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?
It’s because the wavelength and frequency are inversely related. When the wavelength is low and the frequency is high, the wavelength is also moving very slowly, compared to the frequency which is moving very quickly. Since the frequency is changing so quickly, the power-per-unit-frequency is lower at higher frequencies, and higher at lower frequencies (at least relative to the power-per-unit-wavelength).
Let me try and use a car analogy:
You’re driving home through Wisconsin, and you live on the border between Wisconsin and Minnesota. The mile markers on the road decrease as you go, reaching 0 at the state border, where you happen to live.
The cows along the highway are evenly distributed, so if you count the cows as you drive, but restart your count every mile when you see the mile marker, you will reach the same number of cows every mile.
Now, the frequency is inversely related to the mile number. The frequency in this case refers to your children in the back seat asking, “Are we there yet?” They know damn well how far it is to home, because they can just look at the mile markers. Regardless, their rate of asking increases as the mile markers go down. When you’re at mile marker 100, they ask once every 10 minutes. When you’re at mile marker 1, they ask 10 times per minute.
If you instead look at the number of cows between “Are we there yet?” asks, then you will find that the cows-per-ask is much different from the cows-per-mile. At high distances (low frequencies), the cows-per-ask is very high, while at low distances (high frequencies), the cows-per-ask is very low.
Now, the article is looking at power-per-unit-frequency, so you’d actually have to measure the rate in change of how often the kids ask “Are we there yet?” And that would give you a little different result. You might need calculus to correctly calculate the derivative of the number of asks. But hopefully this illustrates that you can get different results, by using a different per-thing to measure your value.
This covers it all well, but I think a simple explanation is that although “W/m^2/x” looks the same on the axes, it’s not the same. f=1/w, so one axis is W/m^2/f and one is W/m^2*f. The article makes a big deal out of the differences as if the x axis were the only difference, but they’re just very different things being plotted.