A CENTURY and a quarter ago the French physicist Jean Bernard Leon Foucault made an approximate measurement of the speed of light. His determination, which amateurs can easily duplicate, was made with an apparatus that consisted of four basic parts. A mirror that rotated at a known speed reflected a beam of light from a bright slit to a fixed mirror placed a known distance from the rotating mirror. The fixed mirror reflected the beam back to the rotating mirror. During the round trip of the beam the rotating mirror turned through a small angle. Foucault calculated the angle by observing with an eyepiece the displacement of the reflected image of the slit. In order to determine the speed he divided the distance by the interval of time required for the mirror to rotate through the observed angle. The calculated speed turned out to be 298,000 kilometers per second, which is equivalent to 185,168 miles per second.

About 50 years ago a finely wrought version of the same instrument was designed by the American physicist A. A. Michelson. In 1926 it indicated a speed of 299,769 kilometers, which is close to the currently accepted value of 299,792.5 kilometers (186,282 miles) per second. Experiments of this kind have fascinated Sam Epstein (3929 Soud1 Orange Drive, Los Angeles, Calif. 90008). Last year Epstein, who is a chemist, built a homemade version of Michelson's instrument, primarily to learn how closely he could approach Michelson's result. Epstein describes his experiment.

"I did not aspire to duplicate Michelson's experiment, which was performed over a distance of 22 miles, since I had available a working distance of only about 2,000 feet. The experiment can be done over still shorter distances, however, by folding the light beam with additional fixed mirrors to make a total path of some 2,000 feet. The result is achieved at the expense of slit-image intensity, which decreases as the number of reflections increases. Alternatively, even shorter working distances can be accommodated by rotating the mirror at speeds proportionately higher than the 7,200 revolutions per minute of my apparatus. The total length of the triangular path between the two reflecting surfaces of my rotating mirror (via the fixed mirrors) was 1.131 kilometers (3,711 feet). The distance from the slit image, which appears on a translucent screen, to the rotating mirror was 18.57 meters (60.93 feet). I refer to the path as the radius arm.

"This combination of working distance, mirror speed and radius arm resulted in an observed displacement of the slit image of more than 10 centimeters with respect to the position of the image when the rotating mirror was at rest. I measured the displacement of the image to within .01 centimeter. I was therefore able to determine the speed of light to within .1 percent of the accepted value.

"Light reflected by the rotating mirror falls on the distant fixed mirrors only a small percentage of the time. It arrives at the screen as a series of short flashes that constitute a small fraction of the light transmitted by the slit. Although the well-known effect called persistence of vision causes the observer to see a continuous image of the slit, the image is relatively dim. For this reason a highintensity light must be used. My light source is a carbon arc between graphite electrodes; it is the kind found in professional motion-picture projectors.

"A household appliance such as a toaster, an iron or a room heater of about 1,000 watts must be connected in series with the arc as a ballast resistor to limit the current to about 10 amperes. The light can be made even brighter by inserting a full-wave rectifier of silicon diodes in the circuit. Silicon diodes rated for 10 amperes at a reverse potential of 200 volts or more are currently available from dealers in surplus materials for less than 25 cents each. All connections in the circuit must be tight to avoid secondary arcing.

"The arc can be struck by pushing the carbons together momentarily and pulling them apart. An alternative is to place the electrodes almost in contact and then brush both tips simultaneously with a third electrode held in one hand. The hazard of receiving an electric shock can be avoided by standing on a dry, non-conducting surface such as a rubber mat, wearing dry leather gloves and adjusting one electrode at a time.

"The arc lamp can be constructed largely from Transite, an asbestos board that is available from dealers in lumber. To confine the light the working parts of the lamp should be enclosed in a Transite housing fitted with a ventilation chimney, although the outer ends of the graphite electrodes must be accessible so that they can be pushed inward from time to time as the arc consumes the graphite. The length of the arc can be monitored continuously by focusing a reflected image of the glowing tips of the electrodes on a small observing screen outside the housing [see illustration at left]. A carbon arc should never be observed directly without eye protection such as a welder's eye shield. I found by experiment that the optimum space between the tips of the electrodes is about five millimeters.

"The slit and the condenser lens should be placed so that the images of the glowing tips of the electrodes fall beyond the ends of the slit. Light from the arc should pass through the slit but light from the glowing electrodes should not. The condenser lens should be far enough from the arc so that the glass does not heat up excessively.

"The distance between the collimating lens and the slit must be adjusted to equal exactly the focal length of the lens. The diameter of this lens should be sufficient to intercept rays that diverge from the full width of the slit. Excess light from the ends of the slit that would diverge beyond the collimating lens is blocked by a screen with an aperture equal in diameter to the width of the collimating lens [see illustration at right]. Ordinary two-inch magnifying glasses of about six-inch focal length serve as both the condensing lens and the collimating lens in my apparatus. A11 components on the optical bench must be solidly mounted and centered on the optical axis of the system.

"The rotating mirror consists of a pair of front-surface aluminized mirrors, each a quarter of an inch thick, cemented back to back with epoxy. They need be only slightly larger than is necessary to intercept the collimated beam. The mirror is clamped by a cell that is rigidly attached to a flange on the shaft of the motor. I improvised the cell with wood and strap metal. All edges of the mirror and the reflecting surfaces inside the cell were cushioned with foam rubber during assembly.

"The fixed mirrors are supported by cells improvised from wood. They can be rotated around both their horizontal and their vertical axes. Unless the first fixed mirror is mounted at exactly the same level as the rotating mirror, which is unlikely considering the distance between them, an adjustable auxiliary mirror must also be inserted in the optical train to deflect the light beam from the rotating mirror to its target.

"The base of the first of my two auxiliary mirrors also supports a vacuum phototube. The cathode of the tube receives two flashes of light during each revolution of the two-sided mirror. The resulting pulses of unidirectional electric current from the tube are used to measure the speed at which the mirror rotates.

"The rotating mirror is turned by the variable-speed motor of a sewing machine. Mine is a Dayton motor rated at one-fifth horsepower. It operates on 115 volts of alternating current at a maximum of 2.4 amperes at 10,000 r.p.m. The motor is designed to operate with a special speed controller. Both the motor and its companion controller are available from W. W. Grainger, Inc., an electrical-supply firm with retail outlets in all major U.S. cities.

"The controller alone is not capable of adjusting the speed of the motor to the accuracy required by the experiment. I set the controller to operate the motor at about 8,000 r.p.m., and then I energize the controller with a variable autotransformer, such as a Variac. The autotransformer is adjusted to reduce the speed to exactly 7,200 r.p.m.

"Various schemes can be contrived to measure the rate at which the rotating mirror turns. The phototube develops two pulses of direct current for each revolution of the mirror. The pulses can be amplified to flash a small neon lamp at the same rate. An inexpensive crystal-controlled oscillator could be installed to cause a neighboring neon lamp to flash at the rate of 7,200 flashes per second. The resulting stroboscopic effect would indicate synchronization between the two.

"Alternatively, the output of the phototube can be connected to the vertical plates of a cathode-ray oscilloscope while the horizontal plates are energized by a constant frequency of, say, 60 hertz. The display of two stationary pips on the face of the tube would indicate that the mirror is rotating at the rate of 7,200 r.p.m. I time the speed with the oscilloscope mainly because I happen to own one.

"The output of the phototube appears as a pulse of voltage across the 27,000 ohm resistor [see illustration at left]. It is fed to the vertical deflection plates of the oscilloscope through a double-pole, double-throw switch. The other side of the switch serves for applying the 60-hertz frequency of the power line to the plates, thus providing a means of checking the sweep frequency that is applied to the horizontal plates of the instrument. The 60-hertz frequency can be taken from any low-potential source in the circuit, such as the filament winding of the power transformer.

"If the slit-image screen is in the same plane as the slit and the rotating mirror, the rotating mirror will alternately reflect to the screen a direct image of the brilliantly lighted slit and its relatively dim image from the stationary mirrors. The dim image would be lost in the glare of the bright one. To avoid that effect I adjusted the second stationary mirror so that the image of the slit would be reflected from the reverse side of the rotating mirror to the second auxiliary mirror on the viewing platform at a small downward angle. The auxiliary mirror in turn reflected the light upward through an achromatic lens that focused the image of the slit on the translucent screen, where it could be viewed at a comfortable angle outside the plane of the direct image.

"The achromatic lens and a pointer made of sheet metal are mounted on a screw-operated carriage that can be displaced laterally about 15 centimeters with respect to the light beam [see illustration at right]. The pointer slopes downward across the screen. In it there is a small aperture through which the image of the slit can be observed. A sharp bend below the aperture allows the pointer to traverse a small shelf or table that records the position of the observed image as indicated by the pointer.

"The base of the assembly is slotted for lateral adjustment with respect to the beam. The lead screw that moves the carriage was made of stud-bolt stock, which is available from most dealers in hardware, as are the smooth rods that function as ways on which the carriage slides. The remainder of the construction is largely of wood and commonly available bolts.

"The assembled apparatus must be adjusted at night, and the experiments are of course done at night. At least two assistants are needed to adjust and operate the system. The team can communicate by prearranged flashlight signals or by citizen's-band radio telephones.

"The stationary mirrors must be installed on solid supports. The length of the path from the first surface of the rotating mirror through all stationary mirrors to the second surface of the rotating mirror must be measured as accurately as possible, preferably with a surveyor's transit. The technique of using the transit is explained in all elementary textbooks on surveying. Try to measure the path to within at least 30 centimeters. Put the observing screen at least 18 meters from the rotating mirror.

"Adjust the condenser lens to the position where the slit is filled with the image of the arc and the images of the tips of the glowing electrodes fall on the slit screen outside the jaws of the slit. For the initial trial the width of the slit can be set at about three millimeters. The collimating lens is then placed at a distance slightly greater than its focal length from the slit and in line with the rotating mirror.

"At the center of a six-inch square of white cardboard draw a circle equal in diameter to the diameter of the collimating lens. With the arc lamp in operation and the rotating mirror blocked in any position at which it reflects light in a convenient direction, have an assistant intercept the collimated beam about a meter from the mirror with the screen of white cardboard. The diameter of the spot of light that falls on the cardboard must equal the diameter of the circle on the card. If it does not, move the collimating lens toward or away from the slit until the diameters match.

"Meanwhile a second assistant should monitor the arc lamp and adjust the electrodes to maintain the size of the arc. The first assistant then moves about 10 meters farther away from the mirror and checks the diameter of the beam again to see if the collimating lens needs further adjustment. The collimation adjustment is adequate when the diameter of the light beam remains unchanged through a distance of 20 meters.

"All my stationary mirrors were fitted with dust covers. To prevent dew from forming on the surfaces do not remove the covers in the evening until the temperature stabilizes. The experiment should be undertaken only during fair weather with little or no wind.

"The rotating mirror and the first auxiliary mirror are now adjusted to reflect the beam to the first stationary mirror, where an assistant sights on the beam and positions the mirror to intercept it. The rotating mirror should then be locked so that it cannot turn. (The slightest fraction of a degree of rotation will throw the beam off target.) The clamping screws of the auxiliary mirror are carefully tightened. Only the screws that control the horizontal translational adjustment of the first stationary mirror should be tightened at this point. The second stationary mirror is aligned with the first, and the vertical and horizontal rotational screws of the first mirror and the horizontal translational screws of the second are tightened.

"The second stationary mirror is now aligned with the reverse side of the rotating mirror. After the second auxiliary mirror on the image-viewing platform has been adjusted to reflect the beam through the focusing lens the slit should be visible on the viewing screen. The width of the slit is adjusted at the optical bench for the best quality of image, and a fine line is drawn on the recording table to indicate the zero position of the slit image. The rotating mirror is freed and the light is directed to the phototube housing, which is turned so that the cathode of the phototube intercepts the beam squarely.

"A team of three people is also needed to operate the apparatus. One member observes the waveform on the oscilloscope and adjusts the autotransformer to maintain the speed of the rotating mirror at exactly 7,200 r.p.m. Another maintains the spacing between the electrodes of the arc to illuminate the slit uniformly. The third keeps the pointer aligned with the image of the slit and measures the excursion of the image from its zero position.

"After the apparatus has been turned on and has warmed up, the double-pole, double-throw switch is operated to display the 60-hertz wave of the power supply. The sweep rate of the oscilloscope is adjusted to form exactly one complete sine wave. The switch is thrown to its other position, and the autotransformer is adjusted to the point where the oscilloscope displays two needlelike spikes. If the amplitude of the spikes appears to exceed the height of the oscilloscope screen or the waveform is otherwise distorted, the width of the phototube window and the controls of the oscilloscope are adjusted experimentally until two distinct spikes are displayed. When they appear, stop the motor. Recheck the zero position of the slit image by adjusting the rotating mirror by hand.

"The motor is started again and gradually brought up to speed (7,200 r.p.m.) by means of the autotransformer. The observer follows the displacement of the image of the slit by moving the pointer until the motor operator announces '7,200 r.p.m.' He then reports that he has recorded the position of the displaced image. The system can now be turned off.

"The observer measures the distance between the line on the recording table (zero) and the tip of the pointer at its displaced position to the nearest .01 centimeter, using a vernier caliper and a magnifying glass. Repeat the experiment at least 10 times. The average of 10 or more measurements of the displacement of the image is accepted as the final result.

"The velocity of light is now calculated as follows. The total distance traveled by light from the front of my rotating mirror to its reverse side was 1.131 kilometers. The distance between the rotating mirror and the image of the slit on the screen was 1,857 centimeters (60.93 feet). The displacement of the image on the screen between its zero position and its final position averaged (for 10 measurements) 10.55 centimeters. The average angle through which the rotating mirror turned from the position of zero image displacement to the average final position of image displacement is equal to arc tangent 10.55 / (2 X 1,857) = .1627 degree. The motor was turning the mirror at the rate of 7,200 /60 = 120 r.p.m., or 120 X 360 = 43,200 angular degrees per second. Light traveled from the front surface to the reverse surface of the rotating mirror during the time required for the mirror to turn .1627 degree in .1627/43,200 or 3.766 X 10 second. According to these measurements, light would travel in one second 1.131/(3.766 x 10) = 300,318 kilometers per second (186,608 miles per second). As I have mentioned, the accepted value for the velocity of light in air is 299,792.5 kilometers per second.

"Obviously my measurements require refining. For example, with my apparatus an error of .01 centimeter in reading the displacement of the image of the slit leads to an error of about 200 kilometers per second in the calculated speed. The timing of the speed of the rotating mirror is equally critical. Although the 60-hertz frequency of public utility power lines is carefully monitored so that electric clocks keep reasonably good time on the average, the rate at any specific instant may well be a few tenths of a hertz too high or too low. I recommend that the speed of the rotating mirror be checked against a frequency standard of known accuracy, such as the 500- or 600-hertz signals that are transmitted by radio stations WWV (Colorado) and WWVH (Hawaii) on the carrier frequencies of 2.5, 5, 10, 15 and 20 megahertz by the National Bureau of Standards. Other refinements that would improve the accuracy of my system would include a more accurate measurement of the optical path and indeed of all other dimensions.

"Investigators have been attempting to determine the value of c, the velocity of light, for more than 300 years. Its determination to within a few meters per second still eludes the best experiments. In fact, it has been suggested in recent years that nature does not impose an absolutely fixed speed limit on the universe. Does c change with the passage of time? Amateurs may not find it possible to build apparatus capable of checking that question, but it is both informative and fun to try."

Bibliography

MICHELSON AND THE SPEED OF LIGHT. Bernard Jaffe. Doubleday & Company, Inc., 1960.

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