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  • Discuss the rainbow formation by thin films.

The bright colors seen in an oil slick floating on water or in a sunlit soap bubble are caused by interference. The brightest colors are those that interfere constructively. This interference is between light reflected from different surfaces of a thin film; thus, the effect is known as thin film interference    . As noticed before, interference effects are most prominent when light interacts with something having a size similar to its wavelength. A thin film is one having a thickness t size 12{t} {} smaller than a few times the wavelength of light, λ size 12{λ} {} . Since color is associated indirectly with λ size 12{λ} {} and since all interference depends in some way on the ratio of λ size 12{λ} {} to the size of the object involved, we should expect to see different colors for different thicknesses of a film, as in [link] .

Soap bubbles reflecting mostly purple and blue light with some regions of orange.
These soap bubbles exhibit brilliant colors when exposed to sunlight. (credit: Scott Robinson, Flickr)

What causes thin film interference? [link] shows how light reflected from the top and bottom surfaces of a film can interfere. Incident light is only partially reflected from the top surface of the film (ray 1). The remainder enters the film and is itself partially reflected from the bottom surface. Part of the light reflected from the bottom surface can emerge from the top of the film (ray 2) and interfere with light reflected from the top (ray 1). Since the ray that enters the film travels a greater distance, it may be in or out of phase with the ray reflected from the top. However, consider for a moment, again, the bubbles in [link] . The bubbles are darkest where they are thinnest. Furthermore, if you observe a soap bubble carefully, you will note it gets dark at the point where it breaks. For very thin films, the difference in path lengths of ray 1 and ray 2 in [link] is negligible; so why should they interfere destructively and not constructively? The answer is that a phase change can occur upon reflection. The rule is as follows:

When light reflects from a medium having an index of refraction greater than that of the medium in which it is traveling, a 180º phase change (or a λ / 2 shift) occurs.

The figure shows three materials, or media, stacked one upon the other. The topmost medium is labeled n one, the next is labeled n two and its thickness is t, and the lowest is labeled n three. A light ray labeled incident light starts in the n one medium and propagates down and to the right to strike the n one n two interface. The ray gets partially reflected and partially refracted. The partially reflected ray is labeled ray one. The refracted ray continues downward in the n two medium and is reflected back up from the n two n three interface. This reflected ray, labeled ray two, refracts again upon passing up through the n two n one interface and continues upward parallel to ray one. Ray one and ray two then enter an observer’s eye.
Light striking a thin film is partially reflected (ray 1) and partially refracted at the top surface. The refracted ray is partially reflected at the bottom surface and emerges as ray 2. These rays will interfere in a way that depends on the thickness of the film and the indices of refraction of the various media.

If the film in [link] is a soap bubble (essentially water with air on both sides), then there is a λ / 2 size 12{λ/2} {} shift for ray 1 and none for ray 2. Thus, when the film is very thin, the path length difference between the two rays is negligible, they are exactly out of phase, and destructive interference will occur at all wavelengths and so the soap bubble will be dark here.

The thickness of the film relative to the wavelength of light is the other crucial factor in thin film interference. Ray 2 in [link] travels a greater distance than ray 1. For light incident perpendicular to the surface, ray 2 travels a distance approximately 2 t size 12{2t} {} farther than ray 1. When this distance is an integral or half-integral multiple of the wavelength in the medium ( λ n = λ / n size 12{λ rSub { size 8{n} } =λ/n} {} , where λ size 12{λ} {} is the wavelength in vacuum and n size 12{n} {} is the index of refraction), constructive or destructive interference occurs, depending also on whether there is a phase change in either ray.

Questions & Answers

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