Question

Why is it that thermal radiation of a black body usually described by a spectral distribution function rather than an intensity vs frequency curve?

I have a vague explanation for this: Any measured intensity of radiation will contain a spectrum of frequencies which are impossible to separate (even with a very good spectrometer, one can only measure the intensity of an interval). So it is practically impossible to assign a particular intensity to a particular frequency.

Is my reasoning correct?

Answer 1

It's true that you can't talk about intensity without referring to some specific frequency range, but the reason is the definition of intensity itself, not the inherent limits of our measuring devices. Intensity, also called irradiance, is defined as power per unit area. Typically it takes into account radiation at all frequencies (or wavelengths), but you can also talk about the intensity within a particular band like 400 nm?700 nm.

If you wanted to create a graph of intensity versus frequency, you could certainly do so by dividing the frequency axis into bins and plotting one point for each bin representing the total intensity detected within that frequency range. Obviously, the smaller you can make the bins, the more detailed information you get about the spectrum, but the intensity values become correspondingly smaller (and harder to measure accurately) as the bins get smaller. Besides, if everyone did that, different plots from different experiments would be very difficult to compare unless they all decided on a standard bin size.

In order to make data from different experiments comparable, you normalize the intensities by dividing each intensity measurement by the width of the bin. In the limit as the bin width goes to zero, this is just the spectral irradiance.