 Hi, well I'm Professor Steven Nesheva and I want to tell you a little bit about the connection between Plank or plunk black bodies and what's called the Steppen-Boltzmann formula. So I think you may already be familiar with this with the Steppen-Boltzmann curve, which I'll just remind you on this x-axis here. I've got temperature and on the vertical axis what's being measured is the intensity or flux and the idea is that you have a you have a body like the Sun or maybe the Earth and since all objects glow and this is telling you how much it glows. What's the total intensity of light that comes off that object and as you probably know from experience the hotter something is the more it glows. So I've drawn two points on that graph. One would be the temperature of the Earth which says that it's going to glow with a certain intensity and another one at the temperature of the Sun. This is a little bit misleading in this in that really the Sun is much much hotter, so this would be really much farther over to the right. But it gets the idea across that the Earth radiates with a certain amount of intensity and the Sun radiates with much higher intensity. The formula is given by this, the Steppen-Boltzmann formula says there's a constant sigma, multiply that by the temperature raised to the fourth power and that's what that curve is. So the question to address here is how does that come about? And the way we think about that is that we for any either one of these cases we try to imagine what would be the spectral distribution, that is to say, what is the intensity you know according to wavelength by wavelength and here it's quite it's quite distinctive and the idea goes something like this. The Sun, we're over here, emits with a high intensity at a low wavelength of light. This is a wavelength scale that I've got here and you may already know this, that the peak of the Sun's light happens at about 0.5 microns, which translates to 500 nanometers, and you notice the scale goes from 0.1 to 1, it's a long scale to 10, so 0.5 microns or 500 nanometers is about right there. And in fact the visible range runs from about say 300 to about 700 so that's the that's the visible range. You can also see from this that the Sun also emits in the shorter wavelength, which is the ultraviolet side, and also in what's called the near IR side. Most of the Sun's emits in the visible range, but there's this these big wings. So this curve that I've drawn here, it's called a plonk black body, and it's there's a characteristic curve for any object at any given temperature. The other thing that I've drawn here is a plonk black body curve for something that's at the temperature of the Earth. So let me just annotate that. That's that was a plonk black body for the Sun, and this is a plonk black body for the Earth. You notice a couple things about this. It's lower that so the total intensity is much lower than the energy emitted by the Sun. In fact, I've really exaggerated this quite a lot that this curve would actually be quite tiny compared to that of the Sun, but I wanted to show you them both at the same time. The other thing to notice is that the peak of the spectral emission for the plonk black body function for the Earth happens way over here at a much longer wavelength. It's far outside the visible range. It's way over here. It peaks at 10 micrometers, which people can't even see. So you can't see the Earth glowing. You have 10 special instruments to measure it. So I want to now connect what we've just said to the Stefan Boltzmann picture. It's the area underneath here that we plot under the Stefan Boltzmann. So you can see the area under the Sun's plonk black body curve is really high. The area under the Earth's plonk black body curve is much lower. And again, that's quite exaggerated. This is much bigger than that. Let's see. I've talked about the visible range, the area underneath the plonk black body. The remaining point that I wanted to make about this is this distinction that we make between long wave and short wave. It's very simple. We more or less say, well, I'm going to call short wave to be more or less the range that the Sun emits in, which we're going to call more or less from 0.1 micrometers out to somewhere between, you know, here and here. We'll call that around three microns, three micrometers. Okay, so that's going to be short wave, 0.1 to three micrometers. And then we're going to call long wave to be more or less where the Earth radiates most of its light, which we're going to call three to, let's say, a hundred microns. Okay.