STANDING LIGHT WAVES; REPETITION OF WIENER’S EXPERIMENT ON A PHOTOELECTRIC SURFACE*

F. Ives and T. Fry

In 1890 Wiener** carried out his experiment, which became widely known in optics. Placing a photographic layer at a small angle to a metallic mirror and illuminating it, he found in the developed layer traces of the antinodes and nodes of standing light waves. Later a similar experiment was performed by Drude and Nernst, who detected standing waves by means of a thin fluorescent layer. In both experiments the observed effect was associated with the electric vector.

Investigations carried out by us recently, and aimed at clarifying the influence of purely optical factors on the photoelectric effect in thin films of alkali metals, have led us to the conclusion that the photoelectric emission of such films is directly connected with the amount of energy absorbed by the film. In accordance with this point of view, which has already received sufficient substantiation¹, the effects observed in polarized light are a natural consequence of the fact—following from a detailed analysis of the optical data—that the amount of energy absorbed by a thin layer differs very greatly from that which would be absorbed if volume absorption by the illuminated metal played a substantial role, as had previously been assumed. We can calculate the absorption of the film from the optical constants of the film and of the metal on which it is placed. The method of calculation is equivalent to determining the interference pattern above the surface of a pure metal and the “immersion” following from it of the film of the alkali metal into the interference pattern. From this point of view, the thin film of alkali metal here plays the role of the test surface in the experiments of Wiener and of Drude and Nernst, with the distinction, however, that it does not form an angle with the reflecting surface, as in those cases, but is in close contact with it. The experiment we propose, undertaken by us for the purpose of further experimental confirmation of our theory of photoelectric action, consisted in raising the light-sensitive film to various heights above the surface of the metal reflecting the light; in doing so we attempted to establish whether changes in the flux of energy, as found by calculation, affect photoelectric emission. The experiment so arranged is, in essence, a modification of Wiener’s experiment and justifies the title of the article chosen by us.

The idea of the experiment is explained by Fig. 1. In the lower part of the figure the metal serving as a substrate is shown, for example a piece of platinum. On it, on its left side, a thin layer of alkali metal is deposited, which, on the basis of various considerations, should be regarded as consisting of one or two atomic layers. On the left is shown the dependence of the energy density, plotted in arbitrary units, on the distance to the surface for the case when the electric vectors of rays incident at an angle of 60° are directed respectively parallel (case I) and per—

* F. Ives and Fry, Journ. Opt. Soc. America, 23, 74, 1933, translated by S. V. Cherdynsev.
* See Wood, Optics*, 2nd ed., p. 175, where a detailed description is given of both the experiment mentioned in the text and other experiments with standing waves.

perpendicular (case ⊥) to the plane of incidence. It should be expected that inside the alkali-metal layer the intensity in case (∥) will be much greater than in case (⊥), since experiment shows that the photocurrent in the first case is much stronger. In addition, it should be expected that at different distances from the surface the ratios of the intensity values corresponding to cases (∥) and (⊥) will vary widely from one another.

In the right-hand part of Fig. 1 the alkali-metal film is raised above the surface of the plate. It is obvious that, in the position shown here, this film will successively intersect the nodes and antinodes of the standing light waves, and we should expect that changes in the photocurrent will correspond to changes in the intensity in the interference pattern depicted at left. Thus, for example, at the height marked by the lower dashed straight line, the currents in cases (∥) and (⊥) will be the same, whereas at the height corresponding to the upper dashed straight line the ⊥-current will be much stronger than the ∥-current, which contradicts the phenomenon usually observed.

Fig. 1. Schematic reproduction of the experiment.

It is practically impossible to raise the alkali-metal film while leaving it suspended in the air; therefore it is necessary to place some support beneath it. We used as such a support a quartz wedge obtained by evaporating or sublimating a tungsten filament coated with quartz. By properly choosing the distance and position of the filament relative to the platinum plate, one can obtain a wedge-shaped layer of quartz, the thickness of which is smaller the greater the distance from the given point of the layer to the filament. This wedge-shaped layer is then coated with a film of alkali metal, which is sufficiently uniform in thickness, since the discussion concerns qualitative investigations.

By introducing a reflecting layer of quartz, we thereby change the distribution of energy to some extent, but this change can be taken into account by calculation and thus its influence on the results of the experiments can be eliminated. The experimental part of the work consists chiefly in fabricating a quartz wedge in an evacuated tube and in introducing into it a small amount of alkali metal, for example cesium, which is evaporated until a photoelectrically sensitive conducting film forms on the wedge. The photoelectric emission of different regions of the film, corresponding to different wedge thicknesses, is then investigated at various angles of incidence, states of polarization, and wavelengths of light. For comparison, calculations were made of the densities of electrical energy at different points of an ideal wedge from the optical constants of the substances used. Agreement of the experimental data with the calculated data should serve as a criterion for the applicability of the assumptions made by us concerning the role of optical factors in the photoelectric effect in thin films.

Experimental setup

The diagram of the photocell used in our work is reproduced in Fig. 2. The quartz wedge on the platinum (W), prepared by the described

in the manner described above, is fixed on a sliding support connected with the iron part \(I\), and by means of an external magnet can be moved along the tube to ensure uniform coverage of the cesium layer, as well as for its convenient positioning inside the collector. The tube has the form of a cylinder and is mounted so that it can be moved parallel to its horizontal axis and rotated in such a way that light can fall on the plate at any desired angle. The rotating screw is provided with a dial for counting the angles. Cesium is introduced by distillation into the side tube \(B\), whence a small quantity of it can be transferred into the main tube, so as to serve as a supply for spontaneous evaporation at room temperature, which proves sufficient for the formation of a photosensitive film. One of the greatest experimental difficulties in these experiments consists in the fact that cesium diffuses throughout the tube, depositing on all the walls, in consequence of which leakage currents arise. To reduce the latter to a minimum, the tube was made very long, and the anode was placed in a glass envelope closed at the end from which the lead-in wire was introduced. In addition, cesium was introduced in a very small amount, and the experiments were carried out with cesium films that had not reached full development; nevertheless, the sensitivity of the film proved sufficient for accurate measurements.

Fig. 2. Diagram of the photocell.

It remains to describe briefly the appearance and properties of the quartz wedge deposited on platinum. In reflected light, a series of faintly colored interference bands is visible in the wedge, at intervals of approximately \(4\text{–}5\ \mathrm{mm}\) from one another. After the wedge has been for a long time in contact with alkali-metal vapors, the bands acquire an intense coloration, owing to secondary reflection of light from the cesium layer toward the platinum surface. At the ends the wedge becomes almost black, especially in its thicker parts. It is possible that part of the absorbed light should be attributed to a slight granularity (frilling) of the quartz layer, and there is no doubt that this roughness depolarizes the light, thereby distorting the results of measurements of the photoelectric effect under the action of light polarized in a given plane. In the present work all measurements were made with cesium films whose thickness was so small that their influence on the distribution of intensity in the interference pattern could be neglected. For larger film thicknesses this influence must be taken into account in the calculations, which entails undesirable complications.

The light source was an incandescent lamp with a tungsten filament, provided with a quartz window. The light passed through a quartz monochromator and was polarized by means of a quartz double-image Rochon prism. Behind it, in the path of the double beam, was placed a variable-angle prism composed of two wedges of fused quartz; by rotating it, the transition was effected from one plane of polarization of the light to any other. The light spot on the photocell had a diameter of about \(1\ \mathrm{mm}\), and the optical part of the setup was illustrated in such a way that

STANDING LIGHT WAVES

the spot did not shift noticeably when the plane of polarization was rotated. The photocurrent was measured with a Compton electrometer with current leakage resistance according to the constant-deflection method.

Calculation of the intensities in the alkali-metal film

The method of calculation that we used is, in the main, quite analogous to the method published in one of our earlier works*. There it was shown that the electric-field intensity inside the film and, in the case of a deposited massive substrate, can easily be determined with the aid of certain preliminary calculations dealing with reflection from a clean surface. The entire computational process may be divided into the following stages:

a) First we ignore the presence of the film and determine the phase and amplitude of the electric-field intensity in the reflected ray near the reflecting (clean) surface.

b) The intensity found in this way is added vectorially to the electric-field intensity in the incident ray; thus the resultant field intensity \(E\) is determined, which we would have in the absence of the film.

c) Then we take into account the presence of the film, for which the normal component \(E_z\) is reduced by a certain numerical factor \(\dfrac{g}{g_1}\), dependent on the optical constants of the film. In the case of waves, this factor replaces the multiplier by which one must multiply the gradient of the potential when passing through a surface separating two media with different dielectric constants**.

In this way we find the normal component of the electric-field intensity \(E_1\) inside the film, and the tangential component \(E_1\) remains equal to the tangential component of \(E\).

In another of our papers***, it was shown that the absorption \(A_z\) by a thin film (lamellar absorbing power) is proportional to the quantity \((E_1)^2\), or, in accordance with what was said above,

\[ (E_x)^2 + |E_y|^2 + \left|\frac{g}{g_1}\right|^2 |E_z|^2 . \]

We can therefore determine the amount of energy absorbed by the film directly from

\[ |E_x|^2,\quad |E_y|^2,\quad |E_z|^2 \]

and the factor

\[ \left|\frac{g}{g_1}\right|^2 . \]

Our present problem differs from the one we analyzed only in that, in the case of interest to us, the substrate is no longer homogeneous; it now consists of massive platinum covered with a layer of quartz. But since this difference changes nothing in the above reasoning, we can calculate the absorption coefficients by the same formula as before, now understanding by \(E_x\), \(E_y\), and \(E_z\) the components of the electric-field intensity directly above the complex sur-

* The limit of film thicknesses for which the approximate theory under consideration is permissible is indicated in footnote 4 on p. 322 of the cited paper.

** In the case where the film has magnetic permeability equal to 1 and is in contact with air or vacuum, the ratio \(\dfrac{g}{g_1}\) becomes simply equal to \(\dfrac{1}{(N+iK_0)^2}\), where \(N\) and \(K_0\) are the optical constants of the film.

*** See footnote 4, p. 324. For absorption in thin films, Fry introduces the new term lamellar absorbing power, as distinct from bulk absorbing power (absorption of a massive substance). This term can be applied not only to a free film or to a film placed on the surface of another substance (cesium–silver), but also to the surface layer of the massive metal itself. Thus, for example, the author calculated lamellar absorbing power for the case “silver on silver,” and it turned out that the course of these absorption curves differs sharply from the course of the absorption curves for massive silver, known from optical data (see Fig. 23 in Savostianova’s paper, “Selective Photoeffect”). Translator’s note.

city of the quartz plate. If, however, we assume that the thickness of the quartz wedge does not change over the region occupied by the light spot (but changes as the light spot is displaced along the wedge), then the amplitude and phase of the reflected ray, and consequently also \(E\), can readily be determined from the results of another of our articles.

Thus we have at our disposal all the data necessary for carrying out the computational part of our work. Nevertheless, presenting the results in graphical form would be rather difficult in practice, were our problem not simplified by the circumstance that the quartz thickness \(t\) and the wavelength of light enter the formula for reflection only in the form of the ratio \(\frac{t}{\lambda}\), which we can therefore introduce as the single variable. The curves shown in Fig. 3 reproduce the results of the calculations for various angles of incidence. On the abscissas everywhere is plotted \(\frac{t}{\lambda}\).

To explain the ordinates of these curves, we shall have to go back and recall the course of our reasoning. We indicated that the absorption coefficient of our film is proportional to

\[ \left|E_x\right|^2+\left|E_y\right|^2+\left|\frac{g}{g_1}\right|^2\left|E_z\right|^2, \]

but we have not yet said anything about the coefficient of proportionality. Using the exact formula (89) in the article “Plane Waves of Light III,” we find that this coefficient contains as a factor the expression \(\frac{1}{\lambda \cos I}\), as well as other factors independent of \(\lambda\), \(t\), and \(I\), and therefore of no interest to us. Denoting them together by the letter \(B\), we obtain:

\[ \lambda A_L = B\left( \left|E_x\right|^2+\left|E_y\right|^2+ \left|\frac{g}{g_1}\right|^2\left|E_z\right|^2 \right)\sec I. \]

Fig. 3. Calculated energy density on the surface of a quartz wedge deposited on platinum, as a function of the ratio of thickness to wavelength.

Now we can explain the meaning of the ordinates of our curves: along the ordinates are plotted the quantities

\[ \left|E_x\right|^2\sec I,\quad \left|E_y\right|^2\sec I,\quad \left|E_z\right|^2\sec I, \]

which enter the expression for \(\lambda A_L\).

STANDING LIGHT WAVES

It is very simple to use our graphs. If the polarization of the light is such that the electric vector is perpendicular to the plane of incidence, then \(E_x\) and \(E_z\) are zero and the absorption coefficient of the film is determined directly, up to a constant factor, by dividing the ordinate of the \(y\)-curve by the wavelength \(\lambda\). If, however, the electric vector is parallel to the plane of incidence, then the ordinate of the \(z\)-curve should be multiplied by the “inhomogeneity factor” \(\left|\dfrac{g}{g_1}\right|^2\) and added to the ordinate of the \(x\)-curve. Dividing the result by \(\lambda\), we obtain (up to the same constant factor \(B\)) the absorption coefficient for this plane of incidence.

For a certain given wavelength and a certain given angle of incidence, the change in the absorption coefficient as the light spot moves along the wedge may be determined from the change of the ordinate of the curve corresponding to the given angle of incidence, when moving along the abscissa axis. In this case there is not even any need to divide by \(\lambda\), since for the given curve \(\lambda\) is constant and may be included in the factor \(B\).

Similarly, if the position of the light spot on the wedge is fixed and the angle of incidence is varied, then in order to determine the change in the absorption coefficient one must collect the points of the various curves lying on one vertical straight line intersecting the whole family of curves. The divisor \(\lambda\) can again be regarded as included in the numerical factor \(B\).

If, however, we are interested in the change of the absorption coefficient with wavelength, while all other quantities remain constant, then we must choose the curve corresponding to the given angle of incidence and regard the wavelengths, in reciprocal scale, as plotted along the abscissa axis. In this case the divisor \(\lambda\) is of essential significance.

Examples of curves obtained by these methods will be given below, in comparison with the results of experiments and calculations.

Turning once more to the curves in Fig. 3, let us note that we acted, strictly speaking, not quite correctly in using only one pair of values of the optical constants of platinum \((N = 1.866,\ K_0 = 2.726)\) and one value \((N = 1.4602)\) of the refractive index of quartz. No appreciable errors can arise from this in the present case, in view of the fact that these quantities remain practically constant over the entire visible spectrum. However, an exact theory must take into account the change of the optical constants with wavelength.

Experimental results

The experiments whose results will be presented here were carried out with two tubes of different construction. The first of them, owing to certain design imperfections, could be used only at large angles of incidence of light on the plate; with this tube measurements were made at an angle of incidence equal to \(60^\circ\): the change of the photocurrent was investigated with displacement along the wedge and with change of wavelength at a fixed angle of incidence. The second tube, free from this shortcoming, was used to investigate the dependence of the photocurrent on the angle of incidence of light. Of course, one cannot expect a direct connection between the two series of measurements, corresponding respectively to the two tubes, but this is of almost no importance, since any dependence of interest to us can be followed within one of the two series of measurements.

Let us first consider the change of the photocurrent with the thickness of the wedge. The measurements give curves of the type shown in Fig. 4, where along the abscissa axes is plotted, in millimeters, the distance of the light spot on the wedge from the zero line (the latter could be determined quite accurately). The hydrogen method of preparing the wedge does not allow one to assert that it has in ...

in cross section, a triangular shape. Therefore the abscissas should be considered as arbitrary reference points placed in order of increasing thickness of the wedge. Examining the curves in Fig. 4, we are convinced that the conclusions of the theory are essentially confirmed by experiment. On

Fig. 4. Calculated and observed values of the photocurrents as the spot is moved along the wedge; angle of incidence \(=60^\circ\).

the photoelectric emission curve we see successive maxima and minima. The curves corresponding to the two different polarization planes of the incident light intersect each other periodically. In this way it is possible, with sufficient accuracy, to determine the interval of wedge thicknesses covered by these measurements. For example, it was found that points \(1\) and \(12\), at wavelength \(\lambda=5461\ \text{Å}\) and angle of incidence \(60^\circ\), correspond to the values

\[ \frac{t}{\lambda}=0.51 \quad\text{and}\quad \frac{t}{\lambda}=1.22, \]

as is seen from the broken curves calculated in the upper drawing of Fig. 3, carried out in

assuming that \(\left|\dfrac{g}{g_1}\right|^2=1\). For the wavelength \(7000\) Å, at the boundaries of the interval we have, by virtue of the inverse proportionality to the wavelength, \(\dfrac{t}{\lambda}=0.4\) and \(\dfrac{t}{\lambda}=0.95\). From these data the discontinuous curves in the lower drawing were constructed, the maxima and minima being displaced in exactly the direction expected.

It should be noted that, for a number of reasons, we are entitled to expect only qualitative agreement between theory and experiment, as well as agreement in the positions of the maxima. Indeed, first, the dimensions of the light spot cannot be regarded as small in comparison with the length of the interference fringes observed on the wedge. Secondly, the quartz wedge undoubtedly scatters a considerable fraction of the light, in consequence of which its transmission changes and the surface ceases to be mirror-reflecting, as the theory requires. This circumstance causes, among other things, a decrease of the photocurrent with increasing wedge thickness. The fact that the upper surface of the wedge is, in all probability, not plane we have already indicated. These, to a greater or lesser degree inevitable, deviations from the ideal conditions manifest themselves in the fact that the maxima and minima become less sharply expressed and their position is displaced somewhat. Taking these limitations into account, the agreement between theory and experiment must be recognized as quite satisfactory.

Let us now turn to the curves of the distribution of photoelectric emission over the spectrum for different positions of the light spot on the wedge. In Fig. 5, in the upper left-hand corner, the dependence of the photocurrent on the wavelength is given for pure platinum; this curve was taken from a portion of the cathode screened off from the filament, which served to ignite the quartz. The emission increases with decreasing wavelength, and it proves somewhat greater in the case when the electric vector of the incident light is polarized in the plane of incidence, which is characteristic of very thin cesium films on platinum. In the wavelength interval studied there are neither maxima nor minima. The other curves in Fig. 5 (except the lower right) represent the observed spectral distribution of the photocurrents, respectively, for points 4, 7, 10, and 13 on the wedge. These curves differ greatly in form both from the preceding curve and from one another. They show not only sharply expressed maxima and minima of emission within the visible spectrum, but also a periodic alternation in the magnitude of the photocurrent for the two planes of polarization. We observe neither maxima resembling those obtained upon sensitization of the surface by a silent discharge nor those obtained by other known methods.

Our curves 3 make it possible to compare the experimental results obtained with the theoretical conclusions. For a complete comparison it would be necessary to know both the intrinsic photoelectric emission of the layers of the alkali metal, as a function of wavelength, and the factor at \(E_z\), which takes account of the influence of the optical constants of the film. But at present we do not yet have any sufficiently definite data for these quantities for cesium. The factor at \(E_z\) undoubtedly depends on the structure of the film, and we cannot even be certain that it remains one and the same when a film is formed on pure platinum and on a quartz substrate. In view of this incompleteness of our knowledge, we had to proceed in a simplified way: we multiplied the experimental emission curve for cesium on pure platinum (the left upper part of Fig. 5) by the ratio of the emissions, taking it from curves 3, doing this for different values of \(\dfrac{t}{\lambda}\), the scale for the \(\parallel\)- and \(\perp\)-curves being chosen in an arbitrary manner. An illustration of the results thus obtained may be the lower right-hand drawing in Fig. 5, where the curves are presented for the case \(\dfrac{t}{\lambda}=0.5\). They reveal an extraor-

Fig. 5. Curves of the spectral distribution of photocurrents for different positions of the light spot on the wedge.

remarkably close agreement with the experimental curves taken at position 10 of the wedge (upper right drawing in Fig. 5).* Thus we see that, in the most essential features, the results of the experiments are in satisfactory agreement with theory.

It remains for us to consider the dependence of the photoelectric emission on the angle of incidence of the light. A typical curve of this dependence for a thin layer of an alkali metal on platinum is shown in the upper left drawing of Fig. 6. The emission caused by light polarized in the plane in which the electric vector lies in the plane of incidence has a sharp maximum at about \(80^\circ\) and then rapidly falls with further increase of the angle, becoming zero at \(90^\circ\), whereas for light polarized in the perpendicular plane we observe a monotonic decrease of the photocurrent from \(0^\circ\) to \(90^\circ\). The following drawings in Fig. 6 present families of dependence curves of the photocurrent on the angle for a number of positions of the light spot on the wedge in the second tube. We see that the curves obtained have the most varied form.**

The mutual arrangement of the curves for the two planes of polarization changes all the time, and instead of one maximum corresponding to the pure platinum, a whole series of maxima appears. As in the preceding case, we can, with the aid of the curves, construct the dependence curves on the angle, which in the main confirm the results of the experiments. Examples of such curves are given in Fig. 7. For the sake of simplification these curves have been calculated under the assumption that

\[ \left|\frac{g}{g_1}\right|^2 = 1 . \]

Their form in the main corresponds to the form of the experimental curves in Fig. 6. For the reason already mentioned, the roughness of the surface of the quartz imposes the observed photocurrents at small angles of incidence as too large, but in general the agreement is quite satisfactory. This comparison shows, among other things, that the quartz wedge in the second tube had a considerable thickness over the entire interval accessible for measurements, since curves corresponding to values

\[ \frac{t}{\lambda} < 0.4 \]

could not be obtained. We obtained them, nevertheless, from another experiment, of which we shall report on another occasion.

Conclusions

The results of the work presented, from the optical point of view, give a further and more detailed confirmation of the interpretation of Wiener’s experiments that is provided by the classical wave theory of light. Using a photoelectric surface as a test surface, it is possible to make quantitative measurements, whereas the photographic layer and fluorescent screen permitted only purely qualitative observations. True, the measurements described here are in some respects rather crude, but one may hope to increase their accuracy by increasing the dimensions of the apparatus and by developing a method for producing sufficiently long and transparent wedges; if, in addition, it proves possible to determine exactly the intrinsic photoelectric emission of the alkali metal and its optical constants, then it will be possible to undertake a completely exact quantitative experimental verification of the theoretical calculations. At present there can no longer be any doubt that the phenomenon under investigation fits completely within the framework of the classical wave theory of light, and this point of view must be borne in mind in setting up further experiments.

* When the thickness of the wedge is changed, the form of the calculated curve retains the same character; thus agreement with experiment continues to hold also for large values of \(t/\lambda\); in this case the determination of the thickness is made from the curves in Fig. 4.

** The disagreement observed in a number of cases (2, 4) of both curves at \(0^\circ\) may be explained by a slight displacement of the light spot on the wedge during the transition from one state of polarization of the light to the other, if one also takes into account possible inhomogeneities in the structure of the wedge.

Fig. 6. Dependence of photocurrents on angles of incidence for various positions of the light spot on the wedge.

\[ \lambda = 5500 \]

Fig. 7. Curves of dependence on angles for different values of \(\dfrac{t}{\lambda}\).

From the standpoint of the theory of the photoelectric effect, which was of primary interest to us, the results of our experiments provide additional confirmation of our explanation of photoelectric emission in thin layers of alkali metal. They make it possible to determine the dependence between the photocurrent and the density of the electrical energy in the case where the photosensitive layer is raised to a certain height above the base metal; the investigation of this dependence was the principal aim of our work. At the same time, along the way and in agreement with the predictions of the theory, entirely new photoelectric phenomena were observed, to the description of which this article is devoted.

The experiments we have carried out bear directly on the question of the spectral maxima and minima of emission in photocells with sensitized alkali-metal surfaces. The similarity of the emission maxima observed here when the layer is lifted above the metallic base with the maxima found in surfaces subjected to a silent discharge in an atmosphere of hydrogen or to similar processes is so striking that it suggests the inadequacy of the concept that relates these maxima to different atoms and crystalline properties; in any case, it is not yet produced purely by optical factors.* In support of the possibility of another explanation, we shall point to a highly sensitive photocell in which the cathode, containing cesium, is formed on an oxidized silver plate. Recently, in our laboratory, we succeeded in making a photocell of this type with a backing of mirror-like polished silver. Cathodes of these photocells possess an interference coloration, which indicates that the silver oxide plays the role of the quartz spacer in our work. The spectral maxima and minima of these photocells, without any doubt, depend on the optical factors discussed above. For further deepening of this question, we still lack knowledge of the intrinsic emission capacity of the photoelectric layer.

The main content of this article may to some extent be regarded as preliminary material for further investigations of cesium–silver–oxide photocells.

LITERATURE

1. Ives, The vectorial Photoelectric Effect in Thin Film of Alkali Metals, Phys. Rev., 38, 1209, 1931.
2. Ives and Briggs, The Photoelectric Effect from Thin Films of Alkali Metal on Silver., Phys. Rev., 38, 1477, 1931.
3. Ives and Briggs, The Depth of Origin of Photoelectrons, Phys. Rev., 40, 802, 1932.
4. See Wood, Optics, 3rd ed., p. 173.
5. Fry, Plane Waves of Light III, Absorption by Metals, J. O. S. A. 22, 307—332, 1932.
6. Fry, Plane Waves of Light II, Reflection and Refraction, J. O. S. A., 16, 1-25, 1928; see in particular § 17.

* Zurman’s interesting experiment (Phys. Zs. 32, 216, 1931), in which treatment of the surface with vapors of naphthalene and paraffin affects the selective photoeffect of potassium surfaces, receives rather an optical explanation than the chemical one proposed by Zurman.