives an elementary quantum derivation of formula (3).

From formula (3) follows the principal remarkable property of Cherenkov radiation—its directionality. Despite the brevity of the exposition, it is characteristic that S. I. Vavilov draws the reader’s attention to certain conclusions from the interference interpretation of Cherenkov radiation that had not yet been verified experimentally. In particular, he points to the possibility of observing the Cherenkov effect at electron velocities lower than the velocity of light, but when experimenting with thin films (p. 124).

3. PROPERTIES OF LIGHT EMITTED BY AN ABSORBING MEDIUM

This part begins with a very fresh and profound formulation of the question of the applicability of the separate concepts of “light source” and “medium”:

“Optics, in almost its entire scope, is built upon the tacit assumption that the properties of light and its internal structure are entirely determined by the characteristics of the source and of the medium, separately characterized by constant quantitative features....

Such an assumption, however, is valid only approximately and there are cases—often and practically important—in which it is necessary to abandon it and pass to a more general conception of source and medium as a whole, organically connected....

...The premise mentioned above for solving optical problems concerning the possibility of a separate interpretation of the light source and the medium ...”

actually equivalent to the assumption that the distance \(r\) between the radiating particles of the substance and the particles that absorb or scatter light is much greater than the length of the light wave \(\lambda\)... This assumption is almost always strictly satisfied if processes occurring in the light source itself are excluded from consideration, and it is assumed that the medium in which the light propagates does not itself emit light...

Strictly speaking, they can never be used for the vast range of everyday cases involving media that glow and at the same time absorb light. Such are, first of all, the light sources themselves (incandescent bodies, gas-discharge and luminescent lamps) and, further, media that scatter light and luminesce” (pp. 133–134).

S. I. Vavilov emphasizes that “the active role of neighboring molecules capable of absorbing light is usually lost from view. Owing to resonance, such particles can act on the luminous center and change the character of its radiation (above all, weaken it), while distant molecules only passively absorb light. In addition, neighboring molecules determine the initial, principal link in the process of displacement (migration) of the excitation energy in the medium” (p. 134).

S. I. Vavilov points out that the simplest and clearest conditions for observing phenomena connected with the indicated interactions of molecules are found in liquid and solid luminescent media. In the present case, the condensed phase of a substance has an advantage over the gaseous one, for it “does not allow interacting neighboring molecules to move away from one another during the short time of the excited state” (p. 134).

“It is important to emphasize once again that in solutions of complex molecules resonant inductive transitions must occur more often, because the viscosity of the medium makes it difficult for interacting molecules to separate appreciably during the excited state; as a result, resonance can develop fully even when the ‘sharpness of tuning’ is insufficient” (p. 144).

Thus the fruitfulness of experimental investigations of the luminescence of liquids and solids for solving the basic problem of source—medium becomes clear.

In analyzing the possible effects in this case, S. I. Vavilov draws attention to the existence of a “feedback” between nearby molecules, which in the case of complex molecules must lead to a nonselective weakening of the radiation energy (quenching).

In addition, absorption of radiation by a layer of nearby molecules must be anomalous. Under ordinary conditions, with a large thickness of the entire luminescent layer, this effect is masked

with normal absorption by the distant layers, but in experiments with thin layers anomalous absorption must come to the fore.

Finally, the above-mentioned migration of energy will affect quenching and cause depolarization of the radiation.

S. I. Vavilov notes that in the literature an incorrect notion has become established regarding the migration of energy without the mediation of radiation as a purely quantum effect. In fact, this effect should also occur according to classical conceptions, by virtue of the inductive interaction of nearby dipoles.

Strictly speaking, from the standpoint of the problem of source–medium, the book also presents the principal results of a number of works by S. I. Vavilov, his collaborators, and his students on the study of luminescence.

This problem proved to be the axis around which an enormous body of theoretical and experimental material was grouped.

The difficulty of all these experiments lay in separating “nontrivial” changes of light, connected with the indicated effects, from “trivial” ones caused by ordinary repeated absorption and emission over large distances. The “trivial” effects naturally increase with the thickness of the layer. The “nontrivial” effects persist at such small thicknesses when ordinary absorption and re-emission can no longer take place. However, the “nontrivial” effects are connected with the overlap of the absorption and emission spectra (F. M. Pekerman), just as are the “trivial” ones.

An increase in concentration leads to a decrease in the distance between molecules and, consequently, to an intensification of the interaction between them. In Fig. 7 (Fig. 44, p. 141) are shown the characteristic “nontrivial” dependences on concentration of the degree of polarization, the lifetime of the excited state, and the yield of luminescence.

Attempts to explain the course of these curves on the basis of the overly concrete structure of molecules had until then led to contradictions with experiment. S. I. Vavilov therefore chose a different, semi-phenomenological path, leaving aside the law of interaction of molecules.

This methodological device proved exceptionally successful in the present case. It was possible not only to explain many facts, but also to predict a number of new facts, which were soon discovered.

The history of science knows many examples of such reasonable and successful restriction of the tasks of theory at a definite stage of its development. It seems to us that, in choosing the path for solving this problem, not the least role was played by S. I. Vavilov’s works in the field of the history of science and philosophy.

In the book, the theory developed by S. I. Vavilov is set forth in fairly great detail. In this theory there figure the probabilities of various processes occurring inside molecules (internal quenching) and arising in the interaction of molecules with one another, while at first the structure of the molecules is not specified at all.

Fig. 7. Change in the degree of polarization $\dfrac{P}{P_0}$, the yield $\dfrac{L}{L_0}$, and the mean duration of the excited state $\dfrac{\tau}{\tau_0}$ in a solution of fluorescein in glycerine at room temperature.

For the consideration of concentration depolarization, it was, of course, nevertheless necessary to make the model of the molecule somewhat more concrete. As such, in agreement with the experimental data, a dipole was adopted.

This leads to the following formula (formula (57), p. 157) for the degree of polarization at small concentrations:

$$ \frac{1}{P}=\frac{1}{P_0}+\frac{1}{P_0}\,\frac{3-P_0}{3}\,\frac{c\tau_0}{k^2}, \tag{4} $$

where $\dfrac{1}{k^2}$ usually has the meaning of the rate of increase of the sphere of action of a molecule after the onset of resonance coupling between neighboring molecules, i.e. the rate of establishment of resonance coupling. This formula agrees with the experimental data of B. Ya. Sveshnikov and P. P. Feofilov.

Energy migration must lead to depolarization of the radiation during the period of luminescence decay. Here the predictions of the theory

proved to be in good agreement with the results of the experiments of A. N. Sevchenko and M. D. Galanin.

The book gives the corresponding experimental data and discusses in detail the features of the observed regularities.

The theory of concentration quenching does not make use of any specific model of the molecule. It is clear that energy migration must lead to an intensification of quenching. The book gives intermediate derivations leading to the formula for concentration quenching. This formula, in its general form, contains five constants. S. I. Vavilov writes: “These constants are empirical, but they are not arbitrary; they are quite definite, since they enter into the expressions for other independent physical processes” (the processes of decay and depolarization are meant.—V. F.) (p. 172). The book presents extensive experimental material accumulated by S. I. Vavilov’s collaborators and quantitatively confirming the theory of concentration quenching based on the concept of energy migration.

The same theory also accommodates the “nontrivial” quenching by extraneous absorbing substances. This quenching arises as a result of inductive resonance coupling between the luminescing molecules and the molecules of the quencher. Therefore the quenching is accompanied by a shortening of the lifetime of the emitting molecules.

Perhaps the most elegant experiments confirming the concept of energy migration are the experiments on depolarization and quenching of luminescence in a “one-dimensional” medium (pp. 187–189).

For these experiments, “porous” glass of I. V. Grebenshchikov was used. In this completely transparent glass there are long pores with a diameter of the order of \(10^{-6}\) cm. The glass is impregnated with a luminescing solution. The distance between the luminophore molecules under quenching is just of the same order. “Most of the dissolved molecules will therefore be arranged one after another, ‘one-dimensionally,’ in the form of chains” (p. 187).

In the “one-dimensional” case each molecule has fewer neighbors than in the normal, three-dimensional case, and therefore the quenching should be smaller. The curves in Fig. 8 (Fig. 60, p. 188) show that this is indeed so.

“‘One-dimensional’ experiments ... may be regarded as a new, very distinctive argument in favor of the theory of resonance migration of excitation energy” (p. 189).

The book concludes with a description of experiments by S. I. Vavilov and M. D. Galanin on the study of absorption in thin luminescing layers. In accordance with what was said above, they found an absorption anomaly associated with the interaction of nearby molecules.

Indeed, it was found that the “coefficient of selective absorption at distances smaller than \(\lambda\) from the emitting molecules begins to increase, and the more so, the smaller the thickness. ... The newly discovered experimental phenomenon is insignificant in magnitude, but it has fundamental significance—it seems to throw a bridge between ordinary optics, with source and medium separated, and the optics of emitting and absorbing media, when the concepts of source and medium are difficult to separate” (p. 193).

Fig. 8. Concentration quenching of solutions of acid dyes: \(a\)—aqueous fluorescein solution; \(б\)—alkaline solution of sodium salt of perylenetetracarboxylic acid. \(1\)—quenching in a cuvette; \(2\)—quenching in porous glass (according to measurements by F. M. Pekerman).

Our review, of course, cannot convey the full richness of the contents of S. I. Vavilov’s book.

Before us, undoubtedly, are entirely new chapters of optics. Old, familiar concepts acquire another, deeper meaning, and new problems arise. The boundaries of the old “linear” optics become clear, and paths for the further development of optics open up.

The book as a whole represents at once both a summing-up and a program for further action.

Unfortunately, the realization of this program will take place without its author.