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For instance, this paper uses ##cm^{-1}## for water and yet ##cm^2 / \mu g## for other substances (such as chlorophyll, cellulose and lignin). I have seen the same in other literature.

For a given wavelength, I am trying to calculate the

*extinction length*##L=4.6/\alpha## (the thickness of material required to absorb 99% of incident light). For water this calculation is straightforward. For instance, at a wavelength of 10 micron, the absorption coefficient of water is ##\alpha \approx 1000\ cm^{-1}##, corresponding to ##L \approx 40 \ \mu m##.

But how do we handle this calculation when the absorption coefficient of the material is instead given by ##cm^2 / \mu g##?

Any explanation is greatly appreciated.