2 00:00:11,489 --> 00:00:15,389 The way that electromagnetic radiation or light exchanges 3 00:00:15,389 --> 00:00:20,470 energy with objects, is mostly through the electric field. 4 00:00:20,470 --> 00:00:27,110 What happens is, the electric field of the light that's coming in acts on 5 00:00:27,110 --> 00:00:33,540 the charged oscillator of the the object that we're talking about. 6 00:00:33,540 --> 00:00:36,500 And if the frequency is the Greek letter Nu, 7 00:00:36,500 --> 00:00:39,220 the frequency of the light is pretty much 8 00:00:39,220 --> 00:00:42,980 the same as the frequency of the this oscillator. 9 00:00:42,980 --> 00:00:45,868 Then the energy from this light being carried 10 00:00:45,868 --> 00:00:49,960 to the vacuum can be dumped into this oscillator. 11 00:00:49,960 --> 00:00:52,675 And you can heat the thing up through the vacuum. 13 00:00:55,700 --> 00:01:01,490 We're going to talk about the light that comes off of an object. 14 00:01:01,490 --> 00:01:03,635 Because this is a two-way street. 15 00:01:03,635 --> 00:01:06,520 If the light can come in and be 16 00:01:06,520 --> 00:01:10,095 absorbed by this oscillating piece of matter, 17 00:01:10,095 --> 00:01:13,530 if you have this matter being oscillated just because it's warm, 18 00:01:13,530 --> 00:01:17,050 it can also create light and send it back out. 19 00:01:17,050 --> 00:01:21,390 And so we're going to talk about the kinds of light that this object emits 20 00:01:21,390 --> 00:01:23,580 by thinking about a spectrum. 21 00:01:23,580 --> 00:01:27,400 Which is a plot of how bright the light is 22 00:01:27,400 --> 00:01:31,160 as a function of the different frequencies, or wavelengths, or colors, 23 00:01:31,160 --> 00:01:35,570 or however you want to describe the different kinds of light. 24 00:01:35,570 --> 00:01:38,340 It's a plot that looks kind of like this. 25 00:01:38,340 --> 00:01:41,980 It's got an Intensity on the vertical axis. 26 00:01:41,980 --> 00:01:47,060 And then we're going to use wave numbers on the horizontal axis 27 00:01:47,060 --> 00:01:49,530 as our index of "colors". 28 00:01:49,530 --> 00:01:56,960 The units on the Intensity axis are watts per square meter, per wave number. 29 00:01:56,960 --> 00:02:01,720 And the reason why that's done is because that way if you have 30 00:02:02,800 --> 00:02:09,190 a range of light color say between one and two wave number units. 31 00:02:09,190 --> 00:02:12,970 One and two waves per centimeter, for example. 32 00:02:12,970 --> 00:02:16,655 Then the area under this curve is going to be equal to 33 00:02:16,655 --> 00:02:22,400 watts per meter squared per n times n, and the n's would cancel. 34 00:02:22,400 --> 00:02:27,240 Leaving us just with a total of watts per square meter. 35 00:02:27,240 --> 00:02:32,570 So that means that these plots are drawn so that the area under the total curve is 36 00:02:32,570 --> 00:02:37,990 the total energy leaving the object, in nice units that you now 37 00:02:37,990 --> 00:02:42,260 understand, of watts per square meter of the surface of the object. 38 00:02:44,070 --> 00:02:49,040 So what those spectra look like, are these sort of humps. 39 00:02:49,040 --> 00:02:51,060 I've drawn three of these different humps. 40 00:02:51,060 --> 00:02:52,910 This one's sort of off of the top of the chalkboard there. 41 00:02:54,238 --> 00:02:59,371 Because you get different curves depending how warm 42 00:02:59,371 --> 00:03:04,715 the object is. Ss the object, 44 00:03:06,580 --> 00:03:12,480 gets warmer, the peak energy, which is where the intensity is the strongest, 45 00:03:12,480 --> 00:03:19,230 shifts in this direction, toward shorter wavelength, or higher wave number, 46 00:03:19,230 --> 00:03:21,190 more energetic light. 47 00:03:21,190 --> 00:03:23,960 So you probably have known this before by 48 00:03:23,960 --> 00:03:27,310 thinking about the idea of red hot and white hot. 49 00:03:27,310 --> 00:03:31,550 An object just at room temperature is shining light. 50 00:03:31,550 --> 00:03:33,900 But it's all in the infrared, so we can't see it 51 00:03:33,900 --> 00:03:37,080 with our eyes that can only see in the visible range. 52 00:03:37,080 --> 00:03:40,170 But as the object gets hotter and hotter, 53 00:03:40,170 --> 00:03:44,134 the tail starts to encroach in the visible range, and 55 00:03:44,858 --> 00:03:47,730 you start to see some red color there. 56 00:03:47,730 --> 00:03:49,880 And then if it gets really hot, it can 57 00:03:49,880 --> 00:03:53,110 fill up the whole visible range, and that's when something gets white-hot. 58 00:03:53,110 --> 00:03:55,840 White hot is much hotter than red hot. 59 00:03:55,840 --> 00:04:00,500 You already sort of knew that, right? The other thing about this 60 00:04:02,700 --> 00:04:07,700 spectrum is that it gets much bigger as you get hotter. 61 00:04:07,700 --> 00:04:10,700 And it turns out that there's a formula describing this. 62 00:04:10,700 --> 00:04:11,620 It's right here. 63 00:04:11,620 --> 00:04:17,520 The total energy in watts per square meter is given by these three terms. 64 00:04:17,520 --> 00:04:21,910 The first is Epsilon which i'll explain next. 65 00:04:23,270 --> 00:04:26,290 the second is the Stefan–Boltzmann constant which 66 00:04:26,290 --> 00:04:27,720 is just a constant number you can 67 00:04:27,720 --> 00:04:29,640 look up in a book, it never changes. 68 00:04:29,640 --> 00:04:34,680 And then third, is the Temperature in Kelvins raised to the fourth power. 69 00:04:34,680 --> 00:04:36,070 So you raise it to the fourth power. 70 00:04:36,070 --> 00:04:40,520 That means if you double the temperature, the energy flux goes up by a factor of 71 00:04:40,520 --> 00:04:42,200 two to the fourth, which is 16, so 72 00:04:42,200 --> 00:04:46,030 it's a very, very powerful function of temperature. 73 00:04:46,030 --> 00:04:48,600 So, back to this term now, Epsilon. 74 00:04:49,820 --> 00:04:52,948 This relates to 75 00:04:52,948 --> 00:04:58,150 whether the object is what they call a black body or not. 78 00:05:02,478 --> 00:05:05,640 if an object is a black body, it's as though 79 00:05:05,640 --> 00:05:09,230 it's a musical instrument that has all of the notes. 80 00:05:09,230 --> 00:05:11,630 Like a piano that has all the keys, if you 81 00:05:11,630 --> 00:05:14,050 just hit it with a big hammer or something. 82 00:05:14,050 --> 00:05:16,750 Make all of the keys vibrate at once. 83 00:05:16,750 --> 00:05:19,590 You'll get this big wall of sound like this. 84 00:05:19,590 --> 00:05:23,380 But if you have a piano that's missing a bunch of strings in the middle and you do 85 00:05:23,380 --> 00:05:25,560 the same thing, you'll get some low notes and 86 00:05:25,560 --> 00:05:27,620 you'll get some high notes but there will be some 87 00:05:27,620 --> 00:05:29,580 missing stuff in the middle. 88 00:05:29,580 --> 00:05:33,580 So this is what a physicist would call a black body. 89 00:05:33,580 --> 00:05:37,220 Because it makes a smooth black body curve like this. 90 00:05:37,220 --> 00:05:40,522 And the Epsilon value for this would be one. 92 00:05:40,972 --> 00:05:43,880 So you'd put in number one here. 93 00:05:43,880 --> 00:05:46,450 And there's no units to Epsilon it can go 94 00:05:46,450 --> 00:05:50,870 to zero if an object had none of these oscillators, 95 00:05:50,870 --> 00:05:53,080 and couldn't make any infrared light at all, 96 00:05:53,080 --> 00:06:02,918 to one, if it had all of the notes and could make all the different frequencies.