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The Michelson interferometer is historically important for its use by Michelson and Morley in 1887 to provide experimental evidence against the theory of the luminiferous aether. Michelson subsequently used the interferometer to measure the length of the standard metre in terms of the wavelength of an atomic spectral line.
The basic idea of how an interferometer works, is to split a beam of light into two beams; delay one with respect to the other, and then recombine them to observe their interference.