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Thank you. Why would they compress/decompress based on how light is measured? I would assume that the x-axis would reflect the same range of light regardless if the light is measured by length or frequency. Why give different ranges of light?
The x-axis range spans the same region of “photon energy” space in both plots. The data starts at about 280 nm in the first plot, which is 1000 THz (the maximum value in the second plot).
The stretching effect caused by working in different x-axis units is because the units don’t map linearly, but are inversely proportional. A 1 nm wide histogram bin at 1000 nm will contain the histogram counts corresponding to a 0.3 THz wide region at 300 THz in the frequency plot. Another 1 nm wide bin at 200 nm will correspond to a 7.5 THz wide region located at 1500 THz in the frequency plot.
You can get a sense of how this works just by looking at how much space the colorful visible light portion of the spectrum takes up on each plot. In the wavelength plot, by eye I’d say visible light corresponds to about 1/6 the horizontal axis scale. In the frequency plot, it’s more like 1/4.
That normalization is necessary because otherwise exactly how you bin the data would change the vertical scale, even if you used the same units. For example, consider the first plot. Let’s assume the histogram bins are uniformly 1 nm wide. Now imaging rebinning the data into 2 nm wide bins. You would effectively take the contents of 2 bins and combine them into one, so the vertical scale would roughly double. 2 plots would contain the same data but look vastly different in magnitude. But if in both cases you divide by bin width (1 nm or 2 nm, depending) the histogram magnitudes would be equal again. So that’s why the units have to be given in “per nm” or “per THz).