page_title: Speed of light
section_title: Time of flight techniques
hierarchical_section_title: Speed of light / Measurement / Time of flight techniques
caption_attribution_description: English: Apparatus used in physicist Albert A. Michelson, Fred Pease and astronomer Francis Pearson's 1930-35 determination of the speed of light. It consists of a mile long 3 ft diameter vacuum chamber in a Southern California valley containing an optical system with two large concave mirrors at either end. Inside the vacuum chamber a beam of light from an arc lamp is reflected from an eight-sided mirror spinning at 512 revolutions per second, then makes ten passes through the tube, after which it returns and reflects again from the same face of the mirror. During the light beam's ten-mile journey the mirror rotates through a small angle, so the reflected beam has a small angle to the outgoing beam. The apparatus measures this angle, which is proportional to the time of flight of the beam. The tube is evacuated to a pressure of about 10 Torr. E. C. Nichols designed the optics. Michelson died in 1931 with only 36 of the 233 measurement series completed, but Pease and Pearson carried on. The experiment's accuracy was limited by geological instability and condensation problems, but in 1935 a result of 299,774 ± 11 km/s was obtained, the most accurate measurement of the speed of light to that date.
context_page_description: The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is defined as 299792458 metres per second. It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time interval of ​¹⁄₂₉₉₇₉₂₄₅₈ second. According to special relativity, c is the upper limit for the speed at which conventional matter and information can travel. Though this speed is most commonly associated with light, it is also the speed at which all massless particles and field perturbations travel in vacuum, including electromagnetic radiation and gravitational waves. Such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer. Particles with nonzero rest mass can approach c, but can never actually reach it, regardless of the frame of reference in which their speed is measured. In the special and general theories of relativity, c interrelates space and time, and also appears in the famous equation of mass–energy equivalence E = mc².
context_section_description: A method of measuring the speed of light is to measure the time needed for light to travel to a mirror at a known distance and back. This is the working principle behind the Fizeau–Foucault apparatus developed by Hippolyte Fizeau and Léon Foucault.
  The setup as used by Fizeau consists of a beam of light directed at a mirror 8 kilometres (5 mi) away. On the way from the source to the mirror, the beam passes through a rotating cogwheel. At a certain rate of rotation, the beam passes through one gap on the way out and another on the way back, but at slightly higher or lower rates, the beam strikes a tooth and does not pass through the wheel. Knowing the distance between the wheel and the mirror, the number of teeth on the wheel, and the rate of rotation, the speed of light can be calculated.
  The method of Foucault replaces the cogwheel by a rotating mirror. Because the mirror keeps rotating while the light travels to the distant mirror and back, the light is reflected from the rotating mirror at a different angle on its way out than it is on its way back. From this difference in angle, the known speed of rotation and the distance to the distant mirror the speed of light may be calculated.
  Nowadays, using oscilloscopes with time resolutions of less than one nanosecond, the speed of light can be directly measured by timing the delay of a light pulse from a laser or an LED reflected from a mirror. This method is less precise (with errors of the order of 1%) than other modern techniques, but it is sometimes used as a laboratory experiment in college physics classes.
caption: One of the last and most accurate time of flight measurements, Michelson, Pease and Pearson's 1930–35 experiment used a rotating mirror and a one-mile (1.6 km) long vacuum chamber which the light beam traversed 10 times. It achieved accuracy of ±11 km/s.
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