Speed of Light | Done With Mirrors

The Speed of Light series consist of five parts. Quick access links are here.

Part 1 | Earliest Ideas

Part 2 | The Eclipses of Io

Part 3 | Chopping Light Beams

Part 4 | Done With Mirrors

Part 5 | Michelson and Morley

This post highlights the work done by Albert Michelson of the United States to measure c more accurately than anyone before.

Albert Michelson was born in Strelno, Prussia, on December 19, 1852. At the age of two, his family emigrated to Virginia City, Nevada in the United States. The family moved to San Francisco. There he started his formal education in public schools. He graduated from high school in 1869. President Grant appointed him to the U.S. Naval Academy. He returned to become an instructor in physics and chemistry at the Academy after two years of duty.

He continued his studies in Europe and returned to the U.S. in 1883. He accepted positions at several universities in his career. He became Professor of Physics and the first Head of Department at the new University of Chicago in 1892. WW-I interrupted his career as he rejoined the Navy. Upon his return to Chicago, Michelson was granted the Distinguished Service Professorship. In 1929, he resigned to work at Mount Wilson Observatory, Pasadena, CA.

He was awarded the first Nobel Prize to an American scientist in 1907 in the field of Physics for “for his optical precision instruments and the spectroscopic and metrological investigations carried out with their aid”.

Michelson conducted several rounds of trials to more accurately measure the speed of light. He started out making improvements to the spinning mirror method pioneered by Leon Foucault in France several years earlier.

The Foucault Method

When Fizeau used the spinning toothed wheel in 1849 to chop the light beam, his friend and colleague Leon Foucault decided to take another approach. He used a rapidly rotating flat mirror. Bright light was directed to the flat mirror whereupon it traveled to another flat mirror fixed a short distance away as in D in the diagram below. The light would reflect back toward the spinning mirror. In the very short time of travel over and back, the rotating mirror turned a small amount and reflected an angle theta ⊝ away from the original path of the light source. See the animation below. It is slowed in order to show the motions. The experimenter needed to measure D and the rate of rotation of the mirror and the angular deflection theta ⊝ in order to calculate the speed of light. Foucault succeeded with this method.

Kevin McFarland University of Rochester

K. McFarland U of Rochester

Here is the actual appartus. This spinning mirror device is from 1863 housed in the Teyler Museum collection in the Netherlands. What strikes me is the quality of workmanship. The hole on the left is for a compressed air hose. The air drove several small turbine blades to spin just below the arched structure. This rotated the small mirror. The mirror is on the order of an inch in diameter. Below is a close up of the mirror mount.

Teyler Museum

Two round brass covers are in place to protect the mirrored surface. Inside is a round piece of glass with two flat surfaces. These covers would have been removed during rotation. Only one of the flat surfaces was coated to serve as a reflecting mirror. During operation, Foucault noted that a rate of 500 rev/sec was possible. His best result were obtained when a reliable steady rate of 400 rev/sec was used. No, the tiny white hand is not part of the apparatus.

Teyler Museum

Michelson’s Improvements

Michelson used such a device during three rounds of experiments between 1878 and 1883. With his device, he improved upon the control of the rotation rate, added more distance from the small rotating mirror to the distant mirror, and was able to operate at brighter light levels. With his refinements, the margin of experimental error was reduced.

His fourth and fifth rounds of experiments in 1922 to 1926 introduced a new kind of rotating mirror. Instead of a spinning flat mirror, he introduced an eight sided octagonal mirror. In the time the light took to travel to and back from a distant mirror, the octagonal mirror would need to turn 1/8 th of a turn so the experimenter could see reflection.

Michelson conducted his experiments between Mt. Wilson Observatory and San Antonio Peak in southern California, a distance of 35,385 meters. Pressurized air spun the octagonal mirror at a rate of 528 rev/sec. He made changes to the rotating mirror trying 8 sided steel, 12 sided glass and steel, and a 16 sided glass. All results were consistently within 1 km/s of 299,798 km/s. His value for light traveling in air are in error compared to what we know of the value today. Today, the accepted value in air is 299,706 km/s. It is slightly faster than that in a vacuum at 299,792.458 km/s. The speed in a vacuum is the fastest possible.

I invite you to follow this link to a description of the Mt. Wilson test site by Tom Mahood as it appeared in recent years. The excellent page include some rare images and views.

The next and final post in this series will discuss the work by Michelson and Morley to experimentally show evidence for a medium throughout all of space called the ether. Some scientists proposed that light, as with other types of waves, must have a medium upon which to travel. The ether was the medium. Michelson and Morley demonstrated conclusively whether the ether existed. Please join me for that.



18 thoughts on “Speed of Light | Done With Mirrors

    • The rotating mirror had a big advantage. The stationary mirror at distance D could be placed much closer in the same laboratory or building. The did introduce different challenges as you noticed.

      • Jim, I am wondering about something now that I’ve had more time to think about this. The speed of rotation must be known for the calculations of the speed of light. How did Fizeau, Michelson and Morley, lacking even electricity much less electronics, measure the rate of mirror rotation with precision? Do you know?

      • Here is how Foucault did it.
        “Foucault used a plane glass disk that was silvered on one side and blackened on the other as his rotating mirror. It was just 14 mm in diameter and mounted in a ring that was part of the vertical axis of a 24 vane turbine driven by compressed air. The total air pressure was kept constant at 30 cm of water, to within 0.2 mm, and the air was delivered to the turbine by a regulated precision blower. A continuous flow of oil at constant pressure lubricated all bearings. A toothed disk performing two rotations per second under precision clockwork was used as a stroboscope for determining the speed of the mirror. Though Foucault rotated the mirror at 500 turns per second, he stated that the mirror and the disk would keep in step within one part in 10,000 for minutes at a time when the mirror was rotating at 400 turns per second.”
        Michelson also used a stroboscopic method.

        From details according to http://www.setterfield.org/cx4.html#FRM

  1. Excellent, Jim.

    I note something that may not be obvious to some readers: there is no electric light involved here and the light source is steady, not pulsed, as some might assume from the animation. The light is effectively pulsed by the spinning mirror as it briefly passes the stationary one. Also, it is only due to previous experiments, such as those by Fizeau, that Michelson knew which multiple of the rotation rate to use in his calculations, thus demonstrating the knowledge-accumulating nature of the scientific method.

    I agree about the workmanship of the apparatus. It is exquisite. I’m reminded of the Har-Ber Village museum of mainly 19th century artifacts near us, just across the state line in Grove, Oklahoma. It has many devices, principally agricultural in nature, that show similar clever design and precision. The milk/cream separator comes to mind. The industrial revolution was not waiting for the discovery of electricity, it was proceeding apace.

    • The speed in a vacuum is the fastest. In air it is slightly slower.

      Michelson got consistent values when he tested in air. His values were in error and too large when compared to what we know today.

      Maybe I should reword that paragraph in the post. It might be confusing.

  2. There’s that notion again of seeing farther as a result of standing on the shoulders of giants.

    I didn’t know till now that Michelson kept on into the 1920s with his experiments to determine the speed of light. Somehow my high school physics class left me with the impression that Michelson did his experiment once and that was that; I don’t know if the fault was the teacher’s, the textbook’s, or my own.

    • I learned quite a few new things myself in reading up on his history. In his last efforts in the 20’s, he had a long metal pipe which could be evacuated. All his previous measurements were in air.

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