[MUSIC] The way that electromagnetic radiation or light exchanges energy with objects is mostly through the electric field. So what happens is, the electric field of the light that's coming in acts on the, a charged oscillator of the object that we're talking about, and if the frequency, there's a Greek letter nu, the frequency of the light is pretty much the same as the frequency of the, this oscillator, then the energy from this light being carried through the vacuum can be dumped into this oscillator and you can heat the thing up through the vacuum. So we're gonna talk about the light that comes off of an object, because this is a two-way street. If the light can come in and be absorbed by this oscillating piece of matter, if you have this matter being oscillated just because it's warm, it can also create light and send it back out. And so we're gonna talk about the kinds of light that this object emits by thinking about a spectrum, which is a plot of how bright the light is as a function of the different frequencies or wavelengths or colors or however you want to describe the different kinds of light. So it's a plot that looks kind of like this. It's got an intensity on the vertical axis. And then we're going to use wave numbers on the horizontal axis as our index of colors. So the units on the intensity axis are watts per square meter per wave number. And the reason why that's done is because that way if you have a range of light color, say between one and two wave number units, one and two waves per centimeter, for example, then the area under this curve is going to be equal to watts per meter squared per n times n. And the n's will cancel, leaving us just with a total of watts per square meter. So that means that these plots are drawn so that the area under the total curve is the total energy leaving the object in nice units that you now understand of watts per square meter of the surface of the object. So what those spectra look like are these sort of humps. I've drawn three of these different humps. This one's sort of off the top of the chalkboard there. Because you get different curves, depending how, on how warm the object is. So as the object gets warmer, the peak energy, which is where the intensity is the strongest, shifts in this direction toward a shorter wavelength or higher wave number, more energetic light. So you probably had known this before by thinking about sort of red hot and white hot. So an object that's just at room temperature is shining light, but it's all in the infrared, so we can't see it with our eyes that can only see in the visible range. But as the object gets hotter and hotter, it starts to, the tail starts to encroach in the visible range and you start to see some red color there. And then if it gets really hot, it can fill up the whole visible range and that's when something gets white hot. So white hot is much hotter than red hot. You already sort of knew that, right? The other thing about this spectrum is that it gets much bigger as you get hotter. And it turns out that there's a formula describing this. It's right here. The total energy in watts per square meter is given by these three terms. The first is epsilon, which I'll explain next. The second is the Stefan-Boltzmann constant, which is just a constant number you can look up in a book. It never changes. And the third is the temperature in Kelvins raised to the fourth power. So you raise it to the fourth power, that means if you double the temperature, the energy flux goes up by a factor of two to the fourth which is 16. So it's a very very powerful function of temperature. So back to this term now, epsilon. This relates to a quantity, whether the object is what they call a blackbody or not. So [SOUND] if an object is a blackbody, it's as though it's a musical instrument that has all of the notes. So, like a piano that has all the keys, if you just, you know, hit it with a big hammer or something, make all of the keys vibrate at once, you'll get this big wall of sound like this. But if you have a piano that's missing a bunch of strings in the middle and you do the same thing, you'll get some low notes and you'll get some high notes, but there will be some missing stuff in the middle. So this is what they, what a physicist would call a blackbody, because it makes a smooth blackbody curve like this, and the epsilon value for this would be one. So you'd put in a number one here. And there's no units to epsilon. It either goes for zero, if an object had no of these oscillators and couldn't make any infrared light at all, to one if it had all of the notes and could make all the different frequencies. [MUSIC]