- [Instructor] Check out this beautiful photo from the Hubble Telescope. It's so many stars with so many different colors. Why do they have different colors? Well, it turns out that the ones that are reddish or orangish are actually relatively cooler stars. They are at lower temperatures. And the ones that are whitish, like white color over here, you can see, those turn out to be slightly hotter. And the ones that are bluish turn out to be the hottest over here. But my question is, how did we figure this out? I mean, how can we sit on earth and say that, "Hey, the red stars must be cooler and the blue stars must be hotter." Well, that's because we studied the black body radiation. But what exactly is this and what has black body got anything to do with these stars? Well, let's find out. Let's start with what are black bodies and why should we care about them? For that, let's keep an apple outside on a sunny day in a broad daylight, so there's sunlight falling onto it. Remember that sunlight is white light, which make is made of all the colors of the rainbow. The question for us now is what happens to the light once it falls on the apple? Well, some of the light gets reflected, a lot of it is red color, and that's why we see apple to be red color. But what happens to the rest of the colors? Well, they get absorbed. And what we mean by getting absorbed is that remember that light is an electromagnetic wave, which contains electric fields and magnetic fields as well, but we haven't shown the oscillating magnetic fields. But these are the oscillating electric fields. But once they fall on the apple, the electric fields, they will make the electrons jiggle. And as a result, notice the energy from the electromagnetic wave is going into the jiggling energy of the electrons. And this is how the energy from the electromagnetic wave gets converted into the jiggling motion of the electrons or thermal energy of the electrons. And as a result, the temperature of the apple would increase. But wait a second, wait a second. If this was the case, then if you continuously shine light on the apple, its temperature should continuously increase. But that doesn't happen, right? Why doesn't that happen? Well, that's because as the electrons are jiggling, they're gonna produce their own electromagnetic waves. Remember, any accelerated charge will produce electromagnetic waves and therefore, the jiggling electrons will produce their own electromagnetic waves. And we call these electromagnetic waves thermal radiation because that radiation is coming from the thermal motion of the electrons, and because of the thermal radiation, it's losing energy. And so you can see what's going on. It's absorbing energy from the sunlight, but it's also losing energy at the same rate from the thermal radiation. And a balance is achieved, and we say this apple will be at thermal equilibrium, meaning its energy will neither increase nor decrease, so its temperature will stay the same. All the objects that you see around you, something very similar is happening is that thermal equilibrium and they're all giving out thermal radiation. You may be wondering why we can't see the thermal radiation, as we will see in a while, most of this thermal radiation lies in the infrared region, not in the visible region. That's why we can't see it. That's why what you're seeing most cases is just the reflected light, okay? But here's the thing, the light that comes from the star, guess what? It's also thermal radiation. It's coming due to the temperature of the star. Another example is a light that comes from the filament of the bulb. That's also thermal radiation. It's coming because of the temperature of the filament, because of the thermal motion of the electrons inside the filament of the bulb, which means to analyze the stars, I need to analyze the thermal radiations coming from the objects. But the reflected light is a problem. So I only want to analyze objects that do not reflect any light. What kind of objects are those? Ooh, ooh, black objects. If I paint this apple black, the reason it looks black is because it's not reflecting any light. It'll absorb all the light that's incident on it. That's one of the reasons why if you're wearing black clothes in a hot sunny day, it becomes much warmer because it doesn't reflect any light. It absorbs all of it. Now if, of course, it doesn't absorb completely all the color, it does reflect a little bit. That's why you can still see some features. You can still see some reflection of it, but you get the point, right? If this was ideally perfectly black, then it wouldn't reflect any light, and then the only light that I could get from it would be thermal radiation. That's why we love to analyze black bodies because they only give thermal radiation. And therefore, this radiation is also called the black body radiation. And you know what's the cool thing about the black body radiation, it's spectrum, meaning the colors, the different colors that come out and the brightness at which all the different colors come out, all of those details, it only depends on the temperature of the black body. It does not depend upon, say for example, what light will shine on it or it doesn't depend upon, for example, what material it is made of. None of that matters. The characteristics of a black body thermal radiation only depends upon its temperature, which is awesome because that means now I can apply it to stars. Stars also are very similar. They're only also giving out thermal radiation, so I can apply it to the stars, and that's what we'll do now. We'll analyze the thermal radiation that's coming from not properly this apple because I want to increase this temperature and this apple would burn. But maybe we'll take some metal, we'll take some black metal, we'll change its temperature, we'll analyze this black body radiation, and then we can now apply it to the stars. So let's analyze the thermal radiation coming from a metallic box so we can increase its temperature to very high values and it probably wouldn't melt. And how do you analyze it? Well, we can just, you know, find the spectrum using a diffraction grating or a prism that splits all the colors. And of course, because there's also light coming in the invisible region, we also need some detectors for that. But don't worry too much about the practicality. Let's say we all do that. Once we do that, we draw a graph, okay? On the x-axis, we will plot the different wavelengths. So you can see, for example, these are very long wavelengths, which are in the infrared region, which might even go into microwave, it can also go into radio waves, and then here is the visible light. So you have the red part of the spectrum. And then as that wavelength becomes smaller, you have the violet part of the spectrum, and then eventually, it becomes, again, invisible, you go into the ultraviolet. So this is the wavelength. And on the y-axis, we want to plot at what intensity light comes out near each of these wavelengths. And so on the y-axis, we're going to plot the intensity. Technically, intensity represents the amount of radiation energy coming out per second per meter square area of this box. So this way, I don't care about the size of the box. I'm only figuring out, I'm only gonna write down how much each meter square gives out energy per second. That's what we're gonna plot over here. But technically, you can see it's not just intensity, it's intensity per micrometer, which means intensity per wavelength. That's basically what we're talking about. For each wavelength near that region, what is the intensity of light that's coming out? That's why it's intensity per micrometer. But for our purposes, you can just think of this as brightness near each of these wavelengths. So let's begin now, and let's start at very low temperatures, at about 20 degree Celsius. You can see there's also K over here that stands for kelvin. That's another unit of temperature. In fact, that's the standard unit of temperature. And how you go from degree Celsius to kelvin is you just add 273. So 20 plus 273 is 293 kelvin. To go from kelvin to degree Celsius, subtract 273, and there you have it, okay? So what does the graph look like at very low temperatures? Well, it turns out the graph looks like this. What you can immediately see is that not all the wavelengths get the same intensity. In fact, the wavelengths over here gets zero and pretty much zero. It's not technically zero, but for all practical purposes, it is zero. And that's the reason why you can't even see visible light coming out over here. And that's why most things at 20 degrees Celsius, nothing at 10-20 degrees Celsius glows because they do not glow in the invisible light. They glow, however, in the infrared region, and that's how you can detect them with infrared cameras. And a characteristic thing that you see, the curve is, because of the curve, you can see that there will always be one particular wavelength at which you will get the peak value, you get the maximum intensity. For about 20 degrees Celsius, that happens to be somewhere in the long infrared region. Okay, now just let's increase the temperature. Let's heat it up all the way to 3000 kelvin. Again, to convert it into degrees Celsius, just subtract 273, you get about 2,700 something, right, degrees Celsius. But anyways, what does the graph look like now? Well, the graph looks like this. (laughs) What we now find is that the intensities are so, so high that I can even draw it in the same scale. And that kind of makes sense. At very high temperatures, the thermal energy is so high, the electrons are jiggling with such high energies, the thermal radiation comes out with very high energies, therefore, all the wavelengths of light now are gonna give you much higher energies than before. And therefore, the intensities will be much higher, so we can't draw it in the same graph. So we're gonna zoom out. And once we zoom out, this is what it's gonna look like. So the earlier graph, you can imagine it's somewhere over here, very low over here, you can't see it now in the same scale. But now the big change, what big change did we see? Well, first of all, the intensities are much higher than before. But the second big change is that the peak, you can see the peak was earlier over here somewhere. Now it has shifted to the left. At 3000 kelvin, the peak is still in the infrared region. But because the whole graph has shifted, the whole thing has shifted to the left, now a lot of visible light is also coming out. You can see that. And therefore, we will now be able to actually see it glow with our eyes. What color will it look like? Well, all the light is coming out, but not at the same intensity. A lot of brightness, a lot of intensity is in the reddish-orangish region, and therefore, this thing will glow reddish and orangish. So this is what it look like. And now if you look at things like your filament of the bulb or molten steel, pretty much at the same temperature, you can see they glow the same color. We can also understand another thing. Even though filament is giving me that color, it's giving me visible light. Where is the most of the light going? The most of the light coming out from the filament of the bulb is in the infrared region. This is where most of the light is coming out. And look, the visible light is getting, a little bit of energy is coming out. That's why an incandescent bulb actually wastes a lot of electric power because most of it, it just goes out in infrared region. And that's why we switch to LED bulbs because they are much more efficient. Anyways, because the same analysis can apply to the stars, now we can look at some stars, a star which has a similar color, for example, one example of that star is Betelgeuse that you can see from the Earth in the Orion constellation, okay? It has similar color and therefore, we can say the stars that are reddish must be at similar temperature, must be at a lower temperature. This is relatively cool when it comes to stars. All right, now let's increase the temperature even more to about 5,800 kelvin. What does the graph look like? Again, it'll look much higher than before, so I'll have to zoom out. And if I do that, it's gonna look like this. It's the trend remains the same, much higher energies than before. Now the previous graph looks like this. Okay? And another thing, the peak has also shifted more to the left. It has become even shorter. And now notice, the peak is actually somewhere in the visible light, which means it's somewhere near the green region. So at about 5,800 kelvin, the visible light is actually peaking. But what does the color look like? Would it look green? No, because even though a lot of light is coming out from green, you can see there's considerable amount of red and blues and all of the colors are coming out. And as a result, we'll actually see to be pretty much glowing white. So at about 5,800 kelvin, we will see whitish glow. And our sun, for example, is white. It's not yellow. It looks yellow because of the atmosphere. But if you were to go out and look at our sun, it'll actually look about whitish. And guess what? From that, we can say our sun must be pretty much at this temperature. And it turns out to be about at 5,800 kelvin of temperature. And similarly, other stars, which are whitish color must be at similar temperature. And by the way, very quickly, when I say temperature of the star or sun, I'm not talking about the core temperature of the stars. That could be millions of kelvins. Okay? We are talking about the temperature near the outer surface. That is what we're talking about. And that, for sun, is about 5,800 kelvin. We'll do one final temperature increase, let's increase it all the way to about 8,000 kelvin and see what happens. Well, if we do that, now again, you'll get the graph, which is much bigger than before. So I'll again have to zoom out. Same story. And again, you can see the same trend. So this is the earlier graph now, much higher energy than before. And the same trend. Earlier, the peak was near the green light in the visible region. Now, the peak will be somewhere in the ultraviolet, but again, a lot of visible light is still coming out. And this time, notice, because the whole graph has shifted to the left, a lot more energy is coming in the bluish-violetish region. And that's why at very high temperatures, guess what? It will glow bluish-violetish. And therefore, if you now go back to some stars that are bluish in color, for example, this star called Rigel, Rigel, I don't know how you pronounce it, whatever it is. But anyways, it's a bluish star, so I can say that, hey, that must be at a much higher temperature. It must be around 8,000 degrees or 9,000 degree, sorry, 8,000 kelvin or much higher temperature. And there we have it. We can even now draw a color temperature graph, which sort of summarizes, you know, what color we see at different temperatures. So at lower temperatures, it's reddish, orangish, and then it'll go to white, and then it'll start going towards bluish region. This does not represent the peak value. For example, at 5,800, the peak is still green. But because we are seeing multiple colors, this is what the colors will end up looking like to our eyes. If it's too low, then we'll not even be able to see it because most of it will be just in infrared region. This is basically how we can look at the different stars, their colors, and figure out what their temperature is. And when I say temperatures, I'm talking about the temperature in the outer layers, okay? What those temperatures can be. It's a pretty important tool for astronomy.