1 00:00:02,860 --> 00:00:08,368 I said that everything in some sense, that was done for centuries after Newton 2 00:00:08,368 --> 00:00:13,665 was filling in the details to F = MA. I don't want to give you the wrong 3 00:00:13,665 --> 00:00:17,197 impression. There are a lot of fascinating details. 4 00:00:17,197 --> 00:00:23,059 Newton's universe is rich and wonderful, and centuries of work by many, many, many 5 00:00:23,059 --> 00:00:27,650 brilliant people went into producing insights and understandings. 6 00:00:27,650 --> 00:00:33,188 And I wish I had the time to tell you about at least that part of it that I 7 00:00:33,188 --> 00:00:35,665 know. But, we're an astronomy class. 8 00:00:35,665 --> 00:00:40,912 What I'm going to do in the next two clips is give you sort of a highlight 9 00:00:40,912 --> 00:00:46,742 reel of those of the aspects of what has been learned in the 250 years since 10 00:00:46,742 --> 00:00:50,021 Newton and a little bit of the century since. 11 00:00:50,021 --> 00:00:54,336 that will impact what we do and that we will need. 12 00:00:54,336 --> 00:00:59,186 And, we will go through and try to develop, if not as deep an understanding 13 00:00:59,186 --> 00:01:03,642 as we did for gravity which will be central, some intuition and some 14 00:01:03,642 --> 00:01:07,509 understanding for some other important concepts in physics. 15 00:01:07,509 --> 00:01:12,555 And as I said, we'll organize it by the M, the structure of matter, and the F, 16 00:01:12,555 --> 00:01:15,570 the forces that act. [COUGH] And we will start. 17 00:01:15,570 --> 00:01:21,286 Well, let's start with the M side. We'll start with what we know the end of 18 00:01:21,286 --> 00:01:28,189 the 19th century about the structure of matter. By the end of the 19th century, 19 00:01:28,189 --> 00:01:33,172 there we have a pretty comprehensive understanding of the 20 00:01:33,172 --> 00:01:38,118 structure of matter. and its center is what is known as the 21 00:01:38,118 --> 00:01:43,223 atomic theory of matter. All known matter is made up of a 100 or 22 00:01:43,223 --> 00:01:45,936 so types of atoms, immutable units. 23 00:01:45,936 --> 00:01:50,768 they're indexed by an number called Z that runs from one to 24 00:01:50,768 --> 00:01:56,033 whatever a hundred, and roughly high elements with higher ZF, heavier atoms, 25 00:01:56,033 --> 00:01:59,794 more massive atoms. And these characterize the chemical 26 00:01:59,794 --> 00:02:04,580 elements. We understand some rules by which they bind together to form 27 00:02:04,580 --> 00:02:08,410 compounds and molecules and various kinds of objects. 28 00:02:08,410 --> 00:02:12,630 And bulk matter can appear in one of three common states. 29 00:02:12,630 --> 00:02:15,514 We have solids, we have liquids and gases. 30 00:02:15,514 --> 00:02:20,508 And in each, the bulk properties are understood as a consequence of the 31 00:02:20,508 --> 00:02:25,080 microscopic dynamics of the atoms and the molecules that form it. 32 00:02:25,080 --> 00:02:30,630 And, as a good and very helpful to us, example, 33 00:02:30,630 --> 00:02:35,832 one of the forms of energy we discussed when we talked about non-conservation of 34 00:02:35,832 --> 00:02:39,857 mechanical energy was heat. Friction, for example, converts kinetic 35 00:02:39,857 --> 00:02:41,220 energy to heat. And 36 00:02:41,220 --> 00:02:45,707 heat causes a object's temperature to rise, so we know what we mean when 37 00:02:45,707 --> 00:02:48,886 something is hot. We mean, it has a high temperature. 38 00:02:48,886 --> 00:02:53,997 in the context of an atomic theory, we have a good understanding of temperature. 39 00:02:53,997 --> 00:02:58,671 Temperature is simply a measure of the average random motions of atoms and 40 00:02:58,671 --> 00:03:03,408 molecules inside an object which explains why heat is sort of lowest common 41 00:03:03,408 --> 00:03:07,432 denominator of energy. Heat is the energy that something has, 42 00:03:07,432 --> 00:03:12,040 when it's doing its own thing. It's not moving in bulk, but its own 43 00:03:12,040 --> 00:03:15,740 internal degrees of freedom are randomly fluctuating. 44 00:03:15,740 --> 00:03:21,422 And for example, in an ideal gas, that's a gas that's made up of atoms or 45 00:03:21,422 --> 00:03:25,022 molecules, that have no internal degrees of freedom 46 00:03:25,022 --> 00:03:30,658 and are just non-interacting and bumping off each other in the walls. Then, you 47 00:03:30,658 --> 00:03:36,227 can show that temperature gives you the average kinetic energy of a molecule or 48 00:03:36,227 --> 00:03:40,698 an atom or whatever it is, is proportional to the temperature. 49 00:03:40,698 --> 00:03:44,680 And temperature, in this expression, is measured in Kelvin. 50 00:03:44,680 --> 00:03:48,323 Kelvin degrees are the same as centigrade degrees. 51 00:03:48,323 --> 00:03:53,268 That just determines the units in which we measure this con, constant here, K, 52 00:03:53,268 --> 00:03:58,343 which is called Boltzmann's constant. What is not arbitrary of course, is where 53 00:03:58,343 --> 00:04:03,353 you put the zero of T because doubling the temperature relative to that zero 54 00:04:03,353 --> 00:04:08,363 involves doubling the energy, and there is a temperature at which the average 55 00:04:08,363 --> 00:04:11,876 kinetic energy of molecules dissents to complete zero. 56 00:04:11,876 --> 00:04:15,390 This is absolute zero, or -273 or so degrees centigrade. 57 00:04:15,390 --> 00:04:20,268 And this is the origin of that. And using these equations, you can see 58 00:04:20,268 --> 00:04:24,266 that at higher temperatures the molecules bump around more. 59 00:04:24,266 --> 00:04:28,400 A gas exerts a pressure on any container in which you put it. 60 00:04:28,400 --> 00:04:33,709 The pressure is a force per unit area applied in, equally in all directions, 61 00:04:33,709 --> 00:04:39,231 and the pressure times the volume for an ideal guess is given by that same 62 00:04:39,231 --> 00:04:43,975 Boltzmann constant times the temperature times the number of atoms. 63 00:04:43,975 --> 00:04:46,877 In this guess, most guesses are not ideal. 64 00:04:46,877 --> 00:04:52,620 there are all kinds of subtleties here. But, the essence of what we see here is 65 00:04:52,620 --> 00:04:57,877 that temperature is a measure of the random motion of the atoms and that the 66 00:04:57,877 --> 00:05:02,042 pressure and the volume increase with he, rising temperature. 67 00:05:02,042 --> 00:05:07,573 if you take a gas and you cool it at sufficiently low temperatures and if the 68 00:05:07,573 --> 00:05:11,055 pressure if sufficiently high, we'll see that later. 69 00:05:11,055 --> 00:05:16,613 you form a liquid phase which is similar to a gas in that it doesn't have a fixed 70 00:05:16,613 --> 00:05:21,574 shape, the items are moving around, but they are weakly bound. And as a result, 71 00:05:21,574 --> 00:05:26,927 you form a phase called the liquid which is almost incompressible, which means 72 00:05:26,927 --> 00:05:30,779 under reasonable pressures it maintains a constant density. 73 00:05:30,779 --> 00:05:35,414 The volume of a chunk of a given amount of liquid is pretty much fixed. 74 00:05:35,414 --> 00:05:41,249 in both cases, in both phases, the density decreases with temperature. 75 00:05:41,249 --> 00:05:47,718 What that is especially useful to us for? Is it tells us that if you have a 76 00:05:47,718 --> 00:05:54,518 collection of fluid under gravity, then the worm fluid, which is expanded and is 77 00:05:54,518 --> 00:05:59,534 therefore less dense, will rise because it floats above the 78 00:05:59,534 --> 00:06:04,187 cooler liquid. And this brings us to the point that an 79 00:06:04,187 --> 00:06:09,319 equilibrium with gravity the pressure in a collection of fluid 80 00:06:09,319 --> 00:06:13,829 will not be constant and the same at all points on the container. 81 00:06:13,829 --> 00:06:17,212 This is the case in the absence of external forces. 82 00:06:17,212 --> 00:06:22,584 In the presence of an external force like gravity, pressure will, in fact, increase 83 00:06:22,584 --> 00:06:26,696 with depth at a rate proportional to the density of the fluid. 84 00:06:26,696 --> 00:06:32,003 And let's see a demonstration of this, and maybe it'll help us understand what's 85 00:06:32,003 --> 00:06:34,428 going on. In this image, 86 00:06:34,428 --> 00:06:38,282 what we see is very simply, me holding a slinky, 87 00:06:38,282 --> 00:06:41,658 a spring. And, what you see when you look at it is 88 00:06:41,658 --> 00:06:46,935 the following, not very surprising fact, which is that near the top of the spring, 89 00:06:46,935 --> 00:06:50,629 the spring is more stretched than it is near the bottom. 90 00:06:50,629 --> 00:06:53,795 And the way you understand that is quite simple. 91 00:06:53,795 --> 00:06:59,204 A slinky stretches more the more you pull it, and the top half of the slinky is 92 00:06:59,204 --> 00:07:04,665 holding up its own weight, as well as the entire half weight of the bottom half of 93 00:07:04,665 --> 00:07:07,986 the slinky. Whereas, the coils of the slinky very 94 00:07:07,986 --> 00:07:12,731 near the bottom are not holding up anything, and so they're relatively 95 00:07:12,731 --> 00:07:17,136 relaxed and unstretched. The higher up the slinky you go, the more 96 00:07:17,136 --> 00:07:21,948 of the weight the slinky is supporting. And therefore, if you look at it 97 00:07:21,948 --> 00:07:27,574 carefully, you'll see that the degree to which the slinky is stretched decreases 98 00:07:27,574 --> 00:07:32,678 uniformly from top to bottom. What wee see here is me holding a cup of 99 00:07:32,678 --> 00:07:35,752 water. this is to demonstrate the decreasing 100 00:07:35,752 --> 00:07:39,289 pressure with height or increase in pressure with depth. 101 00:07:39,289 --> 00:07:43,836 Now, this is true for the air. We know that at high altitude, air pressure 102 00:07:43,836 --> 00:07:48,763 decreases. But remember, the decrease in pressure is due to the extra weight of 103 00:07:48,763 --> 00:07:53,626 the air, and since air is not very dense. We're going to assume that air pressure 104 00:07:53,626 --> 00:07:58,403 is the same everywhere in this room. Not so for the cup because the density of 105 00:07:58,403 --> 00:08:02,040 water is much larger. The water at the bottom of the cup, just 106 00:08:02,040 --> 00:08:06,868 like the spring at the top of the slinky, is holding up all of the water above it, 107 00:08:06,868 --> 00:08:10,922 whereas the water at the top of the cup is not holding up anything. 108 00:08:10,922 --> 00:08:15,512 And so, I expect the pressure to increase from the top of the cup towards the 109 00:08:15,512 --> 00:08:20,438 bottom respectful of the density of the water in the cup and there's a way to see 110 00:08:20,438 --> 00:08:23,202 this. The way you see this is, we drilled holes 111 00:08:23,202 --> 00:08:28,011 at the edge of the cup. And when I open those holes, if the pressure of the fluid 112 00:08:28,011 --> 00:08:32,819 is identical to the pressure at the top, which is the pressure of the air around 113 00:08:32,819 --> 00:08:37,087 it, then the fluid will happily stay in the cup held in by air pressure. 114 00:08:37,087 --> 00:08:40,764 But, of course, it won't. When I remove my fingers, the fluid will 115 00:08:40,764 --> 00:08:45,123 come splashing out impelled by the excess pressure at the bottom of the cup, 116 00:08:45,123 --> 00:08:49,712 relative to the air pressure which is similar to the pressure at the top of the 117 00:08:49,712 --> 00:08:52,293 cup. And in case you're not certain that this 118 00:08:52,293 --> 00:08:56,767 is due to the weight of the water and to gravity, I will drop the cup. At which 119 00:08:56,767 --> 00:09:01,184 point, fluid becomes weightless, the pressure at the top of the cup and at the 120 00:09:01,184 --> 00:09:04,970 bottom of the cup are now the same, and indeed, the fountain ceases. 121 00:09:04,970 --> 00:09:09,705 So, I hope I've convinced you that, in a fluid and equilibrium under the influence 122 00:09:09,705 --> 00:09:14,323 of gravity, pressure increases with depth depending on the density of the fluid. 123 00:09:14,323 --> 00:09:18,707 This is going to be important in astronomical context in understanding the 124 00:09:18,707 --> 00:09:22,858 structure of things like planets and stars, which contain fluid and are 125 00:09:22,858 --> 00:09:28,119 certainly held together by gravity. we talked about gasses and liquids. 126 00:09:28,119 --> 00:09:32,137 matter comes in a solid state. In a solid, the positions of atoms are 127 00:09:32,137 --> 00:09:35,177 roughly fixed, they can oscillate about those positions. 128 00:09:35,177 --> 00:09:38,658 This allows a solid to maintain its shape under external force. 129 00:09:38,658 --> 00:09:42,968 You can apply pressures and stresses and a solid will react, but only a little 130 00:09:42,968 --> 00:09:45,508 bit. It will not, in fact, change its shape to 131 00:09:45,508 --> 00:09:49,102 suit a container. the slinky we had was a very good example 132 00:09:49,102 --> 00:09:52,406 of a solid object. It deformed in response to gravity, but 133 00:09:52,406 --> 00:09:56,753 it didn't completely stretch out. It gave some small proportionate response 134 00:09:56,753 --> 00:10:01,506 to the stresses that were placed upon it. And the larger those stresses the larger 135 00:10:01,506 --> 00:10:03,940 the response, but the response was limited. 136 00:10:03,940 --> 00:10:08,630 The slinky retained fundamentally its shape even under duress. 137 00:10:08,630 --> 00:10:14,842 In all of these phases, fundamentally the interaction is between each atom or 138 00:10:14,842 --> 00:10:20,570 molecule and those near to it. There is no long distance interaction 139 00:10:20,570 --> 00:10:25,311 or there's a weak interaction between atoms in one side, on one side of the 140 00:10:25,311 --> 00:10:28,346 slinky. And on the other, each side of the bit of 141 00:10:28,346 --> 00:10:33,024 a slinky knows about the bits around it. And the result is that if you, for 142 00:10:33,024 --> 00:10:38,209 example, compress the slinky at what one point or move it at one point, then the 143 00:10:38,209 --> 00:10:43,013 perturbation travels through the material as each piece communicates the 144 00:10:43,013 --> 00:10:48,180 information, if you wish, to the next bit over. And this mechanical deformations of 145 00:10:48,180 --> 00:10:53,191 a solid, of liquid or a gas are called sound wave, and they travel with a speed 146 00:10:53,191 --> 00:10:57,624 characteristic of the material. Now, the most familiar to us, of course, 147 00:10:57,624 --> 00:11:02,699 are the longitudinal sound waves in the air, that is what we hear with our ears. 148 00:11:02,699 --> 00:11:06,633 And let's use that slinky. There's a very nice demonstration of wave 149 00:11:06,633 --> 00:11:09,724 propagation. To do that, let's see what happens when I 150 00:11:09,724 --> 00:11:14,077 let go of the top of the slinky. Remember, the slinky was extended in such 151 00:11:14,077 --> 00:11:18,549 a way that it was in equilibrium. The net force on every bit of it vanished 152 00:11:18,549 --> 00:11:23,438 and this had to do with the fact that it was more extended at the top and less at 153 00:11:23,438 --> 00:11:28,208 the bottom so that this compensated for the pull of gravity on every individual 154 00:11:28,208 --> 00:11:30,831 piece. Now, when I release the top, the top of 155 00:11:30,831 --> 00:11:34,877 the slinky starts falling down. But near the bottom, everything is still 156 00:11:34,877 --> 00:11:37,900 in equilibrium. The bottom of the slinky is not falling. 157 00:11:37,900 --> 00:11:42,839 What we see is a density wave propagating at the appropriate speed, determined by 158 00:11:42,839 --> 00:11:47,230 the slinky, through the slinky. And it is only when this wave reaches the 159 00:11:47,230 --> 00:11:51,132 bottom of the slinky that the bottom begins actually to fall. 160 00:11:51,132 --> 00:11:55,767 Until that time, it is in equilibrium, and the information that something has 161 00:11:55,767 --> 00:12:00,462 happened at the top has not reached it. What we're seeing is a sound wave. You 162 00:12:00,462 --> 00:12:04,914 bang on something at one point and it takes time for that deformation to 163 00:12:04,914 --> 00:12:08,451 propagate through the material and reach the other end. 164 00:12:08,451 --> 00:12:12,531 In this simulation, we are going to be able to make some 165 00:12:12,531 --> 00:12:15,744 waves. So, if I grab the end of this rope, the 166 00:12:15,744 --> 00:12:21,177 dif, disturbance travels at the characteristic speed of sound down the 167 00:12:21,177 --> 00:12:26,280 rope. And frequently we deal not with 168 00:12:26,280 --> 00:12:31,989 random pertivations but with periodic oscillations,, usually in a sign wave 169 00:12:31,989 --> 00:12:36,838 pattern as is done here. Each point on the rope is oscillating 170 00:12:36,838 --> 00:12:42,938 periodically and they're all oscillating with the same frequency, which is the 171 00:12:42,938 --> 00:12:47,005 frequency that this motor is oscillating with. 172 00:12:47,005 --> 00:12:50,916 In this case, it's oscillating with a frequency of 50 something. 173 00:12:51,932 --> 00:12:57,660 And so, frequency F, is the number of oscillations per second. 174 00:12:57,660 --> 00:13:03,234 And so it's measured, since this is a number, in units of inverse second and 175 00:13:03,234 --> 00:13:08,809 once per second is called a hertz. Which is why the frequency of your radio 176 00:13:08,809 --> 00:13:13,566 signal is measured in megahertz if you're listening to FM radio. 177 00:13:13,566 --> 00:13:19,809 And so, I can restart this oscillation, and what we see is that because it takes 178 00:13:19,809 --> 00:13:25,310 longer amount of time for the wave to get farther down the string, this, 179 00:13:25,310 --> 00:13:30,921 the, the position of the string here reflects what happened here a longer time 180 00:13:30,921 --> 00:13:36,676 ago than the position of the string here. And so, the periodic oscillation of the 181 00:13:36,676 --> 00:13:41,280 driving force causes each point on the string to go up and down. 182 00:13:41,280 --> 00:13:45,524 Notice, the wave is moving. The string is not going anywhere. 183 00:13:45,524 --> 00:13:50,057 But, also what it causes is because distance translates to time. 184 00:13:50,057 --> 00:13:56,099 we get a periodic sinusoidal structure in space at any given instant, and that is 185 00:13:56,099 --> 00:14:01,286 characterized typically, by the distance between subsequent peaks. 186 00:14:01,286 --> 00:14:07,460 The distance along which the wave repeats, that's it's wavelength lambda. 187 00:14:07,460 --> 00:14:14,590 And if you think about it, sitting at some point for a second F peaks will come 188 00:14:14,590 --> 00:14:15,460 by. And so, 189 00:14:15,460 --> 00:14:20,036 F peaks will come by, that means the wave will have transferred 190 00:14:20,036 --> 00:14:23,813 a distance of F times the distance between peaks. 191 00:14:23,813 --> 00:14:29,407 In other words, F times lambda is how far the disturbance travels in a second. 192 00:14:29,407 --> 00:14:35,073 So, F times lambda is the speed of the wave which we characteristically call C. 193 00:14:35,073 --> 00:14:40,375 Now, the reason we're dealing with periodic oscillations is a complicated 194 00:14:40,375 --> 00:14:46,550 mathematical theory called free analysis that says, any deformation can be written 195 00:14:46,550 --> 00:14:50,070 as a sum of periodic ones. But, Fourier analysis is 196 00:14:50,070 --> 00:14:53,973 not some abstract mathematics, it's exactly what our ear does. 197 00:14:53,973 --> 00:14:59,154 When your ear hears sounds, it analyzes them into a sum of harmonics and you hear 198 00:14:59,154 --> 00:15:04,144 the pitch of a sound, you hear is given precisely by its frequency, and you can 199 00:15:04,144 --> 00:15:08,622 hear three different notes and distinguish that there are three notes 200 00:15:08,622 --> 00:15:11,693 there. this is biology and not physics, but it 201 00:15:11,693 --> 00:15:15,020 is definitely true. And I can increase the frequency. 202 00:15:15,020 --> 00:15:20,207 And what we see is that when I increase the frequency, the wavelength became 203 00:15:20,207 --> 00:15:25,544 correspondingly smaller, the frequency times the wavelength is a constant the 204 00:15:25,544 --> 00:15:29,869 speed of the wave. a wave is characterized therefore by it's 205 00:15:29,869 --> 00:15:35,294 frequency or it's wavelength, given the speed, those are related, but also by an 206 00:15:35,294 --> 00:15:38,727 amplitude. An amplitude is simply the magnitude of 207 00:15:38,727 --> 00:15:44,288 the largest deformation. So, an amplitude of seventeen is a very small deformation 208 00:15:44,288 --> 00:15:49,140 and an amplitude three times as large, is a very large deformation. 209 00:15:49,140 --> 00:15:54,581 So, periodic disturbances, as we saw, are characterized by their frequency, F, in 210 00:15:54,581 --> 00:16:00,588 hertz the number of cycles per second. if a wave is traveling at a speed C, a 211 00:16:00,588 --> 00:16:05,535 periodic disturbance will produce a periodic wave in space at any given 212 00:16:05,535 --> 00:16:11,189 instant with a wavelength lambda that is related to the speed by this important 213 00:16:11,189 --> 00:16:14,369 relation. Lambda wavelength times frequency is 214 00:16:14,369 --> 00:16:18,885 equal to the speed of the wave. The wave was characterized also by the 215 00:16:18,885 --> 00:16:22,940 amplitude, which is the amount, the maximum amount of the pertubation. 216 00:16:22,940 --> 00:16:27,312 And one of the important things about waves is, the string didn't move. 217 00:16:27,312 --> 00:16:30,845 But clearly, waves carry energy from one place to the other. 218 00:16:30,845 --> 00:16:34,858 You could imagine hooking something at the other end of the string. 219 00:16:34,858 --> 00:16:39,650 I will vibrate this end, the wave will carry it and cause that object to vibrate 220 00:16:39,650 --> 00:16:43,423 giving it kinetic energy. That kinetic energy came from my hand, 221 00:16:43,423 --> 00:16:47,975 and therefore, a wave carries energy. in fact, it carries an energy if it's 222 00:16:47,975 --> 00:16:52,586 periodic per unit time that is constant. Over time, energy is flowing down the 223 00:16:52,586 --> 00:16:55,401 string. and so, you measure an energy flux in 224 00:16:55,401 --> 00:16:58,670 joule per second. A joule per second is known as a watt. 225 00:16:58,670 --> 00:17:03,587 This is the same unit of energy per unit time that you measure the intensity of 226 00:17:03,587 --> 00:17:07,141 your light bulbs in. How much energy does it take to operate 227 00:17:07,141 --> 00:17:10,695 that light bulb for a second. Now, this is a wave on a string. 228 00:17:10,695 --> 00:17:14,469 of course, a wave, like a sound wave that travels in three 229 00:17:14,469 --> 00:17:18,224 dimensions will carry an energy flux that is a density. 230 00:17:18,224 --> 00:17:23,533 Because if the wave is propagating over a wide front each bit of the wave carries 231 00:17:23,533 --> 00:17:26,511 an energy, so we measure the flux in watts per 232 00:17:26,511 --> 00:17:30,655 meter-squared of wavefront. And that energy flux, in watts per 233 00:17:30,655 --> 00:17:34,604 meter-squared, is proportional to the square of the amplitude. 234 00:17:34,604 --> 00:17:39,136 Clearly, the larger the amplitude, the more energy the wave is carrying. 235 00:17:39,136 --> 00:17:43,280 And the flux is going to be measured in watts per meter-squared. 236 00:17:43,280 --> 00:17:47,503 Now, what happens when two waves meet is a very important property of waves. 237 00:17:47,503 --> 00:17:50,600 Let's look at it in a demo and then we'll talk about it. 238 00:17:50,600 --> 00:17:55,250 In this demo, we have a loudspeaker. The loudspeaker will be creating a 239 00:17:55,250 --> 00:17:59,502 periodic wave. And we see the wave fronts are shown in 240 00:17:59,502 --> 00:18:03,529 this picture. They spread away from the loudspeaker. 241 00:18:03,529 --> 00:18:08,751 And what we see here is a measure of the pressure of the density that the 242 00:18:08,751 --> 00:18:12,669 perturbation that the wave represents at one given point. 243 00:18:12,669 --> 00:18:17,376 And we see the characteristic, periodic isolation that we're talking about. 244 00:18:17,376 --> 00:18:21,829 And, one thing you can see is that, unlike waves on a string, we'll talk 245 00:18:21,829 --> 00:18:26,282 about this. But, because these waves are spreading out, the amplitude of 246 00:18:26,282 --> 00:18:31,105 oscillation is larger near the source, then it is far, And anybody who stood 247 00:18:31,105 --> 00:18:35,070 very near a honking car horn is painfully aware of this fact. 248 00:18:35,070 --> 00:18:38,840 we'll talk about that aspect of things in a little bit. 249 00:18:38,840 --> 00:18:42,675 I just thought I'd just point it out while we're seeing it. 250 00:18:42,675 --> 00:18:47,550 But, the interesting thing to note is what happens when, instead of one loud 251 00:18:47,550 --> 00:18:51,515 speaker, we put two speakers. So now, the two speakers are both 252 00:18:51,515 --> 00:18:55,155 creating wavefronts. And we see here what happens as the 253 00:18:55,155 --> 00:18:58,990 wavefronts add, and you notice that I put my detect in a 254 00:18:58,990 --> 00:19:02,820 very interesting point. the two speakers together, 255 00:19:02,820 --> 00:19:07,977 each of which would've produced the noise with the amplitude we saw before, 256 00:19:07,977 --> 00:19:12,160 produces essentially zero noise at the position of this detector. 257 00:19:12,160 --> 00:19:16,656 But if I move the detector a little bit, I will see that it's is not because the 258 00:19:16,656 --> 00:19:19,188 two speakers are not producing noise at all, 259 00:19:19,188 --> 00:19:23,332 I see that indeed at this position, they're producing a far louder noise 260 00:19:23,332 --> 00:19:26,330 together than either one separately. And in fact, 261 00:19:26,330 --> 00:19:31,042 more than twice the sound that each would have produced separately, somehow the 262 00:19:31,042 --> 00:19:35,694 combination of the two speakers is focusing sound into these regions where 263 00:19:35,694 --> 00:19:40,108 the dark bands are and leaving these regions where the grey bands are, the 264 00:19:40,108 --> 00:19:42,554 nodes, where essentially no sound gets to. 265 00:19:42,554 --> 00:19:47,146 Now, the reason that this is possible is because waves can subtract from each 266 00:19:47,146 --> 00:19:51,978 other. When these two waves propagate, it turns they essentially don't interact 267 00:19:51,978 --> 00:19:56,392 with each other at all, that's the approximation that we're working in and 268 00:19:56,392 --> 00:20:00,489 it's valid one for sound waves. And what that means is that the total 269 00:20:00,489 --> 00:20:04,953 dis-perturbation at any point in space and time, is the sum of what it would be 270 00:20:04,953 --> 00:20:09,303 if there was one speaker, and what it would be if there was the other speaker. 271 00:20:09,303 --> 00:20:11,674 And, how does that, adding what one speaker 272 00:20:11,674 --> 00:20:15,456 would produce to what the other speaker would produce, lead to zero? 273 00:20:15,456 --> 00:20:20,027 Well, remember they're both oscillating at exactly the same frequency. So, there 274 00:20:20,027 --> 00:20:24,599 can be a point where because of the time delay from this speaker being different 275 00:20:24,599 --> 00:20:28,663 from the time delay from that speaker, due to the difference in distance. 276 00:20:28,663 --> 00:20:33,291 when a peak from this speaker reaches, it is always timed to arrive at the same 277 00:20:33,291 --> 00:20:37,750 time as a trough from this speaker, so that the two waves that these two create 278 00:20:37,750 --> 00:20:41,983 are always counteracting each other. Waves add, but that addition can amount 279 00:20:41,983 --> 00:20:44,755 to subtraction. And that phenomenon is known as 280 00:20:44,755 --> 00:20:47,462 interference and its characteristic of waves. 281 00:20:47,462 --> 00:20:50,050 So, let's summarize what we've learned here. 282 00:20:50,050 --> 00:20:55,339 A hallmark of wave behavior is that waves are deformations or perturbations to some 283 00:20:55,339 --> 00:21:00,376 equilibrium, and when two waves meet at the same point in space and time, the two 284 00:21:00,376 --> 00:21:03,713 disturbances add. In other words, each wave behaves as 285 00:21:03,713 --> 00:21:07,554 though the other were not there. We just add the disturbances. 286 00:21:07,554 --> 00:21:12,717 What this allows, if the waves are of the same frequency, is that if the time delay 287 00:21:12,717 --> 00:21:15,905 between one source and the other source relative 288 00:21:15,905 --> 00:21:20,591 to your position, is suitably adjusted. In other words the distance difference, 289 00:21:20,591 --> 00:21:23,999 which translates to the time delay, is suitably adjusted. 290 00:21:23,999 --> 00:21:28,868 You can adjust it so peak from one wave precisely meets a trough from the other. 291 00:21:28,868 --> 00:21:33,736 The two waves add in the sense that they subtract, and you can get nodes, you can 292 00:21:33,736 --> 00:21:38,118 get regions of quiet in the vicinity of two speakers producing the same 293 00:21:38,118 --> 00:21:40,825 frequency. this will be important to us. 294 00:21:40,825 --> 00:21:45,713 It's a hallmark of wave behavior. Now, another property of waves that is 295 00:21:45,713 --> 00:21:50,930 going to be useful to us is extremely useful in fact, is something called the 296 00:21:50,930 --> 00:21:54,431 Doper effect. It's the well known phenomenon that the 297 00:21:54,431 --> 00:21:58,922 sound from a moving source sounds different then the sound from a 298 00:21:58,922 --> 00:22:02,951 stationary source. If a source is the noise is approaching 299 00:22:02,951 --> 00:22:05,928 us, it sounds higher in pitch than where it's 300 00:22:05,928 --> 00:22:11,022 stationary. If it's receiving, if it's moving away from us the pitch sounds 301 00:22:11,022 --> 00:22:14,132 lower. the archetypal example of this is the 302 00:22:14,132 --> 00:22:19,341 sound of a race car driving past you. I'll play it in the speakers, perhaps you 303 00:22:19,341 --> 00:22:24,243 can hear it. [SOUND] That [SOUND] whine is the 304 00:22:24,243 --> 00:22:29,835 transition from an elevated pitch as the car approaches you to a decreased pitch, 305 00:22:29,835 --> 00:22:33,149 decreased frequency as the car recedes from you. 306 00:22:33,149 --> 00:22:39,017 And the mathematical formulation of this is due to Doppler in the 19th Century, 307 00:22:39,017 --> 00:22:42,676 and we can understand this rather straight forwardly. 308 00:22:42,676 --> 00:22:47,785 Here is a source producing regular, regularly spaced periodic waves, and an 309 00:22:47,785 --> 00:22:51,662 observer placed over here receives the waves with a time delay. 310 00:22:51,662 --> 00:22:54,081 It takes time for each wave to reach there. 311 00:22:54,081 --> 00:22:58,695 The time delay is the same for each wave so the time between subsequent floods is 312 00:22:58,695 --> 00:23:01,509 the same as the time between subsequent emissions. 313 00:23:01,509 --> 00:23:05,504 And this is a stationary source. The frequency with which his ear is 314 00:23:05,504 --> 00:23:10,062 oscillating is the same as the frequency with which this source is producing the 315 00:23:10,062 --> 00:23:11,176 sound. That is true. 316 00:23:11,176 --> 00:23:16,073 Now, let's move on to the case where the source is moving and let's again place an 317 00:23:16,073 --> 00:23:19,775 observer over here. And we see that what's going on is that 318 00:23:19,775 --> 00:23:24,254 the wavefronts appear compressed on this side, they're compressed, of course, 319 00:23:24,254 --> 00:23:28,494 because between the emission of one wave and the next the source moves. 320 00:23:28,494 --> 00:23:32,794 And so, the distance between the wavefronts, as seen by the observer here, 321 00:23:32,794 --> 00:23:36,078 is smaller than it would be were the source stationary. 322 00:23:36,078 --> 00:23:40,617 And we can easily compute the relation between the two because the distance 323 00:23:40,617 --> 00:23:44,320 between subsequent wavefronts as they arrive at this observer, 324 00:23:44,320 --> 00:23:50,316 lambda, which is the wavelength that this observer sees, is equal to the distance 325 00:23:50,316 --> 00:23:56,222 between the two wave fronts when they were omitted minus the distance which the 326 00:23:56,222 --> 00:24:00,314 source traveled. Because each subsequent wave front has a 327 00:24:00,314 --> 00:24:06,202 shorter distance to travel because in the interim between emitting one wave front 328 00:24:06,202 --> 00:24:11,659 and the following, the source traveled distance given by v times the time 329 00:24:11,659 --> 00:24:15,680 between wave fronts. What's the time between wave fronts? 330 00:24:15,680 --> 00:24:21,352 The time between emissions is one divided by the frequency because this is the 331 00:24:21,352 --> 00:24:25,445 number of seconds. And so, remembering that lambda times f 332 00:24:25,445 --> 00:24:32,481 is c, I can write f as c over lambda. And I get lambda is lambda zero minus, 333 00:24:32,481 --> 00:24:38,544 let me write this correctly. lambda is lambda zero minus v lambda zero 334 00:24:38,544 --> 00:24:44,689 over c, or Doppler's formula, lambda is lambda zero times one minus v over c. 335 00:24:44,689 --> 00:24:51,162 notice that this v was taken to be positive when the source was approaching 336 00:24:51,162 --> 00:24:56,980 the observer and observer on this side, of course, sees the wave dilated. 337 00:24:56,980 --> 00:25:01,519 The wavelength looks longer, the pitch is lower as the car is receding from you. 338 00:25:01,519 --> 00:25:04,680 Each subsequent wave front has a longer distance to go. 339 00:25:04,680 --> 00:25:09,162 That is compensated in this formula by considering v to be negative if the 340 00:25:09,162 --> 00:25:12,898 source is receding, and positive if the source is approaching you. 341 00:25:12,898 --> 00:25:17,667 We talked about heat energy and we need a few properties of heat because heat will 342 00:25:17,667 --> 00:25:21,632 be a dominant form of energy in some environments that we talk about. 343 00:25:21,632 --> 00:25:26,000 And so, it's a property of heat that if you have a hot object in a cooler 344 00:25:26,000 --> 00:25:29,275 environment, then the hot object will lose energy the 345 00:25:29,275 --> 00:25:34,006 environment and this process will continue indefinitely or until such time 346 00:25:34,006 --> 00:25:38,421 as the temperatures equilibrate. Because as the source looses heat, the 347 00:25:38,421 --> 00:25:43,151 environment gains heat and warms up. And eventually, if the temperatures are 348 00:25:43,151 --> 00:25:46,367 equal, then we have equilibrium, and heat flow stops. 349 00:25:46,367 --> 00:25:51,728 But so long as you have warm sun in cold space, the sun will continue to lose heat 350 00:25:51,728 --> 00:25:54,945 to space. And until such time as either space heats 351 00:25:54,945 --> 00:25:58,137 up or sun cools down, this process will continue. 352 00:25:58,137 --> 00:26:02,700 There will be a constant flux of energy out of the sun into space. 353 00:26:02,700 --> 00:26:08,233 And, there are several ways by which this transfer of heat from a hotter to a 354 00:26:08,233 --> 00:26:12,658 cooler body can occur. One is called conduction, this is where 355 00:26:12,658 --> 00:26:15,908 heat is transferred through continuous contact. 356 00:26:15,908 --> 00:26:18,837 And this is not an in, great importance. 357 00:26:18,837 --> 00:26:24,053 In astronomy, heat conduction on astronomical scales is rare. 358 00:26:24,053 --> 00:26:29,766 A second phenomenon is convection. This is basically like trucking. 359 00:26:29,766 --> 00:26:35,892 This is what happens when the physical motion of the fluid carries energy. 360 00:26:35,892 --> 00:26:41,616 this works very well if you have volume of fluid that is heated from 361 00:26:41,616 --> 00:26:44,550 below. That happens when you boil water on your 362 00:26:44,550 --> 00:26:47,233 stove, it also happens in stars, say, where a 363 00:26:47,233 --> 00:26:50,416 hot core is heating the atmosphere from the inside. 364 00:26:50,416 --> 00:26:55,721 What happens is that at the bottom of the pot or the bottom of the atmosphere the 365 00:26:55,721 --> 00:26:58,280 fluid is heated. The heated fluid expands. 366 00:26:58,280 --> 00:27:03,073 The expanded heated fluid is lighter, less dense then the surrounding fluid. 367 00:27:03,073 --> 00:27:05,818 And therefore, floats to the top and rises. 368 00:27:05,818 --> 00:27:11,046 Cooler fluid descends to take it's place. And what you have is a energy transfer 369 00:27:11,046 --> 00:27:16,144 from the bottom to the top by heated fluid physically moving from one part to 370 00:27:16,144 --> 00:27:19,151 the other. And this does occur in astronomical 371 00:27:19,151 --> 00:27:22,491 phenomenon. None of this, of course, is helpful to 372 00:27:22,491 --> 00:27:27,947 the sun in losing its energy to space because the sun is not in contact with 373 00:27:27,947 --> 00:27:31,702 anything nor is there any fluid around it to convect. 374 00:27:31,702 --> 00:27:35,316 The way the sun loses energy to space is radiation. 375 00:27:35,316 --> 00:27:40,772 It turns out that every object, unless its at zero temperature, glows and that 376 00:27:40,772 --> 00:27:46,776 phenom, that mechanism of energy loss is radiation heat transfer, and essentially 377 00:27:46,776 --> 00:27:51,809 the radiation question is sunlight. Sunlight is the way the sun attempts to 378 00:27:51,809 --> 00:27:55,031 heat up space, losing energy because it's warmer. 379 00:27:55,031 --> 00:27:58,521 And we'll come back to this calculation in a moment. 380 00:27:58,521 --> 00:28:01,781 But, let's understand something about this 381 00:28:01,781 --> 00:28:03,970 heat flux, energy flux problem. 382 00:28:03,970 --> 00:28:06,441 And so, the sun is hot and so it radiates. 383 00:28:06,441 --> 00:28:10,660 And we'll learn how to compute how hot it is and how much it radiates. 384 00:28:10,660 --> 00:28:15,300 But for now, let's assume that the sun is radiating energy at a constant rate. 385 00:28:15,300 --> 00:28:19,097 Why is the rate constant? Because the properties of the sun are 386 00:28:19,097 --> 00:28:23,859 unchanging, the properties of space are unchanging. So, the rate at which the sun 387 00:28:23,859 --> 00:28:26,029 loses energy to space is therefore unchanging. 388 00:28:26,029 --> 00:28:30,549 We call that rate the luminosity, and it's measured in joules per second, in 389 00:28:30,549 --> 00:28:33,141 watts. The sun like a light bulb produces a 390 00:28:33,141 --> 00:28:37,813 certain amount of energy or loses a certain amount of energy to space every 391 00:28:37,813 --> 00:28:41,595 second and we'll figure out this number, obviously. 392 00:28:41,595 --> 00:28:43,940 It's a great many light bulbs. 393 00:28:43,940 --> 00:28:49,196 Now, what interests us often is how bright the sunlight is at some given 394 00:28:49,196 --> 00:28:53,795 location in space. And what that implies is put some uniform 395 00:28:53,795 --> 00:28:57,154 detector, say, an eye with a fixed surface area. 396 00:28:57,154 --> 00:29:03,286 And as we saw or as this diagram shows, if this is something the size of your eye 397 00:29:03,286 --> 00:29:08,178 or of your detector, the farther it goes, the less sunlight it traps. 398 00:29:08,178 --> 00:29:13,800 Because essentially, the sun makes produces radiation in all directions. 399 00:29:13,800 --> 00:29:19,125 And so, at any distance, the sunlight is spread uniformly across 400 00:29:19,125 --> 00:29:25,260 the surface of a ball [SOUND] or a sphere of radius R. 401 00:29:25,260 --> 00:29:30,929 And, if you are at some distance and you place your detector, your detector takes 402 00:29:30,929 --> 00:29:35,710 up some fraction of that sphere. If you are twice as far, the sphere is 403 00:29:35,710 --> 00:29:40,901 larger and your detector now takes a smaller fraction of this larger sphere. 404 00:29:40,901 --> 00:29:45,956 And the result will be that your detector, since all of the suns rays pass 405 00:29:45,956 --> 00:29:51,215 through this sphere and all of the sun rays a little later pass through this 406 00:29:51,215 --> 00:29:54,743 sphere as well, the net total amount of energy passing 407 00:29:54,743 --> 00:29:59,301 through each sphere is the same. But the total amount passing through a 408 00:29:59,301 --> 00:30:04,373 fixed detector decreases because the spheres grow larger whereas the detector 409 00:30:04,373 --> 00:30:07,519 does not. Mathematically, the statement is that at 410 00:30:07,519 --> 00:30:12,141 a distance R, the radiation is distributed uniformly on the surface of a 411 00:30:12,141 --> 00:30:14,837 sphere. So, energy per second received by a 412 00:30:14,837 --> 00:30:19,717 square-meter of detector will be the luminosity divided by the surface of a 413 00:30:19,717 --> 00:30:23,183 sphere across which the radiation is spread uniformly. 414 00:30:23,183 --> 00:30:26,521 And so, the sun energy is diluted by a factor of R 415 00:30:26,521 --> 00:30:30,969 squared as it travels out into space. Light, of course, is going to be of 416 00:30:30,969 --> 00:30:34,665 incredible importance in our understanding of the universe. 417 00:30:34,665 --> 00:30:38,110 It's the main way we perceive our environment on Earth. 418 00:30:38,110 --> 00:30:43,122 It is certainly the main way that we receive information from distant places 419 00:30:43,122 --> 00:30:47,946 in the universe, so the properties of light will be extremely important to us. 420 00:30:47,946 --> 00:30:51,931 So, light light, of course, is the main way we as 421 00:30:51,931 --> 00:30:56,429 humans perceive the world around us. It's also the main way that we as 422 00:30:56,429 --> 00:31:01,584 astronomers learn about distant objects. The nature and the properties of light 423 00:31:01,584 --> 00:31:04,366 are going to be extremely important to us. 424 00:31:04,366 --> 00:31:09,468 And the first of these is the speed. So, light carries energy away from the 425 00:31:09,468 --> 00:31:14,106 sun to Earth to warm us. and the speed at which light propagates 426 00:31:14,106 --> 00:31:17,552 is huge. It's about three times ten to the eighth 427 00:31:17,552 --> 00:31:21,130 meters per second. this may, this large number makes 428 00:31:21,130 --> 00:31:25,635 accurate measurement difficult. First, really good measurement was in 429 00:31:25,635 --> 00:31:31,134 1850 by Foucault and Fizeau, though there were earlier less precise measurements. 430 00:31:31,134 --> 00:31:34,494 Now, in a classic experiment in 1670, our old 431 00:31:34,494 --> 00:31:41,068 friend Newton made the discovery that the sunlight, white colorless light from the 432 00:31:41,068 --> 00:31:44,240 sun, in fact contains all colors of light. 433 00:31:44,240 --> 00:31:50,505 he found a way to split a beam of white light into beams of various colors. 434 00:31:50,505 --> 00:31:54,760 He was using a prism, today we use a defraction grading. 435 00:31:54,760 --> 00:31:58,892 And he conjectured that the nature of light was that light was a stream of 436 00:31:58,892 --> 00:32:03,025 particles, of course, he had all the mechanics know how to understand the 437 00:32:03,025 --> 00:32:06,993 stream of particles, light moved in straight lines, light particles which 438 00:32:06,993 --> 00:32:11,117 upon no forces act. Moved at a constant velocity, it seemed a 439 00:32:11,117 --> 00:32:15,845 lot like mechanical particle model of light would be likely. 440 00:32:15,845 --> 00:32:21,399 This is one of the rare cases where Newton was wrong because in 1799, only 441 00:32:21,399 --> 00:32:25,752 120 years later, Young observes light waves interfering. 442 00:32:25,752 --> 00:32:29,430 So, he makes the observation that you can take 443 00:32:29,430 --> 00:32:35,485 light and you can construct these interference effects where light waves 444 00:32:35,485 --> 00:32:41,311 add and subtract, and you get nodes. This interference was a hallmark of wave 445 00:32:41,311 --> 00:32:44,991 phenomena, so Newton, for once, was actually wrong. 446 00:32:44,991 --> 00:32:48,287 Light is a wave. But never count Newton out. 447 00:32:48,287 --> 00:32:51,890 We'll come back to this point in the next clip. 448 00:32:51,890 --> 00:32:56,030 And that same Young, three years later, shows that 449 00:32:56,030 --> 00:33:02,350 our eyes while they are extremely accurate in giving directional 450 00:33:02,350 --> 00:33:05,584 perspective. So, they tell us very precisely which 451 00:33:05,584 --> 00:33:10,732 direction light is coming from, that's how we construct our image of the world, 452 00:33:10,732 --> 00:33:14,098 are in contrast relatively poor as fully analyzers. 453 00:33:14,098 --> 00:33:19,445 Unlike our ears, which can distinguish a great variety of sounds and hear several 454 00:33:19,445 --> 00:33:24,791 simultaneous tones and distinguish them, our eyes are very poor for an analysis 455 00:33:24,791 --> 00:33:29,939 machine. They only are sensitive to the relative intensity of three colors, red, 456 00:33:29,939 --> 00:33:34,180 green and blue, and we'll see in a minute what that leads to. 457 00:33:34,180 --> 00:33:38,681 What we're going to do is an experiment somewhat similar to what Newton did. 458 00:33:38,681 --> 00:33:43,306 So, we have here a beam of white light, and we're going to put a diffraction 459 00:33:43,306 --> 00:33:47,808 grating in front of it, and the diffraction grating splits the white beam 460 00:33:47,808 --> 00:33:51,385 so that the white stripe in the center is somewhat dimmed. 461 00:33:51,385 --> 00:33:55,886 And on both sides, we find the familiar rainbow structure. And so, we see a 462 00:33:55,886 --> 00:34:00,881 stripe of red flaring to orange and yellow and green, and into blue and 463 00:34:00,881 --> 00:34:01,560 violet. And, 464 00:34:01,560 --> 00:34:05,776 we can see what happens when we put a filter in front of the light, 465 00:34:05,776 --> 00:34:09,150 we get red light. And when we feed red light into the 466 00:34:09,150 --> 00:34:13,848 diffraction grating, what we see in the spectrum is that the green and the blue 467 00:34:13,848 --> 00:34:16,981 are missing. Similarly, when we feed green light into 468 00:34:16,981 --> 00:34:21,800 the defraction grating, the blue and the red are missing, and only green light 469 00:34:21,800 --> 00:34:24,330 comes in. So, the defraction grating is not 470 00:34:24,330 --> 00:34:27,945 coloring the light. It is deflecting whatever green light it 471 00:34:27,945 --> 00:34:31,690 gets to that region. Again, putting a blue filter in front of 472 00:34:31,690 --> 00:34:36,453 the beam, we see that only the blue remains in the spectrum. The blue filter 473 00:34:36,453 --> 00:34:41,534 absorbs the green and the red, the green filter absorbs blue and red, and the red 474 00:34:41,534 --> 00:34:46,413 filter absorbs green and blue. these are, it turns out, the primary 475 00:34:46,413 --> 00:34:52,437 colors it has to do with our eyes. here's what happens when you put a cyan 476 00:34:52,437 --> 00:34:56,818 filter in front. A cyan filter absorbs the red light, and 477 00:34:56,818 --> 00:35:04,350 so lets through the blue and the green. Similarly, if we use a magenta filter. 478 00:35:04,350 --> 00:35:09,112 A magenta filter absorbs the green, letting through the blue and the red. 479 00:35:09,112 --> 00:35:12,683 So, what we see as magenta is blue light and red light. 480 00:35:12,683 --> 00:35:16,189 There is also, we can put a yellow filter in, and this 481 00:35:16,189 --> 00:35:19,628 is important. We see that what we perceive as yellow 482 00:35:19,628 --> 00:35:22,803 light is, in fact, light that is missing its blue. 483 00:35:22,803 --> 00:35:26,309 The green and the red are present, the blue is absent, 484 00:35:26,309 --> 00:35:30,012 and we see yellow. And so, if we superpose the yellow and 485 00:35:30,012 --> 00:35:33,650 the magenta filters, the yellow filter absorbs the blue. 486 00:35:33,650 --> 00:35:37,222 The magenta absorbs the green, and what is left is red. 487 00:35:37,222 --> 00:35:40,672 And indeed, superimposing those two filters, we get 488 00:35:40,672 --> 00:35:43,394 red. If we superimpose yellow and cyan, the 489 00:35:43,394 --> 00:35:47,672 yellow absorbs the blue, the cyan the red, what's left is the green. 490 00:35:47,672 --> 00:35:52,079 And we see that very nicely in this picture, and we can keep playing. 491 00:35:52,079 --> 00:35:56,811 We can superimpose the cyan and the magenta, the cyan absorbs the red, the 492 00:35:56,811 --> 00:36:00,530 magenta absorbs the green. Putting them on top of each other, we're 493 00:36:00,530 --> 00:36:02,920 going to be left with blue. So, 494 00:36:02,920 --> 00:36:06,094 this has to do with the way our eyes see colors. 495 00:36:06,094 --> 00:36:11,350 the important thing for us to take away here is that a filter that absorbs the 496 00:36:11,350 --> 00:36:15,004 blue looks yellow. We cannot distinguish this yellow from 497 00:36:15,004 --> 00:36:19,747 the yellow in the spectrum there in between the red and the green that is 498 00:36:19,747 --> 00:36:23,670 pure yellow light. We saw that as Young showed us, light is 499 00:36:23,670 --> 00:36:28,634 a wave, and also as Young showed us, our eye, in fact, has three color detectors. 500 00:36:28,634 --> 00:36:33,597 One sensitive to red light, one sensitive to green light, and one sensitive to 501 00:36:33,597 --> 00:36:36,498 blue. And what we perceive as color is merely 502 00:36:36,498 --> 00:36:40,752 the relative intensity at which those three detectors are excited. 503 00:36:40,752 --> 00:36:45,569 So, yellow light that excites the red and the green approximately equally. 504 00:36:45,569 --> 00:36:50,159 Because in the spectrum, the other light is between red and green cannot be 505 00:36:50,159 --> 00:36:54,014 distinguished from a combination of actual red and green light. 506 00:36:54,014 --> 00:36:57,869 And so, our eye, unlike our ear, is not a very good free analyzer. 507 00:36:57,869 --> 00:37:02,887 so much for biology, but this will be important in understanding some phenomena 508 00:37:02,887 --> 00:37:05,273 later. And then, once we know that light is a 509 00:37:05,273 --> 00:37:09,190 wave, it's not too shocking that color is a property of the wave. 510 00:37:09,190 --> 00:37:12,206 Color turns out to be the frequency of light 511 00:37:12,206 --> 00:37:16,604 visible light has a frequency of order ten to the 12th hertz 512 00:37:16,604 --> 00:37:21,694 even at the rather high speed of light, we can compute the wavelength is pretty 513 00:37:21,694 --> 00:37:24,333 short. It's between 400 and 700 nanometers. 514 00:37:24,333 --> 00:37:29,109 A nanometer is a billionth of a meter, ten to the minus nine meter, and these 515 00:37:29,109 --> 00:37:33,947 are the units in which, typically we measure the wavelengths of visible light, 516 00:37:33,947 --> 00:37:37,949 at least in astronomy. And so, 400 nanometers, the shortest 517 00:37:37,949 --> 00:37:42,180 wavelengths visible light is the blue light as this indicates. 518 00:37:42,180 --> 00:37:46,143 And the red end of the spectrum is the longer wavelengths. 519 00:37:46,143 --> 00:37:50,509 And the order of the colors in the rainbow is according to their 520 00:37:50,509 --> 00:37:54,002 wavelengths. So, that violet light in fact, is at the 521 00:37:54,002 --> 00:37:59,241 short end of the spectrum, green is somewhere in the middle around 550 522 00:37:59,241 --> 00:38:04,010 nanometers is green light and so on. Now, for something completely different. 523 00:38:04,010 --> 00:38:08,979 we talked about gravitation as the force that dominates astronomy. 524 00:38:08,979 --> 00:38:13,028 But, in most of our lives, gravitation of the Earth is important. 525 00:38:13,028 --> 00:38:17,704 But, when we interact which each other or with objects around us, gravitation is 526 00:38:17,704 --> 00:38:21,491 completely unimportant. The gravitational force of a human being 527 00:38:21,491 --> 00:38:25,220 is negligible compared to the other forces we interact with. 528 00:38:25,220 --> 00:38:29,469 The force the tunes out turns out to dominate most of physics is 529 00:38:29,469 --> 00:38:34,053 electromagnetism. And so, we need to understand some things about this. 530 00:38:34,053 --> 00:38:38,902 And, the simplest version of electromagnetism is the force between two 531 00:38:38,902 --> 00:38:42,822 static charged objects. So, there is in the universe a thing 532 00:38:42,822 --> 00:38:46,874 called electric charge. some objects carry electric charge. 533 00:38:46,874 --> 00:38:52,537 You can charge your hair by combing it on a dry day, and the knowing force that 534 00:38:52,537 --> 00:38:57,932 makes your hair stand on end on a dry day is this electrostatic or Coulomb force 535 00:38:57,932 --> 00:39:00,887 which has a formula that will appear familiar. 536 00:39:00,887 --> 00:39:06,026 The force between two objects of charges, q1 and q2, is given by a constant times 537 00:39:06,026 --> 00:39:10,330 the product of the charges, divided by the square of their distance. 538 00:39:10,330 --> 00:39:15,398 This might appear familiar, it's that square of the distance again. 539 00:39:15,398 --> 00:39:20,543 It's not exactly a coincidence. The big difference between electric 540 00:39:20,543 --> 00:39:26,456 charge and mass, or between a Coulomb's law and Newton's law is that Newton's 541 00:39:26,456 --> 00:39:29,067 law, remember had FGMM = GMm over R squared. 542 00:39:29,067 --> 00:39:33,752 And these numbers were positive, and the force was attractive. 543 00:39:33,752 --> 00:39:36,977 Always. Gravitation is a universally attractive 544 00:39:36,977 --> 00:39:40,203 force. Coulomb interactions can be attractive or 545 00:39:40,203 --> 00:39:43,697 repulsive. It turns out that the force is attractive 546 00:39:43,697 --> 00:39:48,736 when the two charges are of opposite sign, so positive and negative charges 547 00:39:48,736 --> 00:39:52,970 attract, and charges of like sign repel with an equal magnitude. 548 00:39:52,970 --> 00:39:57,930 But the sign, the direction of the force, depends on whether the charges are equal 549 00:39:57,930 --> 00:40:01,119 or opposite. This in turn explains why this force does 550 00:40:01,119 --> 00:40:03,836 not dominate the universe, and this force does. 551 00:40:03,836 --> 00:40:08,619 It's not because gravitation is stronger. In fact, we have an unvarying measure of 552 00:40:08,619 --> 00:40:13,343 strength in which gravitation will be a far weaker force than electromagnetism. 553 00:40:13,343 --> 00:40:15,869 But, because opposite charges attract, most 554 00:40:15,869 --> 00:40:19,364 objects are neutral. In the presence of charge, if you have 555 00:40:19,364 --> 00:40:24,124 something that's charged positively, it will attract negative charge until such 556 00:40:24,124 --> 00:40:27,558 time as it reaches equilibrium. In other words, as neutral. 557 00:40:27,558 --> 00:40:31,535 This is not possible for mass. There's no concept of negative mass. 558 00:40:31,535 --> 00:40:35,753 In fact, it's worse than that. We'll discuss the instability of gravity. 559 00:40:35,753 --> 00:40:40,332 This will have profound consequences so I'm not belaboring an obvious point. 560 00:40:40,332 --> 00:40:43,856 And charge, like mass, momentum, energy, etc., is conserved. 561 00:40:43,856 --> 00:40:46,283 You can neither create nor destroy charge. 562 00:40:46,283 --> 00:40:50,544 Though, of course, charge can be transferred from one object to the other. 563 00:40:50,544 --> 00:40:55,161 So, when you comb your hair, the comb is charged with one charge, your hair with 564 00:40:55,161 --> 00:40:58,594 the opposite charge. when atoms form an ionic bond, they 565 00:40:58,594 --> 00:41:02,559 exchange charges and so on. But, the total charge in the universe or 566 00:41:02,559 --> 00:41:05,637 in any enclosed region in the universe is conserved. 567 00:41:05,637 --> 00:41:07,440 And then, you see, 568 00:41:07,440 --> 00:41:12,407 in gravitation, I kept wanting to talk not about the gravitational force, 569 00:41:12,407 --> 00:41:17,582 but the gravitational acceleration. So, you talk about the Earth for example, 570 00:41:17,582 --> 00:41:20,549 generating around it a gravitational field. 571 00:41:20,549 --> 00:41:26,069 The gravitational field is the statement that were a mass to be placed there, it 572 00:41:26,069 --> 00:41:30,485 would experience a force. And, you can compute the force per unit 573 00:41:30,485 --> 00:41:35,410 mass without knowing what the size is of the mass that you would introduce. 574 00:41:35,410 --> 00:41:40,645 And in a similar way, you talk about an electric charge producing an electric 575 00:41:40,645 --> 00:41:46,077 field which is the force per unit charge that would act were a charge to be placed 576 00:41:46,077 --> 00:41:48,890 there. So, a charge create an electric field 577 00:41:48,890 --> 00:41:54,060 around it because another charge were it to be brought there, would be effected. 578 00:41:54,060 --> 00:41:56,874 And a charge is effected by electric field. 579 00:41:56,874 --> 00:42:01,553 A similar phenomenon of a field region around an object in which other 580 00:42:01,553 --> 00:42:04,771 objects might be impacted is encountered with magnets. 581 00:42:04,771 --> 00:42:09,002 A magnet creates around it, something that we can call a magnetic field. 582 00:42:09,002 --> 00:42:13,412 In the presence of such a field, any other magnet, like this little compass, 583 00:42:13,412 --> 00:42:17,702 will align itself in a particular direction at any given point in space. 584 00:42:17,702 --> 00:42:22,409 Of course, it will align itself so that its north pole faces the south pole and 585 00:42:22,409 --> 00:42:24,025 so on. And so, [SOUND] 586 00:42:24,025 --> 00:42:29,171 We can imagine that this region of space has some property called a magnetic field 587 00:42:29,171 --> 00:42:33,759 which is the statement that, were you, remember, there was a field here even 588 00:42:33,759 --> 00:42:38,594 before I brought the compass, that told you that were you to bring the compass, 589 00:42:38,594 --> 00:42:41,322 it would point in such and such a direction. 590 00:42:41,322 --> 00:42:45,600 Now, magnets and electricity initially appear completely unrelated. 591 00:42:45,600 --> 00:42:51,259 And it is known, however, that electric currents in fact produce magnetic fields 592 00:42:51,259 --> 00:42:56,585 in the vicinity of an electric current. Electric current flowing around the coil 593 00:42:56,585 --> 00:43:00,713 behaves very much like a magnet. We call this an electromagnet. 594 00:43:00,713 --> 00:43:06,240 And, we see that we have a magnetic field in the vicinity of an electric current 595 00:43:06,240 --> 00:43:11,292 moving charges create magnetic fields. So this is the first relation between 596 00:43:11,292 --> 00:43:16,477 electricity and magnetism, but there's another relation which is that you have a 597 00:43:16,477 --> 00:43:21,662 changing magnetic field, it will cause charges to move so that this magnet has 598 00:43:21,662 --> 00:43:24,920 absolutely no impact on the charges in this coil. 599 00:43:24,920 --> 00:43:29,972 But if I move the magnet so that the magnetic field in the coil changes, then 600 00:43:29,972 --> 00:43:34,906 while the change is on going, current will flow and current flows means 601 00:43:34,906 --> 00:43:39,717 there's a force on these charge carriers. This implies an electric field. 602 00:43:39,717 --> 00:43:44,462 A changing magnetic field causes an electric field and I can, of course, 603 00:43:44,462 --> 00:43:48,271 cause the change by moving either the magnet or the coil. 604 00:43:48,271 --> 00:43:53,015 And so, changing magnetic fields essentially can be thought of as 605 00:43:53,015 --> 00:43:56,869 generating electric fields. This has profound consequences. 606 00:43:56,869 --> 00:44:01,233 Let's see what they are. The fact that moving charges can create a 607 00:44:01,233 --> 00:44:04,473 magnetic field was discovered in 1820 by Orsted. 608 00:44:04,473 --> 00:44:09,565 And, it turns out that moving charges are also affected by magnetic fields. 609 00:44:09,565 --> 00:44:14,259 We saw that when we moved the coil in the presence of a magnetic field, 610 00:44:14,259 --> 00:44:19,813 Faraday realizes the phenomenon that we were discussing, which is that a changing 611 00:44:19,813 --> 00:44:23,120 magnetic field is tantamount to an electric field. 612 00:44:23,120 --> 00:44:29,607 30 years later, Maxwell writes down what are the collected set of equations 613 00:44:29,607 --> 00:44:35,431 describing electric and magnetic fields. And, in particular, the phenomenon he 614 00:44:35,431 --> 00:44:40,739 needs to add is that a changing electric field creates a magnetic field. 615 00:44:40,739 --> 00:44:45,900 In the presence of a changing electric field, there's a magnetic field. 616 00:44:45,900 --> 00:44:51,537 And the combination of these two phenomena leads in Maxwell's equations as 617 00:44:51,537 --> 00:44:53,938 part of the solutions to propagating waves. 618 00:44:53,938 --> 00:44:58,351 Propagating waves in which essentially an elec, you set up a changing electric 619 00:44:58,351 --> 00:45:02,539 field which creates a magnetic field which creates an electric field which 620 00:45:02,539 --> 00:45:06,226 creates a magnetic field. You solve the differential equation that 621 00:45:06,226 --> 00:45:09,800 this leads to, and you find that it describes a propagating wave. 622 00:45:09,800 --> 00:45:14,212 And Maxwell computes from the properties of magnets and currents and Coulomb's 623 00:45:14,212 --> 00:45:18,569 law, properties that have been measured in the lab, he can compute the velocity 624 00:45:18,569 --> 00:45:22,975 of these waves that he's discovered. And their velocity surprise, surprise, is 625 00:45:22,975 --> 00:45:26,030 precisely c. It co, he didn't get it this precisely, 626 00:45:26,030 --> 00:45:30,762 but it coincides with the speed of light that Fizeau and Foucault had measured 627 00:45:30,762 --> 00:45:34,722 eleven years previously. So, Maxwell has very good reasons to 628 00:45:34,722 --> 00:45:38,992 imagine that he has discovered that light is a wave, as Young said. 629 00:45:38,992 --> 00:45:41,645 In fact, we now know what it is a wave of, 630 00:45:41,645 --> 00:45:46,238 it's an electro-magnetic wave. The disturbance that propagates in space 631 00:45:46,238 --> 00:45:51,154 when a light beam travels through it is an electro-magnetic wave, is an elec, 632 00:45:51,154 --> 00:45:56,524 disturbance in the electric and magnetic fields which have come to take on sort of 633 00:45:56,524 --> 00:46:00,211 a life of their own. Remember, there were ways to calculate 634 00:46:00,211 --> 00:46:04,826 what would happen if you put a charge. And suddenly, they create each other an 635 00:46:04,826 --> 00:46:09,890 they propagate through space far away from the charges that might have created 636 00:46:09,890 --> 00:46:14,805 them in the dim distant past, they have essentially their own existence. 637 00:46:14,805 --> 00:46:20,411 And so, we do talk about these fields as important objects, the understanding that 638 00:46:20,411 --> 00:46:25,603 light is an electromagnetic wave also tells you that you can in principle 639 00:46:25,603 --> 00:46:31,002 imagine oscillating a charge or creating an oscillating electric field at any 640 00:46:31,002 --> 00:46:37,714 weave, wavelength or any frequency. So, we know that we see light from between 641 00:46:37,714 --> 00:46:43,978 400 and 700 nanometers in wavelength. What, what about the solutions to 642 00:46:43,978 --> 00:46:48,371 Maxwell's equation with wavelengths outside this region? 643 00:46:48,371 --> 00:46:54,725 And it turns out that there is an entire huge electromagnetic spectrum out there 644 00:46:54,725 --> 00:47:01,080 ranging from at very high frequency and very short wavelength gamma rays with 645 00:47:01,080 --> 00:47:06,242 wavelengths of down to ten to the fourteen, ten to the fifteen meters and 646 00:47:06,242 --> 00:47:09,412 below. Except though, below that are very hard 647 00:47:09,412 --> 00:47:12,558 to produce, through the x-ray spectrum. 648 00:47:12,558 --> 00:47:18,849 The drugs from wavelengths of about ten to the minus nine to ten to the minus 649 00:47:18,849 --> 00:47:23,530 twelve meters, and then the ultraviolet light which is the 650 00:47:23,530 --> 00:47:29,449 chunk of the spectrum, immediately beyond the deep violet light at 400 nanometers. 651 00:47:29,449 --> 00:47:32,986 that is the shortest wavelength our eyes can see. 652 00:47:32,986 --> 00:47:38,905 And then, on the other side, to the left of the red light we have infrared light 653 00:47:38,905 --> 00:47:44,608 and below that, microwaves and radio waves whose wavelengths can be hundreds 654 00:47:44,608 --> 00:47:48,219 of meters. and so there's this entire spectrum. 655 00:47:48,219 --> 00:47:51,850 And in fact, we're familiar with it, we use it. 656 00:47:51,850 --> 00:47:56,989 our eyes are sensitive only to this tiny little bit of the electromagnetic 657 00:47:56,989 --> 00:47:59,455 spectrum. Our eyes have all kinds of 658 00:47:59,455 --> 00:48:02,881 inefficiencies. But, in this case, our eyes are well 659 00:48:02,881 --> 00:48:07,472 adapted to where we live. if you look down here at the bottom of 660 00:48:07,472 --> 00:48:11,104 this plot, this is the transparency of the atmosphere. 661 00:48:11,104 --> 00:48:16,723 And you see that, for example, gamma rays and x-rays are not very useful despite 662 00:48:16,723 --> 00:48:22,247 Superman claim to the contrary, x-ray vision is not very useful because x-rays 663 00:48:22,247 --> 00:48:26,745 are very quickly absorbed in the atmosphere, they do not penetrate. 664 00:48:26,745 --> 00:48:31,352 Visible light penetrates the atmosphere. A little window in the infra red 665 00:48:31,352 --> 00:48:35,128 penetrates the atmosphere. And then, radio waves penetrate the 666 00:48:35,128 --> 00:48:38,843 atmosphere, well we know that, because that's how we watch TV. 667 00:48:38,843 --> 00:48:43,796 But the wavelengths of radio waves are too long you would need your eyes to be 668 00:48:43,796 --> 00:48:46,643 antenna. They would need to be on the order of 669 00:48:46,643 --> 00:48:49,739 meters in size. We do not have eyes meters in size. 670 00:48:49,739 --> 00:48:54,568 There would also be other limitations. It would be hard to see features of the 671 00:48:54,568 --> 00:48:57,374 universe smaller than a few meters across. 672 00:48:57,374 --> 00:49:02,717 So, given our need for fine resolution, our eyes are well adapted to the 673 00:49:02,717 --> 00:49:08,054 conditions under which we evolve. But the universe, on the other hand, 674 00:49:08,054 --> 00:49:11,925 produces light in, in the entire, across the entire spectrum 675 00:49:11,925 --> 00:49:14,479 from high energy gamma rays to radio waves. 676 00:49:14,479 --> 00:49:19,291 And it's important in order to collect information about the universe to be able 677 00:49:19,291 --> 00:49:22,023 to observe it in all possible frequency bands. 678 00:49:22,023 --> 00:49:26,834 And indeed, with technology, people have developed ways to observe the universe in 679 00:49:26,834 --> 00:49:30,949 all of these frequencies. And at every time that we've developed a 680 00:49:30,949 --> 00:49:35,758 new technology and a new way to look at the universe, there have been new and 681 00:49:35,758 --> 00:49:40,696 often surprising discoveries made. note that observations in many of these 682 00:49:40,696 --> 00:49:45,634 bands, in the ultraviolet and x-rays and in gamma rays for example, need to be 683 00:49:45,634 --> 00:49:50,169 made outside the atmosphere. Putting a very good gamma ray detector on 684 00:49:50,169 --> 00:49:55,127 the ground will not buy you anything, because gamma rays from space will not 685 00:49:55,127 --> 00:49:58,127 penetrate. So, these observatories including, 686 00:49:58,127 --> 00:50:03,542 actually, infrared observatories, tend to be space-born or at least high altitude 687 00:50:03,542 --> 00:50:07,260 balloon flights. radio telescopes can be placed on, are 688 00:50:07,260 --> 00:50:11,180 placed on the ground. Those are these very large dishes that 689 00:50:11,180 --> 00:50:15,170 receive radio waves. And over the course of the class, we will 690 00:50:15,170 --> 00:50:19,422 have occasion to use information collected by all of these bands. 691 00:50:19,422 --> 00:50:24,785 So, it's the richness of the spectrum corresponds to the richness of phenomenon 692 00:50:24,785 --> 00:50:30,710 out there. We're almost done with our discussion. 693 00:50:30,710 --> 00:50:35,851 One last statement now that we have our understanding of the spectrum. 694 00:50:35,851 --> 00:50:39,230 A hot object radiates, that's what we disussed. 695 00:50:39,230 --> 00:50:42,977 Everything radiates as long as it's warmer than the 696 00:50:42,977 --> 00:50:47,929 surroundings for a dense, dark object. So, for an object that essentially 697 00:50:47,929 --> 00:50:52,881 absorbs light that hits it, such as you, me, the Earth, and it turns out, the sun, 698 00:50:52,881 --> 00:50:57,254 the radiation is almost completely characterized, and it's precisely 699 00:50:57,254 --> 00:51:01,755 completely characterized for some idealized black body, an object that 700 00:51:01,755 --> 00:51:05,356 absorbs any light that falls upon it, by the temperature. 701 00:51:05,356 --> 00:51:10,180 It turns out that the nature of the radiation produced by a warm object, 702 00:51:10,180 --> 00:51:14,845 if it's dense, it's essentially a property of light and thermodynamics and 703 00:51:14,845 --> 00:51:20,140 has nothing to do with the object itself. And this is called black body radiation 704 00:51:20,140 --> 00:51:25,950 and it has two important properties. One is, that hotter objects are blue. 705 00:51:25,950 --> 00:51:30,821 This despite the fact that blue is a cold color and red a warm color. 706 00:51:30,821 --> 00:51:36,468 To our intuition it turns out that hotter objects radiate shorter wavelength. 707 00:51:36,468 --> 00:51:41,975 In other words, a blue glow is hotter then a red glow because a red glow has a 708 00:51:41,975 --> 00:51:46,211 longer wavelength. This is summarized in Wien's displacement 709 00:51:46,211 --> 00:51:52,170 law which says that the wavelength that which an object emits more radiation than 710 00:51:52,170 --> 00:51:57,239 any other wavelength, the wavelength of maximum emission, multiplied by the 711 00:51:57,239 --> 00:52:02,034 object's temperature, is actually a constant. So that if you double the 712 00:52:02,034 --> 00:52:06,693 temperature of an object, the wavelength at which it emits is halved. 713 00:52:06,693 --> 00:52:12,515 And Wien's constant is written over here. It's got units of meters times Kelvin, so 714 00:52:12,515 --> 00:52:16,925 wavelength times degree. The other and more familiar statement is 715 00:52:16,925 --> 00:52:22,523 that hotter objects produce more light. This is encoded in the Stefan-Boltzmann 716 00:52:22,523 --> 00:52:28,082 relation which tells us that the rate at which H meters squared of an object 717 00:52:28,082 --> 00:52:31,290 radiates. Of course, a big object radiates more 718 00:52:31,290 --> 00:52:34,987 than a little object if they're the same temperature. 719 00:52:34,987 --> 00:52:40,706 Two light bulbs make more light than one light bulb. So, we need to normalize to 720 00:52:40,706 --> 00:52:45,449 the rate at which an object produces radiation per meter squared, 721 00:52:45,449 --> 00:52:50,742 that's F in watts per meter squared. And the rate at which each meter squared 722 00:52:50,742 --> 00:52:56,173 of an object radiates is proportional to the fourth power of the temperature in 723 00:52:56,173 --> 00:52:59,974 degrees Kelvin. And so doubling the temperature leads to 724 00:52:59,974 --> 00:53:05,336 a sixteen fold increase in radiation and the constant, the Stefanu-Boltzmann 725 00:53:05,336 --> 00:53:09,340 constant, sigma has this numerical value in our units. 726 00:53:09,340 --> 00:53:14,363 And its units are watts per meter squared per degree Kelvin to the fourth. 727 00:53:14,363 --> 00:53:18,960 Let's take a look at what this black body radiation looks like. 728 00:53:18,960 --> 00:53:26,853 Here, we have a plot of the relative intensity in various wavelengths as a 729 00:53:26,853 --> 00:53:35,136 function of the wavelength from near zero to a few times ten to the minus six 730 00:53:35,136 --> 00:53:40,203 micrometers. And so, the visible band is located over 731 00:53:40,203 --> 00:53:41,670 here. And the 732 00:53:41,670 --> 00:53:44,818 black body curve has this characteristic shape. 733 00:53:44,818 --> 00:53:49,641 As I said, it's independent of the material. And the curve I have plotted 734 00:53:49,641 --> 00:53:54,664 here is the curve for an object that glows that has a temperature of about 735 00:53:54,664 --> 00:53:58,616 3,000 degrees Kelvin. 3,000 degrees Kelvin is about the 736 00:53:58,616 --> 00:54:02,701 temperature at, of the filament in an incandescent light bulb. 737 00:54:02,701 --> 00:54:07,992 And what you will notice is that most of the light produced by an incandescent 738 00:54:07,992 --> 00:54:11,731 light bulb's black body radiation, is in fact not light. 739 00:54:11,731 --> 00:54:16,045 It is invisible to us. It is infrared radiation, which heats us, 740 00:54:16,045 --> 00:54:21,750 if you underst, if you talk about people not liking incandescent lamps as being 741 00:54:21,750 --> 00:54:26,760 very inefficient, this is because due to the limitations of the filament. 742 00:54:26,760 --> 00:54:32,048 Filaments melt if you heat them too hot. most of the light produced by an 743 00:54:32,048 --> 00:54:35,875 incandescent lamp is in fact not light, it is just heat. 744 00:54:35,875 --> 00:54:40,820 And so, on the other hand, if we heat the object a little bit. 745 00:54:40,820 --> 00:54:44,807 This is an object with a temperature of say, 6,000 degrees. 746 00:54:44,807 --> 00:54:49,002 This is closer to the sun. And you see that much of the light 747 00:54:49,002 --> 00:54:52,990 produced by the sun is, in fact, in the visible spectrum. 748 00:54:52,990 --> 00:54:58,696 It's very nice of the sun to be adjusted to our atmosphere so that much of the sun 749 00:54:58,696 --> 00:55:03,372 light can, in fact, penetrate our atmosphere, and we can use it to see. 750 00:55:03,372 --> 00:55:08,460 And you also see that the factor of two in temperature leads to this huge 751 00:55:08,460 --> 00:55:11,829 increase. The previous light bulbs graph has been 752 00:55:11,829 --> 00:55:17,439 scaled down here, it looks very small. remember, doubling the temperature 753 00:55:17,439 --> 00:55:21,896 increases the total radiation by a factor of sixteen. 754 00:55:21,896 --> 00:55:27,950 And, it has also moved the maximum from, according to Wien's law, from the 755 00:55:27,950 --> 00:55:31,903 infrared in this case, down into the visible. 756 00:55:31,903 --> 00:55:37,705 And we can add another object say, with an even higher temperature. 757 00:55:37,705 --> 00:55:43,340 let's say, 12,000 degrees. So, another doubling in this case, 758 00:55:44,460 --> 00:55:49,833 the spectrum again increases to the point where the sun's spectrum is negligible 759 00:55:49,833 --> 00:55:55,008 and the peak is now in the ultraviolet. So, we're seeing Wien's displacement to 760 00:55:55,008 --> 00:55:58,060 the left, hotter temperatures mean bluer light. 761 00:55:58,060 --> 00:56:01,775 We're also seeing the Stefan-Boltzmann law in action, 762 00:56:01,775 --> 00:56:05,300 hotter temperatures mean way, way, way more light. 763 00:56:05,300 --> 00:56:10,075 These are all important observations. Let's see what we can do with them. 764 00:56:10,075 --> 00:56:14,514 [SOUND] That was a long, video clip. There was a lot going on there. 765 00:56:14,514 --> 00:56:18,617 We got to go through two and a one-half centuries of physics. 766 00:56:18,617 --> 00:56:23,729 Remember, what we're doing is we're packing our toolkit so that we know what 767 00:56:23,729 --> 00:56:27,024 it is we need to address understanding astronomy. 768 00:56:27,024 --> 00:56:30,836 So, don't despair. rather than trying to summarize all the 769 00:56:30,836 --> 00:56:36,015 disparate things we talked about, let me do an example of an application to actual 770 00:56:36,015 --> 00:56:40,269 astronomy of what we learned about that might clarify some things. 771 00:56:40,269 --> 00:56:44,338 So, lets talk about the sun. We said that the sun radiates its heat. 772 00:56:44,338 --> 00:56:48,531 Let's see what all our various results tell us about solar radiation. 773 00:56:48,531 --> 00:56:53,032 So, we can measure the brightness of sunlight on Earth in watts per meter 774 00:56:53,032 --> 00:56:54,697 squared. How do you do that? 775 00:56:54,697 --> 00:56:59,766 Not put our a meters squared of detector and measure how much sunlight hits it. 776 00:56:59,766 --> 00:57:05,038 Put out a meter squared of something very dark that absorbs all the sunlight, 777 00:57:05,038 --> 00:57:08,135 measure how much energy that thing receives. 778 00:57:08,135 --> 00:57:13,472 And you'll find, the number is called the solar constant, and it is 1,361 watts per 779 00:57:13,472 --> 00:57:17,030 meter squared. So, a meter squared of sunlight will run 780 00:57:17,030 --> 00:57:21,050 a very small hair dryer, or light ten incandescent light bulbs. 781 00:57:21,050 --> 00:57:27,720 So, we know the intensity of solar radiation, in the vicinity of Earth. 782 00:57:27,720 --> 00:57:32,393 Now, we know how far the sun is. The sun is one astronomical unit or 150 783 00:57:32,393 --> 00:57:36,996 million kilometers away. And so, if we know how bright it looks 784 00:57:36,996 --> 00:57:41,239 and we know how far it is, we know that we can compute its 785 00:57:41,239 --> 00:57:44,960 luminosity. Remember, we had that B, the brightness, 786 00:57:44,960 --> 00:57:51,034 is the luminosity divided by the area of the big ball whose radius in this case, 787 00:57:51,034 --> 00:57:54,983 is the distance to the sun or one astronomical unit. 788 00:57:54,983 --> 00:58:00,754 And so, we can com, solve this we know the brightness, we measured it, we know 789 00:58:00,754 --> 00:58:04,398 the distance. We can write an expression for the 790 00:58:04,398 --> 00:58:10,169 luminosity and it's four pi times the distance to the sun squared times the 791 00:58:10,169 --> 00:58:15,073 brightness of the sun. And so, we put in the numbers. 792 00:58:15,073 --> 00:58:19,999 This is 4 pi times 1.5. I'm rounding. 793 00:58:19,999 --> 00:58:25,389 Times ten to the eleven meter squared, times 1361. 794 00:58:25,389 --> 00:58:34,822 And we evaluate the calculation and you find that the sun is a very bright light 795 00:58:34,822 --> 00:58:40,661 bulb, indeed. It has a luminosity of 3.8 times ten to 796 00:58:40,661 --> 00:58:46,500 the 26 watts. That's a lot of energy lost by the sun. 797 00:58:46,500 --> 00:58:49,658 Now, we can measure the radius of the sun 798 00:58:49,658 --> 00:58:54,637 since we know the distance. we can make a small angle calculation. 799 00:58:54,637 --> 00:59:00,567 We measure the angular size of the sun in the sky, and we find that the radius of 800 00:59:00,567 --> 00:59:03,862 the sun is 6.96 times ten to the eighth meter, 801 00:59:03,862 --> 00:59:07,450 that's about 700,000 kilometers. And from this, 802 00:59:07,450 --> 00:59:13,999 we can figure out something else. Because what we know now is that, think 803 00:59:13,999 --> 00:59:18,802 of the sun as a ball. Every square meter of the ball is 804 00:59:18,802 --> 00:59:25,533 radiating light to the outside, you count how many square meters there are on the 805 00:59:25,533 --> 00:59:30,240 surface of a ball. That would be 4 pi times the radius of 806 00:59:30,240 --> 00:59:34,240 the sun squared. If I multiply that by the flux, the 807 00:59:34,240 --> 00:59:40,750 amount of power in watts emitted by each square meter, this should equal L. Since 808 00:59:40,750 --> 00:59:46,633 I know the radius of the sun and the luminosity, the total amount of energy 809 00:59:46,633 --> 00:59:51,340 that's being emitted, I can figure out the flux that each 810 00:59:51,340 --> 00:59:55,813 square meter emits. Now, the lumina, the luminosity, as I 811 00:59:55,813 --> 00:59:59,375 said, is the area of the sun times the flux. 812 00:59:59,375 --> 01:00:05,422 And so, I could compute the flux. the nicest way to do this is to use a 813 01:00:05,422 --> 01:00:10,807 scaling relation, as usual. So, the scaling relation is going to be 814 01:00:10,807 --> 01:00:15,465 that I have that F, which is L over 4 pi times 815 01:00:15,465 --> 01:00:22,640 the radius of the sun squared. and I have that b is L over four pi times the 816 01:00:22,640 --> 01:00:27,998 distance to the sun squared. I can cancel everything around. 817 01:00:27,998 --> 01:00:35,263 Find that L is b times the distance to the sun divided by the radius of the sun 818 01:00:35,263 --> 01:00:39,383 squared. And this relates again, a flux to a flux 819 01:00:39,383 --> 01:00:45,661 through a dimensionless quantity. I recommend this method of computing and 820 01:00:45,661 --> 01:00:50,411 this is 150 million, this is 700,000. That's a big factor. 821 01:00:50,411 --> 01:00:56,943 Every square meter of the sun produces 6.3 times ten to the seven watts, a 822 01:00:56,943 --> 01:01:03,306 square meter of sun produces 63 megawatts of light emitted out towards the 823 01:01:03,306 --> 01:01:07,477 universe. That's a large number, but we can go 824 01:01:07,477 --> 01:01:10,253 further. We have the flux and we know the 825 01:01:10,253 --> 01:01:15,331 Stefan-Boltzmann law, we know that the flux is also equal to sigma, T to the 826 01:01:15,331 --> 01:01:18,446 fourth. Since the sun emits approximately as a 827 01:01:18,446 --> 01:01:22,914 black body, it's dense enough. And so, since we know the flux, we can 828 01:01:22,914 --> 01:01:26,951 compute the temperature, and we can actually find the temperature 829 01:01:26,951 --> 01:01:30,656 of the part of the sun that we see. It's called the photosphere. 830 01:01:30,656 --> 01:01:33,537 It's somewhere outside on the surface of the sun. 831 01:01:33,537 --> 01:01:38,124 And, we find that the temperature is the fourth root of F divided by sigma, the 832 01:01:38,124 --> 01:01:42,888 temperature of the radiating surface of the sun of the photosphere is about 5800 833 01:01:42,888 --> 01:01:46,994 Kelvin. I can use Wien's Law because I know the 834 01:01:46,994 --> 01:01:52,006 temperature to figure out the wavelength of maximum emission for the sun. 835 01:01:52,006 --> 01:01:56,674 The wavelength at which the sun emits more light than anything else. 836 01:01:56,674 --> 01:02:01,411 I take Wien's constant, 0.0029 meters is the value of Wien's constant. 837 01:02:01,411 --> 01:02:06,698 I divide by the temperature of the sun, and I find that the sun produces more 838 01:02:06,698 --> 01:02:11,366 light than any other frequency at a wavelength of 503 nanometers. 839 01:02:11,366 --> 01:02:16,240 And if you look up the table, this is somewhere between the red and the blue, 840 01:02:16,240 --> 01:02:20,509 and indeed it is green. But Ronin, you tell me every 841 01:02:20,509 --> 01:02:24,396 kindergartner knows the sun is yellow. Yes, but not really. 842 01:02:24,396 --> 01:02:27,737 Every kindergartner knows the sun appears yellow. 843 01:02:27,737 --> 01:02:33,057 Why that is consistent with the maximum emission being green, we'll see in the 844 01:02:33,057 --> 01:02:36,125 next clip. In the meantime, go and catch your 845 01:02:36,125 --> 01:02:39,399 breath. We have gone through many, many different 846 01:02:39,399 --> 01:02:43,081 topics here. We have a whole grocery list of new ideas 847 01:02:43,081 --> 01:02:46,559 and new concepts to digest and to learn how to use. 848 01:02:46,559 --> 01:02:49,560 And we'll start applying those very soon.