Foucault's measurements of the speed 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[3] and characterizing absorption bands in the infrared spectrum of sunlight in 1847.

[5]: 124 [3] In 1848−49, Fizeau used, 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.

[5]: 129 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.

The experiment was proposed by Arago, who wrote, Two radiating points placed one near the other and on the same vertical, shine instantly in front of a rotating mirror.

[5]: 128–129 Guided by similar motivations as his former partner, Foucault in 1850 was more interested in settling the particle-versus-wave debate than in determining an accurate absolute value for the speed of light.

[Note 3] 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.

[5]: 130 In Foucault's 1862 experiment, he desired to obtain an accurate absolute value for the speed of light, since his concern was to deduce an improved value for the astronomical unit.

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 could not increase the RM distance in his folded optical arrangement beyond about 20 meters without the image of the slit becoming too dim to accurately measure.

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).

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.

His 1926 repeat of the experiment incorporated still further refinements such as the use of polygonal prism-shaped rotating mirrors (enabling a brighter image) having from eight through sixteen facets and a 22 mile baseline surveyed to fractional parts-per-million accuracy.

Figure 1: In Foucault's experiment, lens L forms an image of slit S at spherical mirror M. If mirror R is stationary, the reflected image of the slit reforms at the original position of slit S regardless of how R is tilted, as shown in the lower annotated figure. However, if R rotates rapidly, the time delay due to the finite speed of light traveling from R to M and back to R results in the reflected image of the slit at S becoming displaced. [ 7 ]
Figure 2: Foucault's determination of the relative speed of light in air vs water. Light from a passing through a slit (not shown) is reflected by mirror m (rotating clockwise around c ) towards the concave spherical mirrors M and M' . Lens L forms images of the slit on the surfaces of the two concave mirrors. The light path from m to M is entirely through air, while the light path from m to M' is mostly through a water-filled tube T . Lens L' compensates for the effects of the water on the focus. The light reflected back from the spherical mirrors is diverted by beam splitter g towards an eyepiece O . If mirror m is stationary, both images of the slit reflected by M and M' reform at position α . If mirror m is rapidly rotating, light reflected from M forms an image of the slit at α' while light reflected from M' forms an image of the slit at α" .
Figure 3: Schematic of the Foucault apparatus. Left panel : Mirror R is stationary. Lens L (not shown) forms an image of slit S on spherical mirror M. The reflected image of the slit reforms at the original position of slit S regardless of how R is tilted. Right panel : Mirror R is rotating rapidly. The reflected light from mirror M bounces from mirror R that has advanced an angle θ during the transit of the light. The telescope detects the reflected image of the slit at angle 2θ relative to the position of slit S . [ 8 ]
Figure 4: Michelson's 1879 repetition of Foucault's speed of light determination incorporated several improvements enabling use of a much longer light path. [ 7 ]