Foucault's measurements of the speed of light

In 1850, Léon Foucault used a rotating mirror to perform a differential measurement of the speed of light in water versus its speed in air. Together with a similar measurement by Hippolyte Fizeau, this result confirmed the wave behavior of light. In 1862, Foucault used a similar apparatus to measure the speed of light in the air, obtaining a value within 0.6% of the modern value. Albert A. Michelson extended that technique in a series of experiments from 1877 to 1930, approaching the modern value to within 0.05%.

Background

In 1834, Charles Wheatstone developed a method of using a rapidly rotating mirror to study electric sparks and applied this method to measure the velocity of electricity in a wire. François Arago proposed the idea that Wheatstone's method could be adapted to a study of the speed of light.

The early-to-mid 1800s were a period of intense debate on the particle-versus-wave nature of light. Although the observation of the Arago spot in 1819 may have seemed to settle the matter definitively in favor of Fresnel's wave theory of light, various concerns continued to appear to be addressed more satisfactorily by Newton's corpuscular theory. Arago expanded upon Wheatstone's concept in an 1838 publication, suggesting that a differential comparison of the speed of light in the air versus water would serve to distinguish between the particle and wave theories of light.

Foucault had worked with Hippolyte Fizeau on projects such as using the Daguerreotype process to take images of the Sun between 1843 and 1845 In 1845, Arago suggested to Fizeau and Foucault that they attempt to measure the speed of light. Sometime in 1849, however, it appears that the two had a falling out, and they parted ways. That year, Fizeau reported the result of using, not a rotating mirror, but a toothed wheel apparatus to perform an absolute measurement of the speed of light in air.

In 1850, Fizeau and Foucault both used rotating mirror devices to perform relative measures of the speed of light in the air versus water.

Foucault employed Paul-Gustave Froment to build a rotary-mirror apparatus

To achieve the high rotational speeds necessary, Foucault abandoned clockwork and used a carefully balanced steam-powered apparatus designed by Charles Cagniard de la Tour. Foucault originally used tin-mercury mirrors, however at speeds exceeding 200 rps, the reflecting layer would break off, so he switched to using new silver mirrors.

The apparatus (Figure 1) involves light passing through slit S, reflecting off a mirror R, and forming an image of the slit on the distant stationary mirror M. The light then passes back to mirror R and is reflected back to the original slit. If mirror R is stationary, then the slit image will reform at S.

If the mirror R is rotating, it will have moved slightly in the time it takes for the light to bounce from R to M and back, and the light will be deflected away from the original source by a small angle, forming an image to the side of the slit. Newton had explained refraction as a pull of the medium upon the light, implying an increased speed of light in the medium. The corpuscular theory of light went into abeyance, completely overshadowed by the wave theory. This state of affairs lasted until 1905, when Einstein presented heuristic arguments that under various circumstances, such as when considering the photoelectric effect, light exhibits behaviors indicative of a particle nature.

For his efforts, Foucault was made chevalier of the Légion d'honneur, and in 1853 was awarded a doctorate from the Sorbonne.) with considerable accuracy. In addition, unlike the case with Fizeau's experiment (which required gauging the rotation rate of an adjustable-speed toothed wheel), he could spin the mirror at a constant, chronometrically determined speed. Foucault's measurement confirmed le Verrier's estimate.

As seen in Figure 3, the displaced image of the source (slit) is at an angle 2θ from the source direction.

{| class="wikitable"

|If the distance between mirrors is h, the time between the first and second reflections on the rotating mirror is 2h/c (c = speed of light). If the mirror rotates at a known constant angular rate ω, it changes angle during the light roundtrip by an amount θ given by:

:<math>\theta = \frac {2h \omega}{c}=\omega t \ . </math>

The speed of light is calculated from the observed angle θ, known angular speed ω and measured distance h as

:<math>c = \frac {2 \omega h}{\theta } \ . </math>

[[File:Michelson's 1879 Refinement of Foucault.png|thumb|center|500px|Figure 4: Michelson's 1879 repetition of Foucault's speed of light determination incorporated several improvements enabling use of a much longer light path.

Between 1877 and 1931, Albert A. Michelson made multiple measurements of the speed of light. His 1877–79 measurements were performed under the auspices of Simon Newcomb, who was also working on measuring the speed of light. Michelson's setup incorporated several refinements on Foucault's original arrangement. As seen in Figure 4, Michelson placed the rotating mirror R near the principal focus of lens L (i.e. the focal point given incident parallel rays of light). If the rotating mirror R were exactly at the principal focus, the moving image of the slit would remain upon the distant plane mirror M (equal in diameter to lens L) as long as the axis of the pencil of light remained on the lens, this being true regardless of the RM distance. Michelson was thus able to increase the RM distance to nearly 2000 feet. To achieve a reasonable value for the RS distance, Michelson used an extremely long focal length lens (150 feet) and compromised on the design by placing R about 15 feet closer to L than the principal focus. This allowed an RS distance of between 28.5 and 33.3 feet. He used carefully calibrated tuning forks to monitor the rotation rate of the air-turbine-powered mirror R, and he would typically measure displacements of the slit image on the order of 115 mm. was only about 4 km/s higher than the current accepted value.

Notes

References

External links

Relative speed of light measurements

"Sur un système d'expériences à l'aide duquel la théorie de l'émission et celle des ondes seront soumises à des épreuves décisives." by F. Arago (1838)
Sur les vitesses relatives de la lumière dans l'air et dans l'eau / par Léon Foucault (1853)
"Sur l'Experience relative a la vitesse comparative de la lumiere dans l'air et dans l'eau." by H. Fizeau and L. Breguet (1850)

Absolute speed of light measurements

Mesure de la vitesse de la lumière ; Étude optique des surfaces / mémoires de Léon Foucault (1913)

Classroom demonstrations

Speed of Light (The Foucault Method)
Measuring the Speed of Light (video, Foucault method) BYU Physics & Astronomy