I thought that the frequency of light was directly inverse to the wavelength by a constant. In other words, I assumed that graphing the frequency of light as a function of wavelength would be a straight inverse line. Because of that, the graphs for the distribution of light from the sun as functions of frequency and wavelength would be exactly the same, but reversed. Yet, this is not what is reported in the linked article. Even more confusing to me is that the different functions peak at different light. When as a function of frequency, the light peaks at infrared. When as a function of wavelength, the light peaks at violet.
What am I misunderstanding? Is the frequency of light not directly proportional to it’s wavelength? Or is this something to do with the way we are measuring the light from the Sun?
In a vacuum c=nu*lamba or the speed of light is equal to the frequency times wavelength. So nu=c/lamba. If you plot 1/x, you don’t get a straight inverse line. You get a multiplicative inverse. So not only is the data flipped, but it also has a distortion that will compress portions and stretch others.
As to why the functions peak at different colors, I believe this is due to an oddity in the axis units. Notice how the irradiance is in W/m^2/nm in the first and W/m^2/THz in the second. Are you familiar with histograms? Think of it like binning the power intensity per nm bin and power intensity per THz bin. Since THz and nm are inversely related, the width of the bins is changing when the basis is changed. This leads to another stretching in the data that is less intuitive.
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).