Counting fringes measures what a ruler cannot
In his 1907 lecture Michelson explains that as one optical path changes, the fringes pass through bright and dark again and again. Counting those cycles compares a mechanical displacement with the wavelength of light. Light crosses the moving arm twice, so the path changes by twice the mirror travel; mix the two up and the length comes out double.
The measurement links a light source, an optical layout and a material standard. A fringe corresponds to a definite length only once the wavelength and the medium the light travels through are specified.
Here the mirror moves along the beam in one arm at normal incidence. The symbols are mirror travel, fringe-cycle count, vacuum wavelength and the fixed refractive index along that arm. The wavelength and travel use the same length unit.
Sources: [1]
A spectral line can contain more than one frequency
Michelson reports searching through the light of many gases and metal vapours. When a line was broad, or was really several lines, the fringes faded as the path difference grew. The red line of cadmium was unusually well suited to comparing the metre with a wavelength.
A fine translation stage was therefore not enough. Changes in the source spectrum can wash out or modulate the very fringes being counted. Michelson treated visibility both as a practical limit on length comparison and as information about the structure of the line.
Sources: [1]
Visibility compares the brightest and darkest fringes
In an ideal two-beam measurement, visibility is the difference between the maximum and minimum intensity divided by their sum. Unequal beam powers, mismatched polarization and background light lower it even when the source is coherent. A low visibility therefore does not by itself measure the width of the line.
With a stable source, the way visibility changes with optical delay carries information about first-order coherence. Turning the whole interferogram into a spectrum also needs an accurately known delay, a treatment of the finite scan window and a correction for the instrument response. Watching one set of fringes disappear tells you much less.
Sources: [1]
Agreement between repeats does not settle accuracy
Michelson compared measurements made by different observers at different times. Their agreement showed the result was reproducible, but its accuracy still depended on the refractive index, thermal expansion, alignment and the reference standard. The historical result did not define today’s SI metre.
The 1907 prize recognized optical precision instruments and the measurements made with them. Retelling it as the ether-drift null result hides the spectroscopy and metrology that the lecture actually develops.
Separate a shifting fringe from a fading one
Read the lecture’s length comparison alongside its discussion of visibility. In the linked model, first hold the source and vibration fixed and move the mirror. Then hold the mean mirror position fixed and increase the vibration. Motion shifts the fringes; averaging over vibration reduces their visibility even though the model’s source remains monochromatic. The Lab has no control for changing the source linewidth.
Sources: [1]