ALTHOUGH most people have observed the colors of thin soap films and some have even studied them in a science class, few have noticed the curious details of the colors. Consider a soap film held vertically in a loop of wire and illuminated with white light. Horizontal colored bands appear from top to bottom. If the film has had time to settle toward the bottom, the top may be dark. This absence of reflected light at the top is due to the extreme thinness of the film there. The darkness is often pointed out in classroom demonstrations as an example of the wave interference properties of light.

What colors lie below this dark, ultrathin portion? Having taught wave interference for some years (but without ever closely examining a real soap film), I thought the first band just below the dark portion would be blue and the colors would then change smoothly through the visible spectrum: blue, green, yellow and red. This progression should occur because the film thickens from top to bottom under the influence of gravity, and the wave interference of light should give a reflected color of a wavelength that increases in proportion to the thickness. Such a progression would be from the shorter wavelengths of blue to the longer wavelengths of red. Once the sequence is finished it should be repeated as the film thickens even more. Eventually toward the bottom of a large film the colored bands should become indistinguishable, causing the film there to look white.

As logical as this argument seemed, I was wrong in several respects. What lies just below the dark region is not a blue band but a relatively wide white one. The whiteness is a great surprise. Below the white area is a yellow-red (orange) band, which is followed by a purple band. Only then does a noticeable blue band finally appear.

Moreover, the sequence of colors is not always the same down the film. The colors that appear depend on the source of white light. In particular they depend on the temperature of the emitting surface of the source. For example, a tungsten lamp from a slide projector may give only one prominent blue band on the entire soap film, whereas direct sunlight (which originates from a hotter surface) gives two prominent blue bands.

I shall first explain theoretically why colors appear on soap films and then discuss the colors on a real soap film. My discussion of the real colors closely follows an unpublished paper by Benjamin Bayman and Bruce G. Eaton of the University of Minnesota. Work along the same lines has been published by Hiroshi Kubota of the University of Tokyo. Finally, I shall describe some soap film formulas given to me by Albie Weiss, an art teacher in Cleveland.

If a thin soap film is illuminated with white light, why should any colors appear in the reflected light? Consider a ray of monochromatic light (call it A) that is incident on and nearly perpendicular to the surface of a thin soap film. A portion of the light (call it ray B) is reflected by the surface. The rest of the light refracts into the film, crosses its thickness and falls on the second surface. Part of the light reaching the second surface is reflected, crosses the thickness of the film again and refracts out of the film. Call this emerging ray C. Rays B and Care returned to the observer, who is on the same side of the film as the light source. These two rays determine whether he sees the film as being bright or dark in the particular color that was initially incident on the film.

The rest of the incident light eventually refracts out of the film, a little of it each time a ray reflects inside the film. Part of this light emerges on the back side of the film and is of no consequence. Part of it emerges toward you, but those rays play only a minor role in what you see.

Whether the film looks dark or bright depends primarily on the relative phases of the waves represented by rays B and C. For example, if the two waves are exactly in phase, they totally interfere constructively and yield bright light. If they are exactly out of phase, they totally interfere destructively and yield darkness. An intermediate case gives brightness of an intermediate value.

The phase difference between the returned waves is measured in terms of either wavelengths or degrees (360 degrees corresponds to one wavelength). Totally constructive interference results when the phase difference is zero or an integral number of wavelengths (or an even number or zero times 180 degrees). Totally destructive interference arises when the difference is an odd number of half wavelengths (or an odd number times 180 degrees).

Since rays B and C originate from the same incident ray A, why should they be anything but in phase and thus why should anything but a bright reflection emerge from the film?

There are two reasons. First, when light is reflected from a surface, it may be shifted in phase by the reflection itself. If the reflection is from a material that has a greater refractive index than the material the ray is already in, the light is shifted in phase by half a wavelength (180 degrees). If the reflection is from a material with a lower refractive index, there is no phase shift. For example, the reflection of the incident ray at the front surface (to produce B) causes a phase shift of half a wavelength because the soap film has a greater refractive index than air; for the converse reason the reflection of C at the back surface causes no phase shift. Hence the reflections from the front and back surfaces result in a phase difference of half a wavelength between the two emerging rays.

A further phase difference is introduced because ray C traverses the thickness of the film twice and therefore travels farther than B. If A is almost perpendicularly incident on the surface of the film, the extra distance is about twice the film's thickness. Suppose the thickness equals half a wavelength. When ray C crosses the thickness of the film twice it emerges after having gone a distance equal to a full wavelength, whereas ray B merely reflects from the front surface. (In a detailed calculation that need not be considered here one must compare the thickness of the film to the wavelength of the light inside the film, which is the incident wavelength in the air divided by the refractive index of the film.)

In summary ray B undergoes a phase shift of half a wavelength because it is reflected, and ray C undergoes a phase shift of a value that depends on the thickness of the film. The phase shift of ray C is apparently one wavelength. Subtraction of the two phase shifts gives the phase difference between the two emerging rays. If the thickness is such that the phase difference is an odd number of half wavelengths, as in this example, the two rays interfere destructively and you see a dark film. If the thickness is such that the phase difference is zero or an integral number of wavelengths, the two emerging rays are in phase and interfere constructively to give bright light.

For the sake of simplicity I considered ray A as being almost perpendicular to the film. The argument holds at any other angle of incidence the only change being that the extra distance traveled by ray C in crossing the film twice would then be more than twice the thickness of the film.

As we have seen, when a soap film is held vertically in a loop of wire, the film slowly flows to the bottom because of its own weight and so the thickness increases from top to bottom. If you shine monochromatic light on the film, you find that at some places along the vertical dimension of the film the thickness happens to be just right for the reflected rays to interfere constructively, and you see bright horizontal bands of color there. Between those bright bands the thickness happens to be right for destructive interference and you see dark horizontal bands. Intermediate between the brightest bands and the darkest lie regions of intermediate interference and thus intermediate brightness.

This standard argument has several subtleties that escaped me until recently. First, how can totally destructive interference arise between rays B and C when they obviously are not of the same amplitude, ray C being weaker than ray B? Even when they are exactly out of phase and destructively interfering the most, the cancellation should be incomplete and some brightness should remain.

The answer lies in the rest of the rays that emerge toward the observer after undergoing multiple reflections inside the film. I said they play a minor role in what you see of the film, but it is here they are needed. In destructive interference all the extra rays are in phase with ray C; their combined amplitude added to the amplitude of ray B equals the amplitude of ray B. Hence the extra and normally ignored rays can give rise to a dark band on the film.

Another subtlety is that if the light originates in a distant point source, no system of bright and dark bands appears on the film. Rays from a distant point source of light arrive at the film parallel to one another and at only one angle of incidence. Therefore the rays returned to the observer all leave the film at the same angle, which by the normal law of reflection is equal to the angle of incidence. Depending on the thickness of the film, the rays can interfere either constructively or destructively, but they all do precisely the same thing and you see either a bright spot or a dark one at the place on the film where the light is reflected to your eye.

With an extended source such as the sun (which occupies half a degree of angle in your field of view) or a nearby lamp, light rays are incident on the film in a range of angles. With your head at a given position you will intercept some ray B and C pairs in which ray C took a path in the film that caused destructive interference between rays B and C, yielding a dark band where the pair left the film. Other ray B and C pairs you intercept may similarly result in constructive interference, and you see a bright band where the pair emerged.

A final subtlety lies in the loss of colors when the film becomes too thick. Interference colors are missing not only in thick soap films but also in commonplace films such as the water on a sidewalk after a rainfall. All the preceding arguments for wave interference remain true when the film is several times thicker than the wavelength of visible light, and so why do the colors disappear?

The answer is simple. With a thicker film several ranges of wavelength across the visible spectrum are subjected to fairly complete constructive interference. When you see the light, enough colors are present for you to see it as being white. As the film becomes even thicker, the wavelength ranges of the brighter light shift, but you still see the composite as being white.

One of the curious features of a vertical soap film is the dark region that develops at the top of the film and slowly spreads downward. Given a chance to settle downward, the soap film may get so thin at the top that its thickness is much less than a wavelength of light. There ray Chas to travel a negligible extra distance in crossing the film and so emerges with essentially no phase shift. Ray B is still shifted in phase half a wavelength by reflection, that shift has nothing to do with the thickness. Thus in a very thin section of the film rays B and C necessarily emerge differing in phase by about half a wavelength; they must interfere destructively. A very thin film is therefore dark.

Suppose you shine white light on the film. The thickness necessary for constructive interference depends on the wavelength of the light. Hence the values giving bright bands differ slightly for each color. This slight difference separates the positions of the differently colored bright bands on the soap film. The colors should change from blue through red (from shorter wavelengths to longer ones) downward along the film as the thickness increases. The fact that this sequence is not found in real soap films is the interesting feature of the work by Bayman and Eaton and by Kubota.

An understanding of the colors on a real soap film requires a quantification of color. Such a quantification is the C.I.E. colorimetric system (for the Commission Internationale de l'Éclairage, which did the work). As a result the coordinates of colors developed in various ways can be plotted on a graph. Two such graphs appear on pages 236 and 240. There the decimal numbers represent the C.I.E. coordinate system, the numbers associated with the names of colors indicate the wavelengths of the colors in nanometers and the numbers printed in color represent various soap-film thicknesses in nanometers.

The first graph shows Bayman and Eaton's calculations for the colors seen in a vertical soap film illuminated by sunlight reaching the film at an angle of 45 degrees. Point a corresponds to the thin top of the film at the place where the first reflected light is perceptible. At greater film thicknesses the locus of color coordinates moves away from point A.. Along the resulting curve, which winds through the chromaticity graph, one sees the film thicknesses (in nanometers).

The ultrathin top position of a settled vertical soap film is not plotted here because the reflected rays from that portion (what I called above rays B and C) almost completely cancel each other in their destructive interference. There is no way to plot darkness on the chromaticity graph. At a somewhat greater thickness the film still looks dark, but it has a blue tint because the blue light begins to be subjected to less complete destructive interference. Hence the first point plotted on the curve in color, point a, lies away from the white center of the graph and toward the blue. Blue light is subjected to this incomplete cancellation before the other colors are because it has the shortest wavelengths in the visible spectrum. The incomplete cancellation begins when the extra distance traveled by the ray crossing the film twice (ray C) becomes at least a small fraction of the wavelength of the light. Then ray C begins to be slightly shifted in phase and is no longer exactly out of phase with ray B. This extra path length is still quite short, but it is more of a fraction of the shorter blue wavelengths than it is of the longer wavelengths for the rest of the colors.

At somewhat greater film thicknesses, roughly from an eighth to a quarter of a wavelength in the visible range, all the colors begin to be subjected to some constructive interference. Thus the color curve moves through point B in the white center of the graph. When you casually examine a vertical soap film, this white region is the first easily distinguishable band below the dark region at the top.

As the film thickens further the color curve moves to point C in the yellow-red (orange), swings through point d in a mixture of blue and red (purple) and finally passes through point e in the first pure blue of the film. (Some people call the blue at the extreme end of the visible spectrum violet.) Next the color curve almost misses the green by moving through point f near the white center. In the soap film you see mostly yellow below the first blue band. The curve thereafter winds around the white center to give bands of purple, blue (but not as pure as before) and finally a pure green. With even greater film thicknesses pure blue does not return, but one more noticeable excursion is made into the green. Eventually the color curve winds its way down into the white center, corresponding to a white bottom on a sufficiently large soap film.

To contrast these results with a cooler white-light source, Bayman and Eaton plotted the color curve for a tungsten filament at 3,000 degrees Kelvin. (They assumed a surface temperature of 5,500 degrees K. for the sun.) In the second graph the pattern is similar in shape to the one for sunlight but is shifted away from the blue and toward the yellow and red. As a result the beginning point a is not blue but lies on the yellow or red side of white. The entire curve shows only one reasonably pure band of blue, together with much purer yellows and reds. The termination point lies in the yellow and red rather than in the white. This shift of the pattern to the red is consistent with the lower temperature of the emitting surface, because with lower temperatures the distribution of radiation shifts to longer wavelengths.

Bayman and Eaton suggested that the differences in the colors of soap films illuminated by different white-light sources can be made most apparent if the films are projected side by side on a wall for easy comparison of the colors. They stabilized their soap films in a glass or plastic housing large enough for the wire to be dipped into a container of soapy water in the bottom of the housing and then oriented vertically, and they employed a large-diameter lens with a focal length of about a foot.

You might like to try a similar setup with other white-light sources of different surface temperatures and with other soap-film solutions such as the ones I shall describe. Calculations of the color curves might be tedious, but now that you have two standards side-by-side comparisons between a standard and a film illuminated by a new light source will help you to calibrate the colors from the new source.

In one form or another the colors of soap films have been discussed by scientists at least since the days of Newton, whose work on soap-film colors is particularly interesting. In his Opticks (see pages 214 through 244 in the copy of the 1730 edition published in 1952 by Dover Publications) he carefully details the colors he found in a soap film illuminated with sunlight. All the subtle features I have discussed are there. Newton, however, conceived light as being corpuscular rather than wavelike, and so his work is an example of using good experimental data for a theory that was wrong. He thought the colors resulted from the different degrees of refraction of the various colors in sunlight by the film, as in his famous demonstration of the separation of colors by a glass prism. The prism demonstration correctly showed that white light is composed of all the colors in the visible spectrum, the composite being white to a human observer, and Newton apparently thought the thickness of the soap bubble somehow separated colors in the same way.

Newton's model for refraction seems strange now. He thought the particles of light were refracted into a material such as a soap film because the material exerted a force on the particles, drawing them near and finally reorienting their direction of travel. He did conceive that several colors would be sent simultaneously to the observer, who then would interpret the net color and its hue according to which of the returned colors was the most intense, but his model did not include wave interference. He also noted the black regions and even the faint blue tint bordering the most intensely black regions, but he interpreted this absence of light as meaning that no light was reflected there.

The cause of the soap-film colors was understood later when Newton's corpuscular model for light lost its hold on science. The details of the dark region took longer to explain. If you examine a vertical soap film, you will find that the very dark region does not fade smoothly into a less dark region with a blue tint; instead you will see a sharp boundary between the two.

In 1939 Sir William Bragg explained the boundary in terms of the molecular arrangements on the surface of the film. As a soap film settles and begins to display colors, many of the thin, long-chain hydrocarbon molecules of the soap migrate to the surface of the film, each molecule lining up perpendicular to the surface with its oxygen-rich end toward the center of the film. Between the two surfaces of these oriented soap molecules are water and more (but unoriented) soap molecules. The film is thinnest when the middle layer is eliminated and the two surfaces of oriented soap molecules lie next to each other.

Such an ultrathin film, with a width of two molecular lengths, is very dark. (At least the perception of blue is difficult.) Bragg suggested that the transition from ultrathin to the state where a soapy layer lies between the two surfaces is not gradual, mainly because as the film thins down to the ultrathin state during its settling the middle layer of soapy water has to be squeezed out of the way. The squeezing produces a ridge. Above the ridge on the film is the dark ultrathin region; below the ridge is the much wider (but still thin) film displaying the blue tint in the dark region.

Bragg also called attention to a beautiful demonstration by Sir James Dewar. If you have access to a vacuum system, you could repeat it. A vertical film is left under a bell jar while the system is evacuated, and then the jar is heated slightly at its base in such a way that the bottom of the wire holding the film is also heated. The heat forces some of the fluid to climb the wire to the top of the film, where the fluid then forms drops that slide down over the dark region at the top. When the drops are illuminated, they appear as a beautiful silver on a very dark background.

Although you can buy soap-bubble solutions in most toy stores, it is easy to make them at home. In this matter I have had assistance from Weiss, who teaches in a junior high school in Cleveland. The simplest solution is a mixture of ordinary soap or detergent and clean water. (Distilled water is the best.) To stabilize the films you can add glycerin, which is available from most drugstores and chemical-supply houses. Many of the detergents already have additives to stabilize the foam they create when they are used for washing. If you mix the detergent (or soap), water and glycerin in a ratio of roughly 1: 3: 3, they will make a film that will last for 45 minutes or so if it is protected from breezes. You might want to vary the ratios to increase the lifetime of the film. The glycerin increases the lifetime but also increases the time you must wait for a vertical film to settle downward and display the dark region at the top.

Other mixtures have been described previously in this department [May, 1969], including the original formula devised by Joseph A. F. Plateau, the pioneer in soap-bubble experiments, whose mixture provides soap films lasting for several hours. Plateau's formula and many other helpful hints are available in the classic book Soap Bubbles: Their Colours and the Forces Which Mould Them, by C. V. Boys. Procedures for manufacturing plastic bubbles and films from polyvinyl acetate and acetone were described in this department in July, 1973.

Recently Weiss showed me a solution of triethanolamine and oleic acid that gave long-lasting films and large bubbles. You can buy four-ounce samples of the solution from him for $ 1.50. For an additional $ 1.50 he also sells a shield and platform on which bubbles can be blown and their colors examined conveniently. Weiss can be reached at his home: 24212 Elm Road, North Olmsted, Ohio 44070.

The colors in Weiss's bubbles are primarily pinks and greens Lying in broad bands. Blues and yellows appear when he blows gently across a bubble. When he moves a cotton swab soaked in ammonia close to a bubble, all the colors of the spectrum appear near the swab, swirling around in a virtual psychedelic display. The ammonia vapor alters the surface tension of the bubble closest to the swab, and the uneven surface tensions there force the surface into circulation patterns. (This is the Marangoni effect, which I described in this department for June.)

Weiss showed me an easy way to blow a soap bubble on a platform. Place a small amount of the fluid on the platform, wetting the entire surface. Similarly wet one end of a drinking straw. Hold that end in the fluid on the platform and blow gently in the other end. Raise the straw as the bubble grows so that you keep the lower end just inside the wall of the bubble. (The bubble will probably burst if it touches the dry portion of the straw.) I have seen Weiss blow bubbles almost a foot in diameter.

Writing in The Physics Teacher for February, 1967, Paul A. Smith of Coe College described how you can make long-lasting soap-gelatin films. Mix 60 milliliters of cold water with one tablespoon of Knox pure gelatin and then heat the mixture to about 90 degrees Celsius in a double boiler. After the gelatin has dissolved thoroughly and all bubbles have disappeared from it add nine milliliters of glycerin and three milliliters of liquid detergent, stirring gently. Keep the solution warm while you make your bubbles or films from it.

With less glycerin the films are hard and dry. Smith suggested that you let the bubbles dry for a few minutes before you mount them (he mounted them on ordinary index cards) or before you let them "roll across the floor." The films can last for days or (with proper protection) even for years.

The interference colors in a soap film depend in part on the fact that what I termed ray C underwent no phase shift owing to its reflection on the back surface of the film. Suppose the back surface consisted not of air but of a material with a refractive index greater than that of the soapy water. Then ray C would be subjected to a phase shift of half a wavelength, just as ray B was from the front surface. As a result of the extra phase shift the requirements for the different interference effects would change: constructive interference would occur when the extra distance traveled by ray C equaled zero or an integral number of wavelengths, and destructive interference would occur when the extra distance was an odd number of half wavelengths. Would the colors in the film change? Would a dark region appear at the top? It would be interesting to find out, but mounting a thin film on a solid surface will take some work.

You might try blowing a gelatin bubble or a soap bubble over a glass slide, positioning the slide just below a surface and then piercing the bubble so that it collapses onto the slide. The glass should have a greater refractive index than the bubble solution has; most glass probably does. You cannot let the bubble shrink too much or you will leave a distorted film on the glass. I have had some success by piercing the bubble with the object on which I mount the film, but I shall leave the details of the colors for you to explore. You might refer to the theoretical results Kubota has already plotted on chromaticity graphs. They appear in a paper of his that is cited in the bibliography for this issue [below].

Bibliography

A GRAPHICAL DEMONSTRATION OF WHITE LIGHT INTERFERENCE. Alan C. Traub in American Journal of Physics, Vol. 21, No. 2, pages 75-82; February, 1953.

INTERFERENCE COLOR. Hiroshi Kubota in Progress in Optics: Vol. 1, edited by E. Wolf. North-Holland Publishing Company, 1961.

SOAP FILM INTERFERENCE PROJECTION. John A. Davis in The Physics Teacher, Vol. 12, No. 3, pages 177-178; March, 1974.

The Society for Amateur Scientists (SAS) is a nonprofit research and educational organization dedicated to helping people enrich their lives by following their passion to take part in scientific adventures of all kinds.