Update: In my haste to finish this “monster” post, I neglected to include an introduction to standing waves, an explanation which is crucial to understanding the experiment. That oversight has been corrected.
A couple of weeks ago I issued a “challenge” to my fellow science bloggers: find, read, and blog about a classic, (preferably pre-WWII) scientific paper. There’s so much interesting historical context and methodological information hidden away that’s worth a second look.
For my part in the challenge, I chose an 1890 paper by Otto Wiener, “Stehende Lichtwellen und die Schwingungsrichtung polarisirten Lichtes,” Ann. Phys. Chem. 38 (1890), 203-243. Loosely translated, the title is, “Standing light waves and the oscillation direction of the polarization of light.”
The experiment that Wiener performed, as we will see, is conceptually simple and elegant. I foolishly thought that this would “translate” into a short, easy to cope with paper. As one can see from the citation above, no such luck: the paper is 40 pages of somewhat antiquated German! I accepted my fate, though, and soldiered on. A description begins below the fold…
In the year 1890, the idea that light is in fact an electromagnetic wave was relatively new. James Clerk Maxwell had demonstrated theoretically in his 1865 paper that the electromagnetic field equations allowed wave solutions which propagated at the velocity of light; this led him to speculate, in his words, that
The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws.
The first person to demonstrate the existence of electromagnetic waves was Heinrich Hertz. In 1887 he experimentally demonstrated that radio waves were consistent with Maxwell’s theory, measuring their velocity, electric field intensity and polarization properties. He also produced radio standing waves by reflection from a zinc plate.
Standing waves are an important part of the discussion which follows, so it is worth taking a moment to explain them. When a monochromatic wave is reflected off of a surface, the reflected wave and the incident wave combine to form waves which oscillate up and down but have no direction of motion: standing waves. This is shown in the animation below:
In this picture, the wave is incident from the left of the image onto a hard surface (not drawn) on the right. The wave reflects from this surface, incurring a change of sign as it does so, and the total wave simply oscillates ‘in place’. It can be seen that there are points in space where there is never any oscillation (nodes of the standing wave) and there are points in space where the oscillations are maximum (the antinodes of the standing wave). For visible light, these oscillations happen much too fast for the eye to detect, and one only registers an average ‘brightness’ of the wave field. The nodes, which contain no light, appear dark, while the antinodes appear bright:
Two important points: First, the distance between successive nodes or antinodes is half the wavelength of the wave. Second, the absolute position of the nodes and antinodes depends on whether the wave ‘changes sign’ upon reflection. The earlier animation was produced assuming that the reflected wave has the opposite sign of the incident wave. A comparison of how the picture changes if the reflected wave has the same sign as the incident wave is shown below:
By 1890, then, scientists were interested in studying standing waves of light: it seems that a number of them remained unconvinced that light truly was just another manifestation of electromagnetic waves! One big obstacle stood in the path of such studies: the smallness of the wavelength of light. Hertz’s radio waves had a wavelength of meters, but visible light has a wavelength on the order of 500 nanometers, or 500 billionths of a meter! Such distances cannot be directly observed with the naked eye, so experimental ingenuity was required – and Otto Wiener provided it.
As we will see, there is some irony associated with Weiner’s work. The majority of the paper is devoted to experiments relating to the so-called “mechanical theory of light”, the idea (invalidated by Einstein’s relativity) that light waves are in fact an oscillation of some as yet undiscovered material medium, dubbed the “aether”. The most important part of Weiner’s work, the interpretation of his results in the context of electromagnetic theory, seems almost an afterthought in the paper!
We’ll discuss the paper in reverse order: we’ll discuss the most ‘timeless’ results first, then backtrack to discuss the other parts of the paper and their historical context.
A beam of light, being an electromagnetic excitation, consists of a combined oscillating electric field E and oscillating magnetic field H, both transverse to the direction of motion, as shown below:
The oscillations of the electric and magnetic field are in phase: that is, when the electric field strength is at a peak, the magnetic field strength is also at a peak. Both fields can induce forces in electrical charges, according to the Lorentz force law:
In optics, however, the electric field is the typically the only field that is considered important, and the ‘polarization’ of the light field is associated with the direction of the electric field; the magnetic field is for the most part ignored. Do we have a justification for this neglect?
In 1890, there was no such justification. Since the structure of the atom was still unknown, there was no clear understanding of how a light field should interact with matter. For instance, what part of the light field is involved in chemical processes such as developing a photograph, the E-field or the H-field?
Wiener developed the following experiment, depicted below, to specify the role of the electric field in optics:
An electromagnetic plane wave is incident normally on a plane mirror, assumed for simplicity to be perfectly reflecting. The combined incident and reflected waves form a standing wave, and a transparent, thin photographic plate is placed in the pattern at an angle from the mirror. At the surface of the metal, the electric field must be zero: the free electrons in the metal move about to cancel the field. But, because of the complementary behavior of the electric and magnetic fields, the magnetic field must have a maximum at the surface!
One can readily calculate that the electric field should have maxima at heights such that
while the magnetic field should have maxima at heights such that
Here is the wavelength of the light. The maximas of the electric field and magnetic field occur at different points in space! By observing the height at which a photographic plate is darkened, one can determine whether the electric or magnetic field, or both, are most important in light-chemical interactions. In Wiener’s own words,
In den Schwingungsknoten der electrischen Kräfte findet ein Minimum, in den Schwingungsbäuchen derselben ein Maximum der chemischen Wirkung statt; oder: die chemische Wirkung der Lichtwelle ist an das Vorhandensein der Schwingungen der electrischen und nicht der magnetischen Kräfte geknüpft.
In the nodes of the electric forces a minimum takes place, in the antinodes of the same a maximum of the chemical effect; or: the chemical effect of the light wave is attached to the presence of the oscillations of the electric and not the magnetic forces.
Wiener had demonstrated, in the context of the electromagnetic theory, that the electric field is the ‘active ingredient’ in light waves.
Wiener’s experimental apparatus was also groundbreaking – and simple! The standing wave pattern of a light wave is too small to be recorded directly in the z-direction, but Wiener overcame this by tilting the film at a very small angle from the mirror surface. In this way, the interference pattern is ‘stretched out’ along the length of the photographic film.
The film itself presented its own challenges, however. The photosensitive layer had to be not only transparent, so the incident and reflective waves could freely travel through it, but also significantly thinner than a wavelength: a thick film would end up being almost uniformly developed. Again quoting Wiener,
Es könnten demnach etwa hundert Wellenzüge längs der Dickenausdehnung einer Gelatineplatte Platz finden.Würde man also die Platte der Wirkung einer stehenden Lichtwelle aussetzen und nach dem Entwickeln betrachten, so müsste man an jeder Stelle der Platte die Wirkung von 100 Wellenzügen übereinandergedeckt sehen; die Platte wäre anscheinend gleichförmig geschwärzt.Eine Untersuchung der stehenden Welle ist vielmehr nur dann denkbar, wenn man ihre Wirkung auf einer Strecke, die einen kleinen Bruchtheil der Wellenlänge beträgt, gesondert erhalten kann.Die nächste Aufgabe war also, zu suchen, ob es möglich sei, eine durchsichtige lichtempfindliche Schicht herzustellen, deren Dicke gegen die Länge einer Lichtwelle hinreichend klein ist.
About hundred wave trains could therefore find along the thickness expansion of a gel plate place. If one would thus expose and after developing would regard the plate to the effect of a standing light wave, then one would have to see the effect covered of 100 wave trains in each place of the plate; the plate would be apparent homogeneously blackened. An investigation of the standing wave is rather conceivable only if one can keep their effect on a distance, which amounts to a small fraction of the wavelength, separate. The next task was thus to search whether it was possible to manufacture a transparent photo-sensitive layer whose thickness is sufficiently small against the length of a light wave.
Wiener considered several of the classic photographic methods of the time. The Daguerrotype method, developed in 1839, involves an exposure on a mirrored surface coated with silver halide particles. Though the active layer is thin, it possesses a high level of reflection, which makes it unsuitable for a standing wave measurement. Another technique, ‘Owed to the good-nature of the Honorable Professor Rose’, is based on the fact that a homogeneous iodine silver layer can be made photosensitive by an application of nitric silver. Again, however, the layer possesses a high level of reflection.
The final decided upon technique is known as a ‘wet plate collodion process‘. Collodion is a celluloid-like film which is sufficiently transparent and thin for the proposed experiment. The thickness was determined by another clever trick: a section of the collodion was wiped away from the glass plate, and a second glass plate was placed upon it to form a wedge shape. Light passing through this wedge surface forms interference fringes, which can be analyzed to determine the plate thickness. Wiener determined his layer to be roughly 1/30th of the wavelength of the light used. As a sodium arc lamp with wavelength approximately 600 nm was used, this implies a photosensitive layer of 20 nm.
As mentioned, the primary investigations of the paper were actually related to the so-called “mechanical theory of light”. In the years before Einstein, there was a strong feeling in the scientific community that light waves, like sound waves and water waves, involved the mechanical vibration of some sort of as-yet unknown substance (dubbed “the aether”). There was much interest in determining the properties of this hypothetical material (a brief summary given here). One important point of contention was the nature of light waves: were they purely transverse (vibrating perpendicular to the direction of motion, like water waves), or did they also consist of longitudinal components (vibrating along the direction of motion, like sound waves). Transverse waves would undergo a 180° phase change upon reflection at a mirror, while longitudinal waves would undergo no phase change.
Wiener performed a number of different experiments to examine how light waves reflected at surfaces. Not surprisingly, regardless of whether the light was polarized or unpolarized, the phase change was always 180°, consistent with the ‘transverse wave’ hypothesis. Of course, by this time the mechanical theory of light was already dying, mortally wounded by the Michelson-Morely experiment‘s inability to detect motion with respect to the aether. Einstein would deal the final blow with his theory of relativity, and Wiener’s investigations of the aether would be mostly forgotten.
His investigations did change Wiener’s own opinion, though. In his own words,
Ehe ich zu den ersten Experimenten dieser Arbeit schritt, waren mir an deren Gelingen im Hinblick auf die electromagnetische Lichttheorie Zweifel aufgestiegen.
Before I walked to the first experiments of this work, me at their success regarding the electromagnetic light theory doubts had ascended.