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Some scientists are remembered for one discovery. Albert Michelson is remembered for a habit: measuring the same thing again and again, each time more precisely, for about fifty years. That habit gave physics a better value for the speed of light and an experiment whose "failure" became one of the most famous results in physics. This post covers his life, his two key experiments, the fringe-shift arithmetic behind the second one, and what his approach can teach you about measurement.
Who was Albert Michelson?
The Nobel Prize facts page gives his birth as 19 December 1852 in Strelno, Prussia (now Strzelno, Poland) and his death as 9 May 1931 in Pasadena, California. He won the 1907 Nobel Prize in Physics "for his optical precision instruments and the spectroscopic and metrological investigations carried out with their aid", while at the University of Chicago.
The American Institute of Physics adds the background. He was brought to America as a small child, grew up in mining towns in California and Nevada, entered the US Naval Academy at Annapolis in 1869 and stayed on as a science instructor. He later worked at the Case School of Applied Science, Clark University and Chicago, and the AIP describes him as the first American scientist to win a Nobel Prize.
How did Michelson measure the speed of light in 1879?
In November 1877, while preparing a classroom demonstration of Foucault's rotating-mirror method, Michelson saw how to make the effect much larger. (The earlier toothed-wheel approach is in our post on Fizeau and the first Earth-based speed of light.) His report, Experimental Determination of the Velocity of Light, describes a first mirror made for 10 dollars that turned 128 times a second over a 500-foot distance. It gave a deflection of the returning light about twenty times larger than Foucault's.
With 2,000 dollars from a private donor, he then built a full version along the sea wall of the Naval Academy, with a lens of 150-foot focal length and a light path of about 2,000 feet each way. The mirror spun at roughly 257 turns a second, and the returning image shifted by more than 110 millimetres, enough to measure with a micrometer. After rejecting thirty earlier sets of readings, he made the final series from 5 June 1879.
His final value, corrected to vacuum, was 299,940 km/s, with a possible error he estimated at 51 km/s. Today the speed of light is defined as 299,792,458 m/s. Michelson was about 148 km/s high, roughly three times his own error estimate. Even a careful experimenter can miss a source of error.
What was the Michelson-Morley experiment?
Physicists then thought light was a wave in an invisible ether. If Earth moves through the ether, light should take slightly different times along and across the direction of motion. Michelson built an interferometer to detect that difference, splitting a beam in two and recombining it so that a tiny change in path shows up as moving fringes.
With Edward Morley he published On the Relative Motion of the Earth and the Luminiferous Ether in 1887. The text on Wikisource describes the apparatus. A stone about 1.5 metres square and 0.3 metres thick floated on mercury so it could be turned smoothly, and mirrors at its corners reflected the light back and forth to make a path of about 11 metres.
They expected a shift of 0.4 fringe as the stone turned. In their words, "The actual displacement was certainly less than the twentieth part of this, and probably less than the fortieth part."
Where does the 0.4 fringe come from?
You can check their prediction with numbers from the paper.
Speed ratio. Earth orbits the Sun at about 29.8 km/s, according to NASA's Earth fact sheet. Divided by about 300,000 km/s for light, v/c is about 10⁻⁴, so (v/c)² is about 10⁻⁸.
Path difference. The paper gives the expected effect as 2D(v/c)². With D = 11 m, that is 2 × 11 × 10⁻⁸ = 2.2 × 10⁻⁷ m.
In wavelengths. The paper says 11 m is about 2 × 10⁷ wavelengths of yellow light, so one wavelength is 11 / (2 × 10⁷) = 5.5 × 10⁻⁷ m.
Fringe shift. 2.2 × 10⁻⁷ / 5.5 × 10⁻⁷ = 0.4 fringe.
Because the shift depends on v², a result 1/40 as large means a speed √(1/40) ≈ 0.16 times as large. The paper concluded that the relative velocity of Earth and ether was probably less than one-sixth of Earth's orbital speed.
Two common slips: forgetting to square v/c, which gives a shift ten thousand times too big, and mixing the arm length with the total path. Fringe-counting of this kind is the same idea as path difference in Young's double-slit problems, which the JEE (Main) syllabus does include.
The AIP notes that the experiment became part of the background from which Einstein's relativity grew, while Michelson himself never fully gave up the ether.
What did he measure next?
He kept improving. The AIP lists his measurement of the international metre against the wavelength of cadmium light, the first measurement of a star's angular diameter, and a 1926 speed-of-light measurement over a 22-mile baseline with an uncertainty of about 4 km/s. He died while writing up a further measurement made in an evacuated pipe a mile long.
What can a student learn from Michelson's way of working?
Make the signal bigger before you measure it. His first gain came from a larger deflection, not a better ruler.
Throw out data honestly, and say so. He reported rejecting thirty early sets and why.
Estimate your error, then test it. His ±51 km/s was too small, a reminder that error bars are a claim you should keep checking.
Take a null result seriously. A clean "nothing" told physics more than a noisy "something".
If a topic like interference keeps slipping away, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, so you can revisit path difference before you try fringe problems.
This week, redo the 0.4-fringe calculation without notes, then halve D and predict the new shift before you work it out.
