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Physics32. Electromagnetic WavesEnergy Carried by Electromagnetic Waves

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