Anderson Video - Burning Holes with Sunlight

Professor Anderson
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<font color="#ffffff">So let's go back to the burning ants question, right. What we said was if</font> <font color="#ffffff">you're sitting here on the earth and the sun is up above you and now I take a big</font> <font color="#ffffff">lens, I can in fact create an intensity here that will burn up the poor little</font> <font color="#ffffff">ant, right. There's a little ant, not so happy.</font> <font color="#ffffff">Let's see why that works, okay?</font> <font color="#ffffff">And let's say that we're going to use a lens to focus the sun line down to an area</font> <font color="#ffffff">which we will call A spot. Okay, so the lens focuses the sunlight</font> <font color="#ffffff">and therefore the intensity at the spot</font> <font color="#ffffff">is gonna be how much power you've collected with</font> <font color="#ffffff">your lens, or how much power is in that spot, divided by the area of that spot.</font> <font color="#ffffff">But how much power you collect with your lens, that is just S at the earth</font> <font color="#ffffff">times the area of the lens.</font> <font color="#ffffff">And then we have to divide by the area of the spot.</font> <font color="#ffffff">So, how big is your spot? Well it's a circular lens and so it's just pi R squared.</font> <font color="#ffffff">Okay, and let's say that the --</font> <font color="#ffffff">the spot is pretty small, let's say that it has a</font> <font color="#ffffff">diameter of about a millimeter, okay? So we'll let R be something like</font> <font color="#ffffff">a half a millimeter, and then we need to know the area of the</font> <font color="#ffffff">lens and that's the pi R of the lens squared, and that can be pretty big, and</font> <font color="#ffffff">let's say that the area ends up about 0.09 square meters. Okay, so it's a lens</font> <font color="#ffffff">maybe that big. We already know S at the Earth, that was our 1390 watts per</font> <font color="#ffffff">square meter, and so now we can put all this stuff together</font> <font color="#ffffff">and calculate the intensity at that spot.</font> <font color="#ffffff">Okay, so the intensity at the spot is going to be</font> <font color="#ffffff">S at the earth, area of that lens, divided by the area of the spot, and S at the</font> <font color="#ffffff">Earth we said was 1390, area of our lens we said was 0.09, we're all in SI</font> <font color="#ffffff">units here, and then we need a pi R squared for this guy, so we have pi times --</font> <font color="#ffffff">a half a millimeter is 5 times 10 to the minus 4 meters, and we got to square that thing.</font> <font color="#ffffff">Okay, so if you punch in all those numbers tell me what you get. When I did</font> <font color="#ffffff">it earlier I got: 1.6 times ten to the eighth watts per square meter.</font> <font color="#ffffff">Okay, and this is with a lens about yay big, anybody else get that number?</font> <font color="#ffffff">How intense is this? It's similar -- to in fact, a little bit bigger but comparable</font> <font color="#ffffff">to the intensity at the surface of the Sun.</font> <font color="#ffffff">Okay, remember the surface of the Sun? We got something like</font> <font color="#ffffff">six times ten to the seven, and now we've got something ten to the eight.</font> <font color="#ffffff">So it's extremely comparable, in fact a little bit bigger,</font> <font color="#ffffff">than the intensity of the surface at the Sun. So it's no wonder that ant burns up,</font> <font color="#ffffff">right? And in fact if you do this experiment yourself, if you go out with a</font> <font color="#ffffff">big lens, like that big, and you go outside on a hot clear day, it's got to</font> <font color="#ffffff">be nice clear day, you can burn holes in concrete, okay? You can burn holes right</font> <font color="#ffffff">into the concrete itself, really fun. I got a big lens in my lab, we'll try it on</font> <font color="#ffffff">one of these really hot days. You got to be a little careful obviously because,</font> <font color="#ffffff">you know, it's an intense spot and you can burn yourself but also you can't</font> <font color="#ffffff">really look at the spot because it's sort of like looking at a welders arc.</font> <font color="#ffffff">It's just so intense that you can hurt your eyeballs when you do this</font> <font color="#ffffff">experiment, they definitely got to be a little careful.</font>
<font color="#ffffff">So let's go back to the burning ants question, right. What we said was if</font> <font color="#ffffff">you're sitting here on the earth and the sun is up above you and now I take a big</font> <font color="#ffffff">lens, I can in fact create an intensity here that will burn up the poor little</font> <font color="#ffffff">ant, right. There's a little ant, not so happy.</font> <font color="#ffffff">Let's see why that works, okay?</font> <font color="#ffffff">And let's say that we're going to use a lens to focus the sun line down to an area</font> <font color="#ffffff">which we will call A spot. Okay, so the lens focuses the sunlight</font> <font color="#ffffff">and therefore the intensity at the spot</font> <font color="#ffffff">is gonna be how much power you've collected with</font> <font color="#ffffff">your lens, or how much power is in that spot, divided by the area of that spot.</font> <font color="#ffffff">But how much power you collect with your lens, that is just S at the earth</font> <font color="#ffffff">times the area of the lens.</font> <font color="#ffffff">And then we have to divide by the area of the spot.</font> <font color="#ffffff">So, how big is your spot? Well it's a circular lens and so it's just pi R squared.</font> <font color="#ffffff">Okay, and let's say that the --</font> <font color="#ffffff">the spot is pretty small, let's say that it has a</font> <font color="#ffffff">diameter of about a millimeter, okay? So we'll let R be something like</font> <font color="#ffffff">a half a millimeter, and then we need to know the area of the</font> <font color="#ffffff">lens and that's the pi R of the lens squared, and that can be pretty big, and</font> <font color="#ffffff">let's say that the area ends up about 0.09 square meters. Okay, so it's a lens</font> <font color="#ffffff">maybe that big. We already know S at the Earth, that was our 1390 watts per</font> <font color="#ffffff">square meter, and so now we can put all this stuff together</font> <font color="#ffffff">and calculate the intensity at that spot.</font> <font color="#ffffff">Okay, so the intensity at the spot is going to be</font> <font color="#ffffff">S at the earth, area of that lens, divided by the area of the spot, and S at the</font> <font color="#ffffff">Earth we said was 1390, area of our lens we said was 0.09, we're all in SI</font> <font color="#ffffff">units here, and then we need a pi R squared for this guy, so we have pi times --</font> <font color="#ffffff">a half a millimeter is 5 times 10 to the minus 4 meters, and we got to square that thing.</font> <font color="#ffffff">Okay, so if you punch in all those numbers tell me what you get. When I did</font> <font color="#ffffff">it earlier I got: 1.6 times ten to the eighth watts per square meter.</font> <font color="#ffffff">Okay, and this is with a lens about yay big, anybody else get that number?</font> <font color="#ffffff">How intense is this? It's similar -- to in fact, a little bit bigger but comparable</font> <font color="#ffffff">to the intensity at the surface of the Sun.</font> <font color="#ffffff">Okay, remember the surface of the Sun? We got something like</font> <font color="#ffffff">six times ten to the seven, and now we've got something ten to the eight.</font> <font color="#ffffff">So it's extremely comparable, in fact a little bit bigger,</font> <font color="#ffffff">than the intensity of the surface at the Sun. So it's no wonder that ant burns up,</font> <font color="#ffffff">right? And in fact if you do this experiment yourself, if you go out with a</font> <font color="#ffffff">big lens, like that big, and you go outside on a hot clear day, it's got to</font> <font color="#ffffff">be nice clear day, you can burn holes in concrete, okay? You can burn holes right</font> <font color="#ffffff">into the concrete itself, really fun. I got a big lens in my lab, we'll try it on</font> <font color="#ffffff">one of these really hot days. You got to be a little careful obviously because,</font> <font color="#ffffff">you know, it's an intense spot and you can burn yourself but also you can't</font> <font color="#ffffff">really look at the spot because it's sort of like looking at a welders arc.</font> <font color="#ffffff">It's just so intense that you can hurt your eyeballs when you do this</font> <font color="#ffffff">experiment, they definitely got to be a little careful.</font>