# Measuring Light Wavelength

January 8, 2021

The earliest accurate determination of wavelength was, I think, by Michelson. Using his invention, the Michelson Interferometer, he could turn a micrometer dial and actually count how many wavelengths he moved a mirror. Reasonable monochromatic light could be had at the time from mercury vapor (or other elemental) discharge tubes or from a monochromator (a spectroscope with a slit on the output to select a color). This was around 1880. I confess I don't know for sure. He was determined to measure the speed of light. Exactly when he worked on wavelength I don't know. I'm sure someone here can add that info.

Michelson was able to count a lot of wavelengths so that the mirror moved enough to get a good average from the mechanical measurement. He was able to measure the wavelength of precisely known colors so that the results were easily reproduced by others. At the time there was a lot of interest in the spectra of excited atoms of elements and of the sun and stars through the new medium of photography. Photographic spectra of a star was done first in 1863.

Once you have a wavelength and the speed, which Michelson also determined to a high degree of accuracy by refining the the rotating mirror method, the frequency is just f=velocity/wavelength. The frequencies are crazy big numbers like the red in a helium-neon laser is 4.7376 x 10^14 per second or 473.76 THz. That's tera-Hertz and it is nice that tera- is also trillion. This is why people use wavelength in nanometers, so that the red from the laser is described as 632.8nm, which is a lot easier. If you read older material you will see that we used a slightly more convenient measure, the Angstrom, which is 1/10 a nanometer. The same light is 6328 \$overset{circ}{A} \$. The Angstrom is abbreviated as a capital 'A' with a little dot or circle over it. (It is in the UTF8 character set but I'm not sure will render for everyone, so I faked it in LaTeX.)

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