The Fizeau–Foucault apparatus (1850) (Figure 1) was designed by the French

France

The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

 physicists

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 Hippolyte Fizeau

Hippolyte Fizeau

Armand Hippolyte Louis Fizeau was a French physicist.-Biography:Fizeau was born in Paris. His earliest work was concerned with improvements in photographic processes. Following suggestions by François Arago, Léon Foucault and Fizeau collaborated in a series of investigations on the interference of...

 and Léon Foucault

Léon Foucault

Jean Bernard Léon Foucault was a French physicist best known for the invention of the Foucault pendulum, a device demonstrating the effect of the Earth's rotation...

 for measuring the speed of light

Speed of light

The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

. The apparatus involves light

Light

Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

 reflecting off a rotating

Rotation

A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...

 mirror

Mirror

A mirror is an object that reflects light or sound in a way that preserves much of its original quality prior to its contact with the mirror. Some mirrors also filter out some wavelengths, while preserving other wavelengths in the reflection...

, toward a stationary mirror some 20 miles (35 kilometers) away. As the rotating mirror will have moved slightly in the time it takes for the light to bounce off the stationary mirror (and return to the rotating mirror), it will thus be deflected away from the original source, by a small angle. 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 dθ/dt, the angle θ is given by:


In other words the speed of light is calculated from the observed angle θ, known rate of rotation, and measured distance h as


The detector is at an angle 2θ from the source direction because the normal to the rotating mirror rotates by θ, decreasing by θ both the angle of incidence of the beam and its angle of reflection.

Foucault based his apparatus on an earlier experiment by Fizeau (Figure 2) who, in 1849, used two fixed mirrors, one partially obscured by a rotating cogwheel. Fizeau's value for light's speed was about 5% too high.

The Fizeau experiment to measure the speed of light

Speed of light

The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

 in water has been viewed as "driving the last nail in the coffin" of Newton

Isaac Newton

Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

's corpuscle theory of light when it showed that light travels more slowly through water than through air. Newton predicted refraction as a pull of the medium upon the light, implying an increased speed of light in the medium. However, Fizeau showed the speed of light in water to be less than in air, not more, by inserting a tube of water in the light path.

Fizeau interferometer

Fizeau also improved interferometry, and today the Fizeau interferometer still is used in a standard method for determining imperfections in surfaces and lenses.

Speed of light in moving media

Using an interferometer, Fizeau determined how the velocity of light is affected by a moving medium, as shown in an idealized form in Figure 3. Water flows in a pipe at velocity v. According to the non-relativistic view at the time of the experiment, the speed of light should be increased when "dragged" along by the water, and decreased when "overcoming" the resistance of the water. That is, the speed of light w in one arm is:


and in the other arm is


with n the index of refraction

Refractive index

In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....

 of water, and c/n the velocity of light in stationary water. As shown in the diagram, one path for the light should take a longer time than the other (clockwise time > counterclockwise time).

The interference pattern between the two beams when the light is recombined at the observer depends upon the transit times over the two paths. Thus, the speed of light in the water can be found as a function of the speed of the water. Fizeau found


This surprising result was instrumental in Einstein's thinking about relativity, and can be derived as an approximation to the law of special relativity expressing addition of velocities, namely:

   

which is accurate when v/c << 1, and agrees with the formula based upon Fizeau's measurements, which satisfied the condition v/c << 1. In deriving this result, a truncated series expansion for small x was used: 1 ⁄ (1+x) ≈ 1 − x + x² −x³ ⁄ (1+x) ≈ 1 − x.

External links

• Diagram showing the original experimental design found in the second volume of Foucalt's collected works: Volume Two - Recueil des travaux scientifiques de Léon Foucault 1878.
• Speed of Light Formal Report (The Foucault Method)
• Light in moving media