FOR THE PRECISE DETERMINATION of length, or of small changes in the density, pressure or temperature of transparent substances, amateur experimenters will find no yardstick more accurate than a simple beam of light as used in a homemade interferometer. All interferometers are based on the principle that light waves that take different paths from a common source can fall out of phase and either cancel or reinforce each other when they reunite. If the source consists of white light, which is a blend of many wavelengths, the interfering waves produce colorful patterns as seen in such natural interferometers as soap bubbles, opals and all colored bird feathers except a few with yellow pigmentation. Interferometers that are commonly used for measuring length split a beam of monochromatic light into two rays that take separate paths until they recombine to interfere. The resulting pattern appears in a monochrome of varying intensity, as discussed in this department some time ago [November, 1956]. Instruments of the type used for measuring the density of fluids or gases, as well as the local distribution of temperature and stress or pressure, also split the beam into two rays, but the rays take essentially the same path. These instruments, known as series interferometers, cause one ray to traverse part of the path more than once; interference occurs at the end of the transit.

The construction of most series interferometers requires the use of machine tools not ordinarily available to amateurs. However, a series interferometer that can be made with ordinary hand tools has now been designed by G. F. Pearce, professor of mechanical engineering at the University of Waterloo in Canada. "The essential part of this instrument," writes Pearce, "consists of a series of three partially transparent mirrors. A beam of light, when passing through the mirrors, may take many paths of differing length. A given ray, for example, may pass through the first mirror, be reflected from the second back to the first and then back again through both the second and the third mirror. A second ray that substantially coincides with the first may traverse both the first and the second mirror and be reflected from the third back to the second for a final reflection to and through the third. Still another ray may traverse the first two mirrors, be reflected from the third back to the first, oscillate for a time between the first and the second mirror and finally complete its transit through the third, as shown in the upper part of the accompanying illustration [Figure 1].

"When the mirrors are about equally spaced and are approximately parallel, the rays that traverse paths A and B, as depicted in the illustration, will interfere to form a pattern of alternate light and dark areas. Other parts of the beam that traverse a variety of path lengths, such as those shown at C and D, form an interference pattern that is superimposed on the interference pattern caused by A and B. This superimposed pattern can be eliminated by inclining the mirrors as shown in the lower part of the illustration. If mirrors P and Q are inclined as indicated, the rays that traverse different paths become separated and emerge in different directions.

"The interference pattern can be observed by simply inserting a collimator lens between the source and the mirror system so that the light passes through the mirrors as a bundle of parallel rays that are focused on a screen by a field lens between the third mirror and the screen [see Figure 2].

"The mechanism I contrived for supporting the mirrors in any relative position was constructed of aluminum plates. Any other substantial material, such as plastic panels or even plywood, may be substituted, however. The partial mirrors can be made by the familiar techniques used by amateurs for silvering the mirrors of reflecting telescopes or can be obtained from suppliers such as the Edmund Scientific Co. in Barrington, N.J., or Henry Prescott in Northfield, Mass. The mirrors I use reflect approximately 40 per cent of the incident light and transmit 60 per cent. They measure about two inches wide by three inches long, but the size is not critical. Homemade instruments of the same type have been operated with partially silvered microscope slides that measure one by three inches.

"The base of the interferometer should be constructed of material at least three-quarters of an inch thick to provide a solid support for two equally sturdy end brackets [see Figure 3]. Apertures that are just a fraction of an inch smaller than the mirrors are cut in the end brackets. One mirror is mounted over the aperture of the bracket that faces the screen. The glass can be attached to the metal by light clips of spring brass or by a few dabs of epoxy cement. The reflecting surface should face away from the screen. The remaining two mirrors are similarly attached over the apertures of two intermediate supporting plates, which can be made of thinner material. One of the intermediate plates is attached to the bracket nearest the screen by a suspension system that consists of four adjusting screws, together with a set of four helical compression springs that space the plate from the bracket. The bracket is drilled and tapped in its four corners for the screws, but the plate is merely drilled with oversize holes that slide easily over the screws when the retaining nuts are turned. These nuts are normally used only for tilting the middle mirror in relation to the mirror closest to the screen. The middle mirror can be attached to its supporting plate by the same technique used for mounting the first mirror; the coated side should face away from the screen.

"The system used for supporting the third mirror is similar. In this case, however, the supporting plate is suspended from the second bracket by only three screws. In my instrument these screws are equipped with heads in the form of worm gears taken from surplus apparatus. Worm gears are not essential, but they are exceptionally convenient for making fine adjustments. Oversize holes were made for the screws in the end bracket; the plate that carries the mirror was drilled and tapped. The threads make a loose fit, so the screws do not bind when the plate is tilted a few degrees. As shown in the accompanying illustration [Figure 4], compression springs maintain the desired spacing between the end bracket and the plate. The coated surface of the third mirror should face toward the screen. The completed interferometer can be supported on any substantial surface, such as the top of a solid bench or table.

"The lenses used for bending the light into a bundle of parallel rays that traverse the mirrors and for focusing it on the screen are of the simple planoconvex type. They need be no larger in diameter than the mirrors. Neither do they have to be achromatic, because the light is monochromatic. My lenses were obtained from the Edmund Scientific Co. A bracket for supporting the collimating lens was improvised from a piece of plywood that in turn is held in position by an apparatus stand. Th position of the lens is adjusted simply by moving the clamp and stand. A comparable arrangement supports the field lens between the mirror system and the screen. Although the interference pattern can be projected onto a screen, prefer to examine it on the ground glass of a camera so that photographs of interesting patterns can be made conveniently. I use a view camera equipped with an extension bellows. Cameras of this type, incidentally, provide many desirable features not found in miniature cameras of more recent design. Often an older model made of wood can be bought for less than $10, complete with a set of plateholders.

"As the source of monochromatic light I use a tubular mercury lamp together with a green filter similar to the Corning Type 4-64 that blocks the transmission of all rays except those emitted by the 5,460-angstrom line of mercury. Rays from the lamp are restricted by an aperture three-sixteenths of an inch in diameter located at the focus of the collimating lens. An alternate source, somewhat less intense, could be provided by a mercury lamp of the General Electric Type H-100A38-4, which must be operated in conjunction with a current-limiting ballast, such as a Type 9T64Y3518. Doubtless an adequate source could be improvised by placing a sheet of dark green plastic, of the kind used for candy wrappers, over the mercury bulb of an ordinary sunlamp, but the precise color of plastic and the number of thicknesses to use for optimum results would have to be determined experimentally.

"The fully assembled interferometer occupies a space about two feet wide and four feet long. Usually I mount the lamp on a small stand on one side of the table that supports the mirror assembly and lenses. The camera rests on a tripod just beyond the opposite side of the table [see illustration above]. With the apparatus so positioned, I first adjust the mirrors for approximately equal spacing; in a typical experiment that might be five-eighths of an inch. Next I check to ensure that the mirror facing the camera (mirror 1 in the illustration) is perpendicular to the base plate. The second mirror is then tilted away from the camera approximately one degree and the third mirror approximately two degrees.

"Next, the system of mirrors is aligned to prevent multiple images from reaching the ground glass when the image of the source is focused by the lens of the camera. Normally this will require both twisting and tilting the interferometer [Figure 6]. As an aid in making the adjustment I insert a disk of transparent plastic about an inch in diameter and three-sixteenths of an inch thick between the two mirrors closest to the light source. The adjustments are made simply by slipping wedges of appropriate thickness between the base and the table top either to incline the assembly toward the camera slightly or to rotate it about its longitudinal axis. If overlapping disks of light in vertical array are observed on the ground glass, the instrument must be tilted; if the disks overlap horizontally, twist is required. When the position of the base has been altered so that the images merge, the orientation of the interferometer is correct.

"During the next procedure-adjusting the mirror spacing-it is convenient to view the image of the light source from a position about midway between the field lens and the first mirror, that is, from position P in the accompanying illustration [Figure 2]. To view the image, the rays can be deflected to the side by inserting a small hand mirror between the field lens and the interferometer mirror, or by removing the field lens temporarily. The image will appear as a series of bright spots in echelon formation that diminish in intensity as shown in the upper part of the accompanying illustration [left]. Adjust the center mirror by the screws that suspend it from the end bracket until the two images closest to the apex of the V coincide. Fine lines of light and shade- the interference fringes-should now be seen. The reason for a solid supporting table will now become apparent: the slightest vibration will disturb the fringes and make them difficult to see. Replace the field lens. A vertical array of images should now be visible at its focal point, as shown in the lower part of the illustration.

"Position the camera so that its iris coincides with the focal point of the field lens. Then alter the position to exclude all images from the ground glass except the second from the top, as illustrated. When the camera is properly focused, an interference pattern of alternate dark and light lines will be seen on the ground glass. The spacing of the lines is determined by the thickness of the plastic disk, as shown by the accompanying illustration [at left below]. If the intensity of the image is uncomfortably low, the pattern can be examined directly by removing the ground glass and observing the lines by means of a small magnifying lens, such as a jewelers' loupe. The fringes can be altered in inclination and spacing by adjusting the tilting mechanism of the bracket nearest the light source.

"When so adjusted, the interferometer is sensitive to the optical properties of any transparent substance placed between the mirrors closest to the light source. The transparent disk of plastic can be used for an initial test. If a mechanical load is applied across the diameter of the disk, for example, the resulting stress will reduce the diameter of the disk and increase its thickness. The distortion will not be uniform. Accordingly some of the transmitted light rays now traverse a path that is optically longer or shorter than other rays, as indicated by the altered interference pattern. To determine the nature of the distortion, first make a photographic negative of the interference pattern of the unstressed disk and a second negative with the disk loaded. Superimpose the negatives in register and make a photographic print through the pair. The print will show the kind of distortion pattern indicated in the accompanying illustration.

"The temperature distribution in air or other transparent media near a hot surface can be determined by observing changes in the density of the medium as reflected by the altered index of refraction. Heat lowers the density of most media and increases the velocity of light in the region of lower density, thus lowering the index of refraction. The effect can be demonstrated by placing a heated wire in front of the transparent plastic disk in the interferometer. Whereas the fringes appear to meet the image of a wire at room temperature at right angles, as depicted at the upper left in the accompanying illustration [below], they curve increasingly as the approach the image in the case of heated wire, as shown at the upper right in the illustration.

"Such patterns can be analyzed in terms of the temperature distribution. Assume the pattern of fringes associated with a heated wire, such as the one in the lower part of the illustration. Select a pair of adjacent fringes, such as those at s and t. A line drawn parallel to the straight portion of the fringes and continued toward the wire will intersect fringes that depart from straightness as they approach the wire. At point v in the illustration, for example, the straight, broken line that has its origin in the straight portion of fringe has crossed the bent-up portion of fringe t. The heated wire has caused a shift of one whole fringe with respect to the center line of fringe s. This means that the light passing through point v has speeded up and is a full wavelength ahead of the light at point w. The amount of shift in terms of wavelength can be similarly determined at any point along the fringe. The index of refraction of a perfect vacuum has been accepted as 1, and that of air is about 1.0003. The density of normal room air can be measured by a barometer. With these data plus the number of wavelengths that the light shifts, as measured by the interferometer, the experimenter can determine the index of refraction of the heated medium and the local temperature by simple arithmetic, using formulas in the illustration [left].

"The first of the equations, on which the formulas are based, was derived independently during the past century by the physicists H. A. Lorentz of Holland and L. V. Lorenz of Denmark. It relates the index of refraction of a gas to its density. As indicated, the index of refraction, - 1, is very closely equal to the product of the density of the medium multiplied by a constant. The constant is therefore equal to the quotient of the difference between the index of refraction and unity divided by the density, a quantity that can be measured by a thermometer and a barometer. If n₁ is the index of refraction of the room air and n₂ is the index of refraction of the heated air, and if P₁ and P₂ are the corresponding densities, then, as indicated in the second set of equations, it can be shown that the difference between the speed of light through the room air and through heated air is equal to the product of the difference in the speed of light through air at room temperature and vacuum multiplied by 1 minus the ratio of the density of the heated to the unheated air. Similarly, the third set of equations relates the difference between the number of wavelengths that traverse air at room temperature and any selected point in the heated region, as measured by the interferometer, to the index of refraction of air at room temperature and the ratio of the density of hot to unheated air.

"Finally, by applying the law that relates the temperature of a gas to its density the formula is derived for computing the temperature of the heated air. To apply the formula the experimenter need only measure the temperature, T₁, of the room air and express the measurement in degrees Kelvin. Because the quantity N is equal to the fringe displacement as measured in fringe widths by the interferometer, the formula can be used to calculate the temperature rise above room air at any point along the center line of the interference fringe. The fringe pattern in the vicinity of a horizontal wire takes the form of a series of concentric ovals, as shown in the upper part of the accompanying illustration [above]. This pattern can be analyzed by the same technique; the temperature data can then be used for making a graph of the isothermals as shown in the lower part of the illustration."

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