1 00:00:00 --> 00:00:00,584 2 00:00:00,584 --> 00:00:04,354 Today, I'm going to talk about light. 3 00:00:04,354 --> 00:00:10,324 Light is an electromagnetic phenomenon, and already in the 4 00:00:10,324 --> 00:00:14,199 sixteenth century, way before Maxwell, 5 00:00:14,199 --> 00:00:20,273 a lot of studies were done of the interaction of light with 6 00:00:20,273 --> 00:00:25,3 water and with glass. And the kind of experiments 7 00:00:25,3 --> 00:00:31,06 that were done follows -- say this is air -- I call that 8 00:00:31,06 --> 00:00:36,567 medium one -- and this is water -- call that 9 00:00:36,567 --> 00:00:42,411 medium two -- and I have a light beam that strikes this surface. 10 00:00:42,411 --> 00:00:48,071 Light comes in like so -- and I define this angle as the angle 11 00:00:48,071 --> 00:00:51,689 of incidence, and I call that theta one. 12 00:00:51,689 --> 00:00:56,698 This is the normal to the surface, and we call that the 13 00:00:56,698 --> 00:01:00,966 angle of incidence. I will see now that some of 14 00:01:00,966 --> 00:01:05,234 that light is reflected -- reflected with an L, 15 00:01:05,234 --> 00:01:10,64 as in lion -- and some of that light goes 16 00:01:10,64 --> 00:01:15,368 into the water, and we call that refracted -- 17 00:01:15,368 --> 00:01:20,311 refracted, with an R, as in Richard -- and this 18 00:01:20,311 --> 00:01:25,684 angle, we'll call theta two. And it was a Dutchman, 19 00:01:25,684 --> 00:01:30,305 Willebrord Snellius, who, in the seventeenth 20 00:01:30,305 --> 00:01:36,538 century, found three rules that govern the relation between 21 00:01:36,538 --> 00:01:42,206 these three light beams. The first one is that this 22 00:01:42,206 --> 00:01:45,459 beam, this beam, and this beam are in one plane. 23 00:01:45,459 --> 00:01:48,643 As you see, that is my plane of the blackboard. 24 00:01:48,643 --> 00:01:51,896 The second thing that he found, that this angle, 25 00:01:51,896 --> 00:01:54,665 theta three, which is called the angle of 26 00:01:54,665 --> 00:01:58,056 reflection, is the same as the angle of incidence. 27 00:01:58,056 --> 00:02:00,548 That was known before him, of course. 28 00:02:00,548 --> 00:02:04,078 And then the third one, which is the most surprising 29 00:02:04,078 --> 00:02:08,3 one, which is called after him, which is called Snell's Law -- 30 00:02:08,3 --> 00:02:13,907 although his name was Snellius -- is that the sine of theta one 31 00:02:13,907 --> 00:02:19,891 divided by the sine of theta two, if we go from air to water, 32 00:02:19,891 --> 00:02:23,881 then that ratio is about one point three. 33 00:02:23,881 --> 00:02:28,768 If you go from air to glass, it's a little higher, 34 00:02:28,768 --> 00:02:34,952 it's like one point five or so. He introduced the idea of index 35 00:02:34,952 --> 00:02:38,343 of refraction, which I will call N, 36 00:02:38,343 --> 00:02:41,734 as in Nancy -- index of refraction. 37 00:02:41,734 --> 00:02:46,622 For vacuum, the index of refraction, 38 00:02:46,622 --> 00:02:51,245 per definition, is one, but it's very closely 39 00:02:51,245 --> 00:02:55,869 the same in air, we always treat it as one in 40 00:02:55,869 --> 00:02:57,655 air. And in water, 41 00:02:57,655 --> 00:03:03,54 the index of refraction is approximately one point three, 42 00:03:03,54 --> 00:03:07,743 and in glass, depending upon what kind of 43 00:03:07,743 --> 00:03:12,051 glass you have, it's about one point five. 44 00:03:12,051 --> 00:03:16,78 And so we can now amend this law, Snell's Law, 45 00:03:16,78 --> 00:03:21,735 by writing here N two divided by N one, 46 00:03:21,735 --> 00:03:26,125 and one being the index of refraction of the medium where 47 00:03:26,125 --> 00:03:30,827 you are, your incident beam -- that's why I put a one here -- 48 00:03:30,827 --> 00:03:35,217 and two being the index of refraction of the medium where 49 00:03:35,217 --> 00:03:38,822 you're traveling to. You're refracted into this 50 00:03:38,822 --> 00:03:40,546 medium. And so you see, 51 00:03:40,546 --> 00:03:45,171 indeed, that since water is one point three, and air is one, 52 00:03:45,171 --> 00:03:49,012 that this ratio for air to water is 53 00:03:49,012 --> 00:03:53,006 one point three. And this is called Snell's Law. 54 00:03:53,006 --> 00:03:57,68 And it is immediately obvious that if you go from air to 55 00:03:57,68 --> 00:04:02,609 water, or you go from air to glass, that angle theta two is 56 00:04:02,609 --> 00:04:07,623 always smaller than the angle theta one, because this number 57 00:04:07,623 --> 00:04:11,533 is larger than one. But if you go from water to 58 00:04:11,533 --> 00:04:16,462 air, then the situation is reversed, and that's what I want 59 00:04:16,462 --> 00:04:19,521 to address now, that's actually quite 60 00:04:19,521 --> 00:04:22,921 interesting. So now, my medium one is now 61 00:04:22,921 --> 00:04:28,206 water, and my medium two is now air. 62 00:04:28,206 --> 00:04:34,638 And so now, I go from here to here, and so here I have my 63 00:04:34,638 --> 00:04:40,955 angle of incidence theta one and here I have my angle of 64 00:04:40,955 --> 00:04:46,583 reflection, that is the theta three, and now here, 65 00:04:46,583 --> 00:04:52,211 I have my angle theta two. And so if I write down, 66 00:04:52,211 --> 00:04:57,954 now, Snell's Law, then I get the 67 00:04:57,954 --> 00:05:03,68 sine of theta one divided by the sine of theta two is now N 68 00:05:03,68 --> 00:05:07,432 two divided by N one, but N two is one, 69 00:05:07,432 --> 00:05:13,158 divided by one point three, if we go from air -- from water 70 00:05:13,158 --> 00:05:16,811 to air. And what is so special here is 71 00:05:16,811 --> 00:05:22,242 that theta two can obviously never be larger than ninety 72 00:05:22,242 --> 00:05:25,697 degrees. And so if you substitute in 73 00:05:25,697 --> 00:05:29,482 here, theta two is ninety degrees, 74 00:05:29,482 --> 00:05:33,355 then you will find that theta one, then, is about fifty 75 00:05:33,355 --> 00:05:36,151 degrees. And if you apply this equation, 76 00:05:36,151 --> 00:05:40,382 and you substitute for theta one, an angle larger than fifty 77 00:05:40,382 --> 00:05:44,398 degrees, you're going to find the sine of theta two being 78 00:05:44,398 --> 00:05:46,836 larger than one, which is nonsense. 79 00:05:46,836 --> 00:05:50,135 It cannot happen. And so nature ignores Snell's 80 00:05:50,135 --> 00:05:53,577 Law, and nature says, "Sorry, I can't do it," and 81 00:05:53,577 --> 00:05:57,091 what nature now does, if the angle of theta one is 82 00:05:57,091 --> 00:06:00,744 too large -- in this case, 83 00:06:00,744 --> 00:06:06,309 with water, larger than fifty degrees -- this is not there 84 00:06:06,309 --> 00:06:11,874 anymore, and all the light is now being reflected off that 85 00:06:11,874 --> 00:06:14,803 surface. And we call that total 86 00:06:14,803 --> 00:06:17,537 reflection. Total reflection. 87 00:06:17,537 --> 00:06:23,2 So total reflection happens when theta one is larger than a 88 00:06:23,2 --> 00:06:28,277 certain critical angle, and the sine of that critical 89 00:06:28,277 --> 00:06:32,997 angle -- for which I write CR -- is N 90 00:06:32,997 --> 00:06:37,224 two divided by N one, but there is a condition. 91 00:06:37,224 --> 00:06:42,462 And the condition is that N one must be larger than N two. 92 00:06:42,462 --> 00:06:46,689 If that's not the case, then there is not total 93 00:06:46,689 --> 00:06:49,813 reflection. And total reflection is 94 00:06:49,813 --> 00:06:54,959 actually very interesting, it has practical applications, 95 00:06:54,959 --> 00:07:00,656 which I will discuss with you shortly, but I first 96 00:07:00,656 --> 00:07:04,682 want to do a demonstration in which I want to show this to 97 00:07:04,682 --> 00:07:05,812 you. I have here, 98 00:07:05,812 --> 00:07:09,625 water, and here is air, and I have a laser beam which I 99 00:07:09,625 --> 00:07:12,45 can shine in, and I can change this angle 100 00:07:12,45 --> 00:07:16,829 theta one, and slowly increase it, and you will see that when I 101 00:07:16,829 --> 00:07:19,371 approach fifty degrees, first of all, 102 00:07:19,371 --> 00:07:22,761 you will see that theta two increases, increases, 103 00:07:22,761 --> 00:07:26,151 increases, and then, when I approach the critical 104 00:07:26,151 --> 00:07:30,812 angle and exceed it, then we have hundred percent 105 00:07:30,812 --> 00:07:34,023 reflection. Let me first turn on the laser 106 00:07:34,023 --> 00:07:38,879 so that there's a little bit of light, and I'm going to show it 107 00:07:38,879 --> 00:07:43,578 to you there for those of you who are not sitting very close, 108 00:07:43,578 --> 00:07:47,807 and that means I have to set the light situation -- OK, 109 00:07:47,807 --> 00:07:50,705 so there you see, the light coming in, 110 00:07:50,705 --> 00:07:55,326 just the way we had it on the blackboard, this is the way it 111 00:07:55,326 --> 00:07:58,929 comes in, in water, this is the reflected part, 112 00:07:58,929 --> 00:08:03,81 and this is the one that is refracted into the air. 113 00:08:03,81 --> 00:08:07,548 So that is this one here. And now I'm going to increase 114 00:08:07,548 --> 00:08:11,562 that angle, when I touch the table, the water will start to 115 00:08:11,562 --> 00:08:14,815 wiggle a little, and you will probably see that. 116 00:08:14,815 --> 0. 117 0. --> 00:08:16,614 So I'm going to in -- OK, 118 00:08:16,614 --> 00:08:20,351 I decre- I'm going to increase that angle, look how I'm 119 00:08:20,351 --> 00:08:23,466 increasing it. Look, that theta two is getting 120 00:08:23,466 --> 00:08:26,719 larger, is going to approach the ninety degrees, 121 00:08:26,719 --> 00:08:29,626 I increase theta one, I increase theta one, 122 00:08:29,626 --> 00:08:35,061 look at theta two, almost ninety degrees, 123 00:08:35,061 --> 00:08:40,985 I'm very close to the critical angle now, I'm almost at it 124 00:08:40,985 --> 00:08:46,285 right now, and now all the light is being reflected. 125 00:08:46,285 --> 00:08:51,585 Hundred percent reflection. A remarkable phenomenon. 126 00:08:51,585 --> 00:08:55,222 And this has practical applications. 127 00:08:55,222 --> 00:09:00,418 And we're going to show you some of these practical 128 00:09:00,418 --> 00:09:02,185 applications, too. 129 00:09:02,185 --> 00:09:08,908 The most important practical application is fiber optics. 130 00:09:08,908 --> 00:09:12,952 If I have a fiber, and it is properly designed -- 131 00:09:12,952 --> 00:09:17,249 so this is a fiber -- and some light comes in here, 132 00:09:17,249 --> 00:09:21,377 and it hits here -- so this is, say, some plastic, 133 00:09:21,377 --> 00:09:26,684 or glass, and this is air -- if this angle of incidence is large 134 00:09:26,684 --> 00:09:30,897 than the critical angle, hundred percent reflected. 135 00:09:30,897 --> 00:09:36,12 And so nothing comes out in the air, hundred percent reflected. 136 00:09:36,12 --> 00:09:39,995 Here, again, the critical 137 00:09:39,995 --> 00:09:42,698 angle is exceeded, and so hundred percent is 138 00:09:42,698 --> 00:09:46,028 reflected, and you can go through this whole thing for 139 00:09:46,028 --> 00:09:48,416 miles on end. You can put even knots in 140 00:09:48,416 --> 00:09:51,747 there, as long as you never exceed the critical angle, 141 00:09:51,747 --> 00:09:55,077 that light will propagate, and there will never be any 142 00:09:55,077 --> 00:09:57,842 loss of light, and that's why people are very 143 00:09:57,842 --> 00:10:01,235 much interested in this. You can transport even images, 144 00:10:01,235 --> 00:10:03,749 as I will show you, through fiber optics. 145 00:10:03,749 --> 00:10:05,571 I have here, uh, fiber optics, 146 00:10:05,571 --> 00:10:09,467 which has four thousand fibers in it, fifty microns in diameter 147 00:10:09,467 --> 00:10:13,301 each, and we have a laser beam here, and 148 00:10:13,301 --> 00:10:18,501 the laser light will come out -- I will show you the laser 149 00:10:18,501 --> 00:10:23,794 light shortly there -- and it doesn't matter what I do with 150 00:10:23,794 --> 00:10:28,995 the fibers, I can even go hundred eighty degrees and shine 151 00:10:28,995 --> 00:10:32,644 them there, as long as, inside the fiber, 152 00:10:32,644 --> 00:10:35,747 I always exceed the critical angle. 153 00:10:35,747 --> 00:10:39,761 Uh, oh, I don't want the television any more, 154 00:10:39,761 --> 00:10:44,597 so we can turn this off, and let's here have the laser 155 00:10:44,597 --> 00:10:48,209 light. There it is. 156 00:10:48,209 --> 00:10:52,234 Here you see the laser light. OK, now look at this, 157 00:10:52,234 --> 00:10:57,063 this bundle that I have here. I turn it into an absurd snake, 158 00:10:57,063 --> 00:11:00,846 almost like an S. All the light still comes out. 159 00:11:00,846 --> 00:11:05,514 So it goes al the way through, I'm going to turn it hundred 160 00:11:05,514 --> 00:11:09,378 eighty degrees around, turn it to the wall there. 161 00:11:09,378 --> 00:11:12,034 There it is. So there's an amazing 162 00:11:12,034 --> 00:11:16,3 phenomenon that this light doesn't get out in the air, 163 00:11:16,3 --> 00:11:19,745 it stays inside the fiber, 164 00:11:19,745 --> 00:11:23,217 and that's the idea behind fiber optics. 165 00:11:23,217 --> 00:11:27,312 I have another, uh, application of fiber optics 166 00:11:27,312 --> 00:11:30,161 right here which is very similar. 167 00:11:30,161 --> 00:11:33,9 You can send an image through fiber optics. 168 00:11:33,9 --> 00:11:38,796 This is my fiber optics, now, thousands of small fibers. 169 00:11:38,796 --> 00:11:43,159 And I send a message in here, this side, an image, 170 00:11:43,159 --> 00:11:46,185 could be a person, could be a text. 171 00:11:46,185 --> 00:11:52,942 And here we have a TV camera. And we can watch that image on 172 00:11:52,942 --> 00:11:58,719 this side of the fiber appear as that image, and this television 173 00:11:58,719 --> 00:12:02,111 camera will be able to see that image. 174 00:12:02,111 --> 00:12:06,695 And let's see whether we can show you that message. 175 00:12:06,695 --> 00:12:12,288 OK, I have to do something here again, I think you're going to 176 00:12:12,288 --> 00:12:16,506 -- ah, there it is. So you actually can see the 177 00:12:16,506 --> 00:12:19,349 individual fibers, you see them? 178 00:12:19,349 --> 00:12:26,461 How -- how interesting. Each one, these are individual 179 00:12:26,461 --> 00:12:30,144 fibers. And their diameter is probably 180 00:12:30,144 --> 00:12:34,623 not much more than fifty or a hundred microns. 181 00:12:34,623 --> 00:12:38,506 Let's see what message there is for you. 182 00:12:38,506 --> 00:12:41,094 Oh man, oh man, exam three. 183 00:12:41,094 --> 00:12:45,175 You don't want to hear about that, do you? 184 00:12:45,175 --> 00:12:49,455 Well, that depends on what the message says. 185 00:12:49,455 --> 00:12:51,148 Problem -- no. No. 186 00:12:51,148 --> 00:12:53,537 Problem one. Problem one. 187 00:12:53,537 --> 00:12:57,807 The figure -- oh, oh, oh, oh, 188 00:12:57,807 --> 00:13:01,202 below -- oh, I must have -- that's the wrong 189 00:13:01,202 --> 00:13:05,939 message, I couldn't possibly meant to give you away the exam, 190 00:13:05,939 --> 00:13:10,361 of course, so I apologize for that, that I showed you the 191 00:13:10,361 --> 00:13:13,914 wrong message. But at least it demonstrated to 192 00:13:13,914 --> 00:13:17,941 you that you can send an image through fiber optics, 193 00:13:17,941 --> 00:13:21,573 even secret messages. Newton had an interesting 194 00:13:21,573 --> 00:13:27,336 explanation for Snell's Law. Newton was the man of planets. 195 00:13:27,336 --> 00:13:32,116 He was the man of particles, masses, accelerations, 196 00:13:32,116 --> 00:13:35,94 F equals M A. And so his explanation came 197 00:13:35,94 --> 00:13:38,712 with particles. He says light, 198 00:13:38,712 --> 00:13:43,014 light are particles. So if this is the surface 199 00:13:43,014 --> 00:13:46,169 between, let's say, air and water, 200 00:13:46,169 --> 00:13:50,28 Newton argued as follows. If light comes in, 201 00:13:50,28 --> 00:13:53,052 it has a certain speed, V one. 202 00:13:53,052 --> 00:13:57,258 And therefore, it has a horizontal component. 203 00:13:57,258 --> 00:14:02,421 And it has a certain vertical component. 204 00:14:02,421 --> 00:14:06,016 And he says that if this light ends up in water, 205 00:14:06,016 --> 00:14:09,995 at the moment that it reaches the surface, it gets an 206 00:14:09,995 --> 00:14:13,132 acceleration perpendicular to the surface. 207 00:14:13,132 --> 00:14:14,815 Why? He didn't tell us. 208 00:14:14,815 --> 00:14:17,493 But he said, it gets an acceleration 209 00:14:17,493 --> 00:14:20,859 perpendicular to the surface. In other words, 210 00:14:20,859 --> 00:14:23,996 this horizontal component does not change. 211 00:14:23,996 --> 00:14:27,974 That remains what it was. But this component changes, 212 00:14:27,974 --> 00:14:31,952 this becomes substantially larger, 213 00:14:31,952 --> 00:14:37,5 depending upon the index of refraction, of course. 214 00:14:37,5 --> 00:14:42,935 And so the new velocity is now in this direction. 215 00:14:42,935 --> 00:14:48,596 And so you see that, indeed, the angle theta one is 216 00:14:48,596 --> 00:14:55,276 larger than the angle theta two. But Snell's Law immediately 217 00:14:55,276 --> 00:15:00,598 follows from this. The sine of theta one -- this 218 00:15:00,598 --> 00:15:03,483 angle, if theta one. 219 00:15:03,483 --> 00:15:05,478 So this angle, if theta one. 220 00:15:05,478 --> 00:15:08,876 So that's this velocity divided by this vector. 221 00:15:08,876 --> 00:15:13,087 And the sine of theta two is this velocity divided by this 222 00:15:13,087 --> 00:15:15,672 vector. But these two velocities are 223 00:15:15,672 --> 00:15:18,406 the same. So you immediately find that 224 00:15:18,406 --> 00:15:22,839 this ratio is V two divided by V one, a great victory for Mr. 225 00:15:22,839 --> 00:15:25,498 Newton. Except there was one problem, 226 00:15:25,498 --> 00:15:29,34 maybe, that it means that V two is larger than V one, 227 00:15:29,34 --> 00:15:33,403 and so Newton argued that the speed of light in water is 228 00:15:33,403 --> 00:15:38,889 larger than the speed of light -- light in air. 229 00:15:38,889 --> 00:15:42,633 And in glass, of course, it would be even 230 00:15:42,633 --> 00:15:45,721 larger. Now, there was a Dutchman, 231 00:15:45,721 --> 00:15:50,025 and the name of Dutchman was Christian Huygens. 232 00:15:50,025 --> 00:15:53,956 H-U-Y-G-E-N-S. And this gentleman suggested 233 00:15:53,956 --> 00:15:59,29 that perhaps light are not particles, that they are waves. 234 00:15:59,29 --> 00:16:04,811 And this guy came up with a genius idea -- which we now know 235 00:16:04,811 --> 00:16:10,376 as Huygens' Principle, at least you call it Huygens' 236 00:16:10,376 --> 00:16:14,164 Principle, but we don't call it Huygens' Principle. 237 00:16:14,164 --> 00:16:17,952 You see, this sound, U Y, is pronounced in Dutch as 238 00:16:17,952 --> 00:16:20,451 [ouwe]. None of you can say [ouwe] 239 00:16:20,451 --> 00:16:23,254 unless you're Dutch. To make it worse, 240 00:16:23,254 --> 00:16:26,512 this sound you don't have either in English. 241 00:16:26,512 --> 00:16:30,299 That's a [kkkkhhhh]. None of you can say [kkkkhhhh] 242 00:16:30,299 --> 00:16:34,087 unless you're Dutch. Let alone that you can say the 243 00:16:34,087 --> 00:16:37,95 combination, Huygens. Anyone who comes forward to me 244 00:16:37,95 --> 00:16:42,425 after this lecture and who knows how to 245 00:16:42,425 --> 00:16:46,038 pronounce the word Huygens, has to be Dutch. 246 00:16:46,038 --> 00:16:48,896 I will be kind to you, and call it, 247 00:16:48,896 --> 00:16:53,098 today, Huygens' Principle. So Huygens came with the 248 00:16:53,098 --> 00:16:55,955 following idea. Here is a source of 249 00:16:55,955 --> 00:17:00,409 electromagnetic waves. And these electromagnetic waves 250 00:17:00,409 --> 00:17:03,098 propagate out in a spherical way. 251 00:17:03,098 --> 00:17:06,628 Not unreasonable. And so you even see here, 252 00:17:06,628 --> 00:17:10,41 the wave crests. And so he defined the surface 253 00:17:10,41 --> 00:17:17,437 at the leading part of the wave, where all points are in phase, 254 00:17:17,437 --> 00:17:22,713 he called that the wave front. So this is the wave front. 255 00:17:22,713 --> 00:17:27,799 And he now postulated that each point of the wave front 256 00:17:27,799 --> 00:17:33,357 individually oscillates at the same frequency as the source, 257 00:17:33,357 --> 00:17:38,82 and produces spherical waves. We call them secondary waves, 258 00:17:38,82 --> 00:17:44,001 often also called wavelets. And that the envelope of the 259 00:17:44,001 --> 00:17:47,916 wave fronts of the secondary waves 260 00:17:47,916 --> 00:17:51,984 is now the new wave front. So it works as follows. 261 00:17:51,984 --> 00:17:56,966 Each point that you can choose, you can choose as many as you 262 00:17:56,966 --> 00:18:01,615 want to, starts to oscillate at the same frequency as the 263 00:18:01,615 --> 00:18:05,683 source, and produces, on its own, spherical waves, 264 00:18:05,683 --> 00:18:09,336 there they go, and the new wave front is then 265 00:18:09,336 --> 00:18:11,993 here. And this is called Huygens' 266 00:18:11,993 --> 00:18:15,314 Principle. Of course, he doesn't give any 267 00:18:15,314 --> 00:18:19,957 explanation of why these points do that. 268 00:18:19,957 --> 00:18:24,349 He hypothesized that. And this principle can explain 269 00:18:24,349 --> 00:18:29,515 Snell's Law in a very easy way. I want you to read up on that 270 00:18:29,515 --> 00:18:32,96 in your book. And you will see that it is 271 00:18:32,96 --> 00:18:37,437 very easy to explain Snell's Law with this principle, 272 00:18:37,437 --> 00:18:41,484 except that now, you will conclude that the sine 273 00:18:41,484 --> 00:18:46,995 of theta one divided by the sine of theta two is V one divided by 274 00:18:46,995 --> 00:18:49,879 V two, and therefore, 275 00:18:49,879 --> 00:18:54,692 Huygens predicted that the speed of light is lower than the 276 00:18:54,692 --> 00:18:58,924 speed of light in air, whereas Newton predicted that 277 00:18:58,924 --> 00:19:03,654 the speed of light in water would be higher than the speed 278 00:19:03,654 --> 00:19:06,973 of light in air. So the question now was, 279 00:19:06,973 --> 00:19:09,877 who was right? Are lights particles, 280 00:19:09,877 --> 00:19:13,943 or are they waves? Well, the wave-particle idea of 281 00:19:13,943 --> 00:19:18,009 light has been a very long-standing 282 00:19:18,009 --> 00:19:21,016 issue in physics, and I will show you, 283 00:19:21,016 --> 00:19:25,971 I think, next week -- or maybe after the exam -- how Young in, 284 00:19:25,971 --> 00:19:29,709 eighteen oh one, conclusively demonstrated that 285 00:19:29,709 --> 00:19:33,365 light are waves. So it looked like Huygens was 286 00:19:33,365 --> 00:19:36,696 going to be the winner. On the other hand, 287 00:19:36,696 --> 00:19:41,733 I showed you last lecture that light can behave like particles. 288 00:19:41,733 --> 00:19:45,47 Photons, bullets, tomatoes, radiation pressure, 289 00:19:45,47 --> 00:19:49,939 that's particles. Mass, the whole thing, 290 00:19:49,939 --> 00:19:53,433 the whole ball of wax. And so maybe Newton was right, 291 00:19:53,433 --> 00:19:56,792 maybe they are particles. Well, they're both right. 292 00:19:56,792 --> 00:20:00,757 There are times that you can actually interpret what you see 293 00:20:00,757 --> 00:20:04,789 best be assuming they're waves, and that there are times that 294 00:20:04,789 --> 00:20:08,149 it's much better to assume that they are particles, 295 00:20:08,149 --> 00:20:11,71 with mass, like in the case of the radiation pressure. 296 00:20:11,71 --> 00:20:14,062 But of course, the key question now, 297 00:20:14,062 --> 00:20:17,287 is, who was right in terms of the speed of light? 298 00:20:17,287 --> 00:20:22,356 Is the light going faster in water, then Newton was 299 00:20:22,356 --> 00:20:26,31 right, or is the light going slower in water, 300 00:20:26,31 --> 00:20:30,534 then Huygens was right. Needless to say that the 301 00:20:30,534 --> 00:20:34,937 Dutchman was right. The speed of light in water is 302 00:20:34,937 --> 00:20:38,173 lower than the speed of light in air. 303 00:20:38,173 --> 00:20:42,217 When we arrived, the speed of light in vacuum, 304 00:20:42,217 --> 00:20:47,519 we used Maxwell's equations. And they allowed us to conclude 305 00:20:47,519 --> 00:20:53,659 that the speed of light, much to everyone's surprise, 306 00:20:53,659 --> 00:20:59,111 depends on epsilon zero and mu zero in a very simple way, 307 00:20:59,111 --> 00:21:04,369 I will call it for now, V, that was one over the square 308 00:21:04,369 --> 00:21:07,192 root of epsilon zero, mu zero. 309 00:21:07,192 --> 00:21:11,476 And we call that C. If you had used Maxwell's 310 00:21:11,476 --> 00:21:16,928 equations as they are valid in materials, in dielectrics, 311 00:21:16,928 --> 00:21:23,159 and also in materials that have magnetic properties, 312 00:21:23,159 --> 00:21:26,063 than it would be exactly the same derivation, 313 00:21:26,063 --> 00:21:30,091 but you would have seen a kappa here, the dielectric constant, 314 00:21:30,091 --> 00:21:33,656 and you would have seen here the magnetic permeability. 315 00:21:33,656 --> 00:21:36,363 Kappa, if you're not in air, but in glass, 316 00:21:36,363 --> 00:21:38,74 and water, is always larger than one. 317 00:21:38,74 --> 00:21:42,767 So you see in front of you that the speed of light in water is 318 00:21:42,767 --> 00:21:45,144 lower than the speed of light in air. 319 00:21:45,144 --> 00:21:48,973 This can also be written as C divided by the square root of 320 00:21:48,973 --> 00:21:53,265 kappa divided by kappa M, and we would nowadays, 321 00:21:53,265 --> 00:21:55,827 simply write that as C divided by N. 322 00:21:55,827 --> 00:22:00,074 So the index of refraction is really the square root of the 323 00:22:00,074 --> 00:22:03,735 product of the dielectric constant and the magnetic 324 00:22:03,735 --> 00:22:06,81 permeability. Now, kappa and kappa of M are 325 00:22:06,81 --> 00:22:09,299 very strong functions of frequency. 326 00:22:09,299 --> 00:22:13,692 And that's not so surprising, because at very high frequency, 327 00:22:13,692 --> 00:22:16,841 the intrinsic electric and magnetic dipoles, 328 00:22:16,841 --> 00:22:21,087 which are being aligned by the alternative external fields, 329 00:22:21,087 --> 00:22:26,446 cannot follow quickly enough. A field wants to drive them in 330 00:22:26,446 --> 00:22:29,167 this direction, and it wants to drive them 331 00:22:29,167 --> 00:22:32,353 back, and forward, and back, and there's just not 332 00:22:32,353 --> 00:22:35,87 enough time to do that. And so you expect that at high 333 00:22:35,87 --> 00:22:39,454 frequencies, the values for kappa are lower than at low 334 00:22:39,454 --> 00:22:42,241 frequencies, which is exactly what you see. 335 00:22:42,241 --> 00:22:45,758 In the case of kappa M, that's only important when you 336 00:22:45,758 --> 00:22:48,811 deal with ferromagnetic materials, because with 337 00:22:48,811 --> 00:22:52,793 paramagnetic and diamagnetic materials, kappa M is always one 338 00:22:52,793 --> 00:22:54,651 anyhow. Or very close to one. 339 00:22:54,651 --> 00:22:58,234 I have chosen water as an example, 340 00:22:58,234 --> 00:23:03,497 to show you the dependence of kappa on the frequency. 341 00:23:03,497 --> 00:23:08,558 This is on the Web, so you can download it and make 342 00:23:08,558 --> 00:23:13,314 yourself a copy. And so if you look here -- this 343 00:23:13,314 --> 00:23:18,172 is for water -- then, you see there the -- at low 344 00:23:18,172 --> 00:23:23,941 frequencies, at zero Hertz, and even at radio frequencies, 345 00:23:23,941 --> 00:23:30,115 at hundred megaHertz -- this is hundred megaHertz, 346 00:23:30,115 --> 00:23:33,098 this is, uh, radio -- these are radio waves 347 00:23:33,098 --> 00:23:37,006 -- notice that the dielectric constant in water is about 348 00:23:37,006 --> 00:23:40,061 eighty, and, um, at, um, at visible light -- 349 00:23:40,061 --> 00:23:44,324 these are the frequencies of visible light -- it's way lower. 350 00:23:44,324 --> 00:23:47,947 We just discussed that. The oscillations go to fast, 351 00:23:47,947 --> 00:23:50,505 the electric dipoles can't follow it. 352 00:23:50,505 --> 00:23:54,199 And so the index of refraction then, for radio waves, 353 00:23:54,199 --> 00:23:56,828 at hundred megaHertz, is roughly nine, 354 00:23:56,828 --> 00:24:01,019 and so the speed of those waves in water is nine times lower 355 00:24:01,019 --> 00:24:05,252 than the speed of light in air -- we 356 00:24:05,252 --> 00:24:08,772 call it speed of light, but it's the speed, 357 00:24:08,772 --> 00:24:13,382 of course, of the radio waves then -- and in the case of 358 00:24:13,382 --> 00:24:16,987 visible light, you see that visible light in 359 00:24:16,987 --> 00:24:21,681 water, the speed is only one point three times lower than 360 00:24:21,681 --> 00:24:24,866 what it would be in air, or, of course, 361 00:24:24,866 --> 00:24:28,051 in vacuum. The frequency effect is very 362 00:24:28,051 --> 00:24:31,487 noticeable. If you take red light and blue 363 00:24:31,487 --> 00:24:36,097 light, they have different frequencies, 364 00:24:36,097 --> 00:24:39,048 and therefore, the index of refraction is 365 00:24:39,048 --> 00:24:41,852 different for red light and blue light. 366 00:24:41,852 --> 00:24:46,204 If I take water -- the numbers I'm going to give you are for 367 00:24:46,204 --> 00:24:50,114 water -- then the index of refraction for red light in 368 00:24:50,114 --> 00:24:54,024 water is one point three three one -- but the index of 369 00:24:54,024 --> 00:24:58,229 refraction for blue light in water is one point three four 370 00:24:58,229 --> 00:25:00,737 three. And we're going to use these 371 00:25:00,737 --> 00:25:04,13 numbers, shortly, to get a deeper understanding 372 00:25:04,13 --> 00:25:07,803 of the rainbow that's behind this, 373 00:25:07,803 --> 00:25:10,772 of course. And so you notice that the blue 374 00:25:10,772 --> 00:25:14,755 light is one percent slower in water than the red light. 375 00:25:14,755 --> 00:25:18,811 And this phenomenon that you see there, that the speed of 376 00:25:18,811 --> 00:25:22,504 electromagnetic radiation depends on the wavelength, 377 00:25:22,504 --> 00:25:26,053 depends on the frequency, we call that dispersion. 378 00:25:26,053 --> 00:25:29,964 It is a good thing that sound in air is not dispersive, 379 00:25:29,964 --> 00:25:34,092 because -- just imagine that high frequencies would travel 380 00:25:34,092 --> 00:25:37,018 faster than low frequencies, 381 00:25:37,018 --> 00:25:39,02 just as an example. Or, or slower, 382 00:25:39,02 --> 00:25:40,84 for that matter. It would mean, 383 00:25:40,84 --> 00:25:44,299 then, that if you go to a concert, and you would listen to 384 00:25:44,299 --> 00:25:47,514 the violins and the bass, that the violins would reach 385 00:25:47,514 --> 00:25:51,336 you first, and then the sound of the bass would reach you later, 386 00:25:51,336 --> 00:25:54,188 and the farther you are away from the orchestra, 387 00:25:54,188 --> 00:25:57,525 the worse that would be. If the effect were very strong, 388 00:25:57,525 --> 00:26:01,286 here in twenty six one hundred, someone sitting in the back row 389 00:26:01,286 --> 00:26:04,381 could not even understand my words, because the high 390 00:26:04,381 --> 00:26:08,627 frequencies would reach that person at a different 391 00:26:08,627 --> 00:26:12,616 time than the low frequencies. So sound in air is 392 00:26:12,616 --> 00:26:15,774 non-dispersive. But glass and water are 393 00:26:15,774 --> 00:26:19,596 dispersive for light, and it's very noticeable. 394 00:26:19,596 --> 00:26:23,917 If I take a piece of glass, and I give it this shape, 395 00:26:23,917 --> 00:26:28,238 the shape of a prism, and I shine some light on here, 396 00:26:28,238 --> 00:26:32,476 light from these light bulbs, or light from the sun, 397 00:26:32,476 --> 00:26:36,133 for that matter, then I can apply Snell's Law 398 00:26:36,133 --> 00:26:40,371 here. I know the angle of incidence, 399 00:26:40,371 --> 00:26:43,167 theta one. I know the index of refraction 400 00:26:43,167 --> 00:26:46,593 -- this is for water, but you can look them up for 401 00:26:46,593 --> 00:26:50,928 glass, of course -- and then you will see there is a difference 402 00:26:50,928 --> 00:26:55,264 of the index of refraction for red light that there is for blue 403 00:26:55,264 --> 00:26:57,571 light. And so, when you reach this 404 00:26:57,571 --> 00:27:00,508 side of the prism, again, you have to apply 405 00:27:00,508 --> 00:27:04,633 Snell's Law, and when you do that, you will see that the red 406 00:27:04,633 --> 00:27:08,758 light doesn't come out at the same angle that the blue light 407 00:27:08,758 --> 00:27:12,884 come out, but the two diverge. That is the 408 00:27:12,884 --> 00:27:15,986 result of the fact that the indices of refraction are 409 00:27:15,986 --> 00:27:19,507 different, but also the result of the fact that we have this 410 00:27:19,507 --> 00:27:21,238 particular shape, funny shape, 411 00:27:21,238 --> 00:27:24,639 namely that this side of the glass is not parallel to this 412 00:27:24,639 --> 00:27:26,489 side. And so if you put a screen 413 00:27:26,489 --> 00:27:29,472 here, you will see colors, you can make a spectrum, 414 00:27:29,472 --> 00:27:33,172 you can convince yourself that the light from these light bulbs 415 00:27:33,172 --> 00:27:36,156 is not just white light, but that it contains many, 416 00:27:36,156 --> 00:27:38,543 many colors. Well, it has to contain many 417 00:27:38,543 --> 00:27:41,467 colors, because if I look at that gentleman there, 418 00:27:41,467 --> 00:27:46,017 he's wearing a red shirt. Where do you think that red 419 00:27:46,017 --> 00:27:49,227 color is coming from? It must come from the light 420 00:27:49,227 --> 00:27:51,968 bulb, so there must be red light in there. 421 00:27:51,968 --> 00:27:55,579 The woman setting next to him is wearing a green shirt, 422 00:27:55,579 --> 00:27:59,257 so there must also be green light in this -- this light. 423 00:27:59,257 --> 00:28:01,464 And the same is true for sunlight. 424 00:28:01,464 --> 00:28:04,941 But the beauty is that, making use of the dispersion, 425 00:28:04,941 --> 00:28:08,418 you can decompose the white light into the individual 426 00:28:08,418 --> 00:28:11,761 colors, and make a spectrum. If you take a piece of 427 00:28:11,761 --> 00:28:14,637 plane-parallel glass, which is window glass, 428 00:28:14,637 --> 00:28:18,539 then you're not going to see colors, 429 00:28:18,539 --> 00:28:22,962 because, if now I shine light on here, white light from the 430 00:28:22,962 --> 00:28:26,85 light bulb, or from the sun, it is true that it will 431 00:28:26,85 --> 00:28:31,12 obviously refract in here. But when you apply Snell's Law 432 00:28:31,12 --> 00:28:35,771 again, here, then it will come out -- all the colors will come 433 00:28:35,771 --> 00:28:39,736 out in the same direction. So the red light comes out 434 00:28:39,736 --> 00:28:44,006 here, and the blue light comes out in the same direction. 435 00:28:44,006 --> 00:28:46,445 And your brains are very special. 436 00:28:46,445 --> 00:28:51,825 If your brains see all colors coming from one direction, 437 00:28:51,825 --> 00:28:55,723 they say, "I see white light. Look at the light bulb. 438 00:28:55,723 --> 00:28:58,871 You say, "Ah, that's white light." But look 439 00:28:58,871 --> 00:29:01,269 at this gentleman, you say, "Hey, 440 00:29:01,269 --> 00:29:04,492 it's red, it must come from that light bulb. 441 00:29:04,492 --> 00:29:08,914 So your brains are special in the sense that they think that 442 00:29:08,914 --> 00:29:11,837 the combination of many colors is white. 443 00:29:11,837 --> 00:29:16,409 And I can show that to you in a -- in a rather convincing way. 444 00:29:16,409 --> 00:29:20,231 You see here a disk. And I would assume that you see 445 00:29:20,231 --> 00:29:25,432 colors on that disk. If not, you have a problem. 446 00:29:25,432 --> 00:29:29,004 And I can fool your brains. What I can do, 447 00:29:29,004 --> 00:29:34,406 I can rotate that disk so fast that your brains get so mixed up 448 00:29:34,406 --> 00:29:39,546 that they're going to say to you, "Yes, that's white light." 449 00:29:39,546 --> 00:29:44,251 So let me first give you some ideal light on that disk, 450 00:29:44,251 --> 00:29:47,388 and I'm going to spin it up a little. 451 00:29:47,388 --> 00:29:49,74 So you agree with me, right? 452 00:29:49,74 --> 00:29:51,918 You still see colors, yes? 453 00:29:51,918 --> 00:29:55,404 Still see colors, right? 454 00:29:55,404 --> 00:29:57,069 OK. You still see colors, 455 00:29:57,069 --> 00:29:57,762 right? Yes. 456 00:29:57,762 --> 00:29:59,15 Haha, haha. Hahahaha. 457 00:29:59,15 --> 00:30:01,439 This is white as it can be for me. 458 00:30:01,439 --> 00:30:03,174 Not too surprising, right? 459 00:30:03,174 --> 00:30:06,504 The same situation when I look at the light bulb. 460 00:30:06,504 --> 00:30:10,736 All these colors are processed by my brains in such a way that 461 00:30:10,736 --> 00:30:14,482 they think, or they -- well, they actually make you see 462 00:30:14,482 --> 00:30:17,257 white light. It's as real as you can have 463 00:30:17,257 --> 00:30:19,547 it. And so this raises the subject 464 00:30:19,547 --> 00:30:23,501 of the illusion of colors, which is what I want to discuss 465 00:30:23,501 --> 00:30:27,803 with you for the remaining part of this 466 00:30:27,803 --> 00:30:30,04 lecture. If you ask a physicist, 467 00:30:30,04 --> 00:30:32,277 "When do you see certain colors? 468 00:30:32,277 --> 00:30:35,741 When to we see red? When do we see blue or green? 469 00:30:35,741 --> 00:30:38,7 Then chances are, that he would give you a 470 00:30:38,7 --> 00:30:41,082 standard answer, and he would say, 471 00:30:41,082 --> 00:30:44,835 "Well, that depends on, uh, on the wavelength in air. 472 00:30:44,835 --> 00:30:49,238 If you tell me what wavelength you're on, then I will tell you 473 00:30:49,238 --> 00:30:53,712 what colors you will see." And I have here a transparency which 474 00:30:53,712 --> 00:30:58,042 makes the connection between wavelength and 475 00:30:58,042 --> 00:31:00,616 these colors. It's also on the web, 476 00:31:00,616 --> 00:31:04,931 so you can also download this. And so if the wavelength of 477 00:31:04,931 --> 00:31:09,472 light in air is about in this range -- one angstrom is ten to 478 00:31:09,472 --> 00:31:13,711 the minus ten meters -- yes, you will probably say that's 479 00:31:13,711 --> 00:31:16,284 red light. When the wavelengths get 480 00:31:16,284 --> 00:31:19,085 shorter, in this range, you would say, 481 00:31:19,085 --> 00:31:23,551 "Yes, that's green light." And when the wavelengths get even 482 00:31:23,551 --> 00:31:27,487 shorter, you would say, "Yes, that's blue light." And 483 00:31:27,487 --> 00:31:32,107 you can't see any wavelength shorter than this, 484 00:31:32,107 --> 00:31:34,788 you're getting to the ultraviolet here, 485 00:31:34,788 --> 00:31:38,246 and you can't see any wavelength longer than this, 486 00:31:38,246 --> 00:31:41,492 that's infrared, and our eyes are not sensitive 487 00:31:41,492 --> 00:31:45,161 for those wavelengths. So this is all nice and dandy, 488 00:31:45,161 --> 00:31:49,465 but we still have the problem of the -- the effect that if you 489 00:31:49,465 --> 00:31:53,064 mix all the colors together, like the rotating disk, 490 00:31:53,064 --> 00:31:57,369 and like looking at the light bulb, that our brains still tell 491 00:31:57,369 --> 00:31:59,697 us that we are seeing white light. 492 00:31:59,697 --> 00:32:03,366 So maybe matters are not really as 493 00:32:03,366 --> 00:32:08,204 simple as we think. And this scheme about colors 494 00:32:08,204 --> 00:32:13,762 has been worked out in quite some detail already in the 495 00:32:13,762 --> 00:32:17,982 seventeenth and in the eighteenth century, 496 00:32:17,982 --> 00:32:23,334 when it was discovered that there was such a thing as 497 00:32:23,334 --> 00:32:27,76 primary colors. Maxwell did some research on 498 00:32:27,76 --> 00:32:32,804 that, and Helmholtz, even the poet Goethe did work 499 00:32:32,804 --> 00:32:34,789 on this. 500 00:32:34,789 --> 00:32:38,76 They discovered that there are primary colors, 501 00:32:38,76 --> 00:32:44,055 and when you mix light -- we call this additive mixing -- the 502 00:32:44,055 --> 00:32:48,202 three primary colors are green, violet, and red, 503 00:32:48,202 --> 00:32:52,703 and when you mix paint, the three primary colors are 504 00:32:52,703 --> 00:32:54,556 yellow, blue, and red. 505 00:32:54,556 --> 00:32:59,763 And the idea behind this is that if you mix the -- the three 506 00:32:59,763 --> 00:33:04,705 primary colors in the right proportion, then you can make 507 00:33:04,705 --> 00:33:09,29 many colors. I want to show you a color 508 00:33:09,29 --> 00:33:14,087 triangle, which is the recipe, tells you how you have to mix 509 00:33:14,087 --> 00:33:17,096 these colors, and in order to do that, 510 00:33:17,096 --> 00:33:21,243 I'm going to make it dark, but not all the way dark. 511 00:33:21,243 --> 00:33:25,878 So here you see the color triangle, and the color triangle 512 00:33:25,878 --> 00:33:29,455 has in the three colors -- the three corners, 513 00:33:29,455 --> 00:33:34,172 the colors red -- one primary color -- and then here it has 514 00:33:34,172 --> 00:33:37,262 violet, and then up there it has green. 515 00:33:37,262 --> 00:33:43,973 And now, I'll tell you how this recipe has to be used. 516 00:33:43,973 --> 00:33:50,75 So I'm going to draw here a color triangle and we have red 517 00:33:50,75 --> 00:33:56,124 here and we have green there, and we have here, 518 00:33:56,124 --> 00:34:00,33 violet. And if you look at this color 519 00:34:00,33 --> 00:34:06,522 triangle, you see all the colors that you can imagine. 520 00:34:06,522 --> 00:34:11,893 Sort of. You see yellow, 521 00:34:11,893 --> 00:34:16,238 and you see here purple, and you see orange, 522 00:34:16,238 --> 00:34:21,29 you even see white. So how do we make these colors, 523 00:34:21,29 --> 00:34:24,523 now? Well, suppose I want to make 524 00:34:24,523 --> 00:34:28,261 this color here. So that's this color, 525 00:34:28,261 --> 00:34:31,494 say. Then you draw three lines -- 526 00:34:31,494 --> 00:34:35,637 one, two, three -- from the three corners, 527 00:34:35,637 --> 00:34:42,507 and this is the amount of red that you have to put in, 528 00:34:42,507 --> 00:34:47,07 and this is the amount of green that you have to put in in the 529 00:34:47,07 --> 00:34:50,436 light, and this is the amount of violet light. 530 00:34:50,436 --> 00:34:52,904 And if you do that, in that ratio, 531 00:34:52,904 --> 00:34:55,672 you would get the color which is here. 532 00:34:55,672 --> 00:34:58,813 If you want to make very nice yellow -- oh, 533 00:34:58,813 --> 00:35:03,301 let's see, let's make some very nice yellow, which is all the 534 00:35:03,301 --> 00:35:07,041 way here, at the edge -- you don't need any violet, 535 00:35:07,041 --> 00:35:12,052 you can do that exclusively with green and with red, 536 00:35:12,052 --> 00:35:15,746 so let's go to this point here, which is yellow, 537 00:35:15,746 --> 00:35:18,969 it would mean, then, that I have to put in 538 00:35:18,969 --> 00:35:22,427 this much red, and I have to put in this much 539 00:35:22,427 --> 00:35:25,335 green. And if I add more and more red, 540 00:35:25,335 --> 00:35:29,186 I go along this line, then I end up here and I get 541 00:35:29,186 --> 00:35:32,094 orange. So I could make orange here by 542 00:35:32,094 --> 00:35:36,81 simply increasing the amount of red -- oh, this should not be 543 00:35:36,81 --> 00:35:39,246 violet, right? Ooh-ooh, ooh-ooh, 544 00:35:39,246 --> 00:35:42,625 this is green. Oh, you should have yelled at 545 00:35:42,625 --> 00:35:46,585 me. So this is green and so if I 546 00:35:46,585 --> 00:35:50,887 want to make orange here, then I simply have to give it 547 00:35:50,887 --> 00:35:55,029 more red and less green. And if you go to an extreme, 548 00:35:55,029 --> 00:35:59,013 and you want to make white light, and you go bingo, 549 00:35:59,013 --> 00:36:03,553 right there in the middle, well, then, you have to give it 550 00:36:03,553 --> 00:36:05,943 this much red, this much green, 551 00:36:05,943 --> 00:36:09,767 and this much violet. And that's the idea that we 552 00:36:09,767 --> 00:36:13,83 just saw, you mix all the colors, and we mix up your 553 00:36:13,83 --> 00:36:18,272 brains as well, and your brains then say, 554 00:36:18,272 --> 00:36:22,928 "Gee, ah, that is white light." So the idea behind the three 555 00:36:22,928 --> 00:36:27,663 primary color theory is that our eye cells, the cells that we 556 00:36:27,663 --> 00:36:31,215 have in the retina, respond differently to the 557 00:36:31,215 --> 00:36:34,845 three primary colors, and that color sensation, 558 00:36:34,845 --> 00:36:38,869 which is, of course what the brains are telling you, 559 00:36:38,869 --> 00:36:43,289 those are the messages that are being sent to the brains, 560 00:36:43,289 --> 00:36:49,128 and they are processed here, that they are the result of the 561 00:36:49,128 --> 00:36:51,147 mixing of these three responses. 562 00:36:51,147 --> 00:36:53,362 And the theory is quite successful. 563 00:36:53,362 --> 00:36:57,139 I'm going to try to make for you the color yellow by mixing 564 00:36:57,139 --> 00:36:59,419 these three colors green and violet. 565 00:36:59,419 --> 00:37:02,805 And if I want to make yellow, then we already argued, 566 00:37:02,805 --> 00:37:05,085 all I need is green, and I need red, 567 00:37:05,085 --> 00:37:08,732 I don't even need violet. And I'm going to do that with a 568 00:37:08,732 --> 00:37:12,575 -- with this nice little box here -- I will raise the screen 569 00:37:12,575 --> 00:37:16,548 because we don't need the screen any more, and I don't think I 570 00:37:16,548 --> 00:37:18,632 need the, uh, the slide any more, 571 00:37:18,632 --> 00:37:23,631 um, John. And this box this box has 572 00:37:23,631 --> 00:37:28,433 three lights in there. Red, green, violet. 573 00:37:28,433 --> 00:37:32,181 And I can change the intensities. 574 00:37:32,181 --> 00:37:38,037 Yes, I can show you, I can make the -- the red less 575 00:37:38,037 --> 00:37:43,191 strong, and I can do the same with the green, 576 00:37:43,191 --> 00:37:51,858 I can make it less strong. And I can do the same with the 577 00:37:51,858 --> 00:37:54,843 violet. And so if I want to make, 578 00:37:54,843 --> 00:37:57,175 for instance, that yellow, 579 00:37:57,175 --> 00:38:01,185 then I can do that with green and red alone, 580 00:38:01,185 --> 00:38:06,874 and I have to give it a lot of green, and a little bit of red. 581 00:38:06,874 --> 00:38:10,791 So a little bit of red, and a lot of green. 582 00:38:10,791 --> 00:38:14,988 Can you adjust it a little? Hmm, I see yellow, 583 00:38:14,988 --> 00:38:17,413 don't you? Who sees yellow? 584 00:38:17,413 --> 00:38:21,983 OK. So we make it a little orange, 585 00:38:21,983 --> 00:38:25,732 then we have to give it a little bit more red -- yes, 586 00:38:25,732 --> 00:38:29,77 I give it a little bit more red -- oh, it becomes orange. 587 00:38:29,77 --> 00:38:33,519 See, so I'm marching, now, here, give it a little bit 588 00:38:33,519 --> 00:38:35,826 more red, and you make it orange. 589 00:38:35,826 --> 00:38:39,576 And what I can even do, I can give them all three the 590 00:38:39,576 --> 00:38:42,748 maximum strength, and I can turn it to white. 591 00:38:42,748 --> 00:38:46,353 So we will fool the brains again, all these colors, 592 00:38:46,353 --> 00:38:50,031 like the rotating disk, like the light from the sun, 593 00:38:50,031 --> 00:38:52,554 like the light from the lights here. 594 00:38:52,554 --> 00:38:56,159 I think I see white light. Your 595 00:38:56,159 --> 00:38:59,13 color TV is based on this principle. 596 00:38:59,13 --> 00:39:02,949 You have three electron guns in your color TV. 597 00:39:02,949 --> 00:39:08,042 And there are three different chemicals on the screen of your 598 00:39:08,042 --> 00:39:11,521 television. And these chemicals are in the 599 00:39:11,521 --> 00:39:15,85 form of very small dots. And if electrons hit one of 600 00:39:15,85 --> 00:39:21,027 these dots, they become violet, and the other chemicals become 601 00:39:21,027 --> 00:39:24,507 green, and the other chemicals become red. 602 00:39:24,507 --> 00:39:28,751 And so the whole idea is, now, that 603 00:39:28,751 --> 00:39:33,014 each beam hits its own chemical dot, that's the way they arrange 604 00:39:33,014 --> 00:39:35,18 things. And by mixing the various 605 00:39:35,18 --> 00:39:39,105 intensities, you can mix the intensities with three primary 606 00:39:39,105 --> 00:39:42,354 colors, and you can see all colors on television. 607 00:39:42,354 --> 00:39:45,331 It works very well. Of course, if you haven't 608 00:39:45,331 --> 00:39:48,986 adjusted your television properly, you may have noticed 609 00:39:48,986 --> 00:39:52,708 that sometimes faces are reddish, or faces are greenish. 610 00:39:52,708 --> 00:39:56,431 Well, that's a matter of just adjusting those three guns 611 00:39:56,431 --> 00:40:00,178 appropriately, and then you can be very 612 00:40:00,178 --> 00:40:02,651 successful, and it's very impressive. 613 00:40:02,651 --> 00:40:05,881 This, uh, three-color scheme works quite nicely. 614 00:40:05,881 --> 00:40:09,179 So, in many cases, the three primary color theory 615 00:40:09,179 --> 00:40:12,615 is quite satisfactory. But there are cases where it 616 00:40:12,615 --> 00:40:15,639 fails bitterly. And those are the ones that I 617 00:40:15,639 --> 00:40:19,349 want to discuss for the remaining ten minutes and forty 618 00:40:19,349 --> 00:40:21,686 seconds. Already, in the nineteenth 619 00:40:21,686 --> 00:40:25,396 century, it was known that there were problems with the 620 00:40:25,396 --> 00:40:26,908 three-color theory. Mr. 621 00:40:26,908 --> 00:40:30,372 Benham, in eighteen ninety five, 622 00:40:30,372 --> 00:40:34,058 invented a top which is named after him, it's called the 623 00:40:34,058 --> 00:40:36,739 Benham top. I have one in my office on my 624 00:40:36,739 --> 00:40:39,219 table. It is a top that has just black 625 00:40:39,219 --> 00:40:41,699 lines on it, no colors. You rotate it, 626 00:40:41,699 --> 00:40:45,051 and you see colors. And we copied that top for you, 627 00:40:45,051 --> 00:40:47,531 and we have that here, this is a copy, 628 00:40:47,531 --> 00:40:50,815 it's a large copy, the top is only this small that 629 00:40:50,815 --> 00:40:52,691 I have. This is a Benham top. 630 00:40:52,691 --> 00:40:56,579 I hope you will agree with me that this is black and white. 631 00:40:56,579 --> 00:41:00,802 Any one of you see colors, let me know now. 632 00:41:00,802 --> 00:41:03,6 I will ask you to leave, then. 633 00:41:03,6 --> 00:41:06,592 OK, so no one sees colors. Good. 634 00:41:06,592 --> 00:41:10,453 So now, I'm going to rotate that for you, 635 00:41:10,453 --> 00:41:15,375 and you will be surprised, what you're going to see. 636 00:41:15,375 --> 00:41:20,49 So there is the Benham top, and I'm going to rotate it 637 00:41:20,49 --> 00:41:24,929 somewhere in the ballpark of about seven Hertz, 638 00:41:24,929 --> 00:41:28,597 five to seven Hertz, let's take a look. 639 00:41:28,597 --> 00:41:32,264 Black and white. Hey, [unintelligible], 640 00:41:32,264 --> 00:41:35,376 what am I seeing? 641 00:41:35,376 --> 00:41:38,301 I'm seeing colors. Not very bright, 642 00:41:38,301 --> 00:41:42,26 but I am seeing colors. I see some rusty brown, 643 00:41:42,26 --> 00:41:46,992 right there in the middle, and then I see something of a 644 00:41:46,992 --> 00:41:50,606 grayish-green, maybe, and dark blue further 645 00:41:50,606 --> 00:41:52,327 out. Who sees colors? 646 00:41:52,327 --> 00:41:55,339 Who doesn't? Oh, you're color-blind, 647 00:41:55,339 --> 00:41:56,888 then. That happens. 648 00:41:56,888 --> 00:42:00,846 Well, you see colors, just with black and white 649 00:42:00,846 --> 00:42:03,943 rotating. And, to make it even worse, 650 00:42:03,943 --> 00:42:07,487 I can reverse the disk. 651 00:42:07,487 --> 00:42:11,991 I first have to stop it, otherwise we burn out the motor 652 00:42:11,991 --> 00:42:14,776 -- and I can reverse, and remember, 653 00:42:14,776 --> 00:42:17,478 the rusty brown was in the center. 654 00:42:17,478 --> 00:42:21,819 And now we're going to rotate it the other way around. 655 00:42:21,819 --> 00:42:26,323 And look again what you see. You're now seeing the rusty 656 00:42:26,323 --> 00:42:30,254 brown near the edge. You see the colors reversed. 657 00:42:30,254 --> 00:42:33,858 A lot of research, uh, was done in this area. 658 00:42:33,858 --> 00:42:37,871 But a complete neurophysiological 659 00:42:37,871 --> 00:42:40,81 explanation is still not available yet, 660 00:42:40,81 --> 00:42:45,219 although there are several very successful models that can 661 00:42:45,219 --> 00:42:47,694 predict what our brains will see. 662 00:42:47,694 --> 00:42:52,258 And when your color cells are stimulated with flicker light, 663 00:42:52,258 --> 00:42:56,976 there are phase delays between the incident -- incident light, 664 00:42:56,976 --> 00:43:00,534 and the response, the messages that are sent to 665 00:43:00,534 --> 00:43:03,705 your brains, which are currents of course. 666 00:43:03,705 --> 00:43:09,043 And the phase delay is different for different colors. 667 00:43:09,043 --> 00:43:13,151 So what we're going here, we're fooling the brains, 668 00:43:13,151 --> 00:43:18,162 we're sending flicker light to the brains with different phase 669 00:43:18,162 --> 00:43:23,092 delays, the phase delays in the center are different from the 670 00:43:23,092 --> 00:43:26,625 phase delays further out. And so the brains, 671 00:43:26,625 --> 00:43:30,651 then, process that in the usual way, and they say, 672 00:43:30,651 --> 00:43:34,594 "Well, I'm sorry, but you're going to see colors. 673 00:43:34,594 --> 00:43:39,36 And that's what you're seeing. The most fabulous example of 674 00:43:39,36 --> 00:43:44,475 where the three-color theory fails -- or at least, 675 00:43:44,475 --> 00:43:48,943 is very incomplete -- is the work done by Edwin Land in the 676 00:43:48,943 --> 00:43:52,179 early fifties. Edwin Land, very famous man, 677 00:43:52,179 --> 00:43:55,261 he was the inventor of the Polaroid film. 678 00:43:55,261 --> 00:43:59,576 He pioneered color theories, and became very famous for a 679 00:43:59,576 --> 00:44:03,582 particular demonstration that I will do for you here. 680 00:44:03,582 --> 00:44:07,28 He gave me two slides, I got them personally from 681 00:44:07,28 --> 00:44:10,362 Edwin Land. And these two slides that I'm 682 00:44:10,362 --> 00:44:15,008 going to show you are black and white slides. 683 00:44:15,008 --> 00:44:19,185 That is non-negotiable. I'm going to show them to you, 684 00:44:19,185 --> 00:44:22,337 they are as black and white as this disk. 685 00:44:22,337 --> 00:44:26,434 He took one of those slides by taking a photograph of 686 00:44:26,434 --> 00:44:29,35 something, and what that something is, 687 00:44:29,35 --> 00:44:31,872 you're going to see very shortly. 688 00:44:31,872 --> 00:44:36,442 And the other black and white slide, he also took -- again, 689 00:44:36,442 --> 00:44:41,328 black and white film -- but he put a red filter in front of his 690 00:44:41,328 --> 00:44:43,062 camera. But believe me, 691 00:44:43,062 --> 00:44:49,469 it is a black and white slide. So you're going to see black 692 00:44:49,469 --> 00:44:53,311 and white slides. And then I'm going to do 693 00:44:53,311 --> 00:44:57,997 something special with those slides, and therefore, 694 00:44:57,997 --> 00:45:03,058 I'd rather go there now, and, um, explain things to you 695 00:45:03,058 --> 00:45:07,556 as they come along. And so I have to make it very 696 00:45:07,556 --> 00:45:12,242 dark -- oh, the screen has to come down, of course, 697 00:45:12,242 --> 00:45:17,584 we're going to need the screen, because we're going to see 698 00:45:17,584 --> 0. slides. 699 0. --> 00:45:20,396 So I'm going to in -- OK, 700 00:45:20,396 --> 0. So two black and white slides. 701 0. --> 00:45:24,282 So I'm going to in -- OK, 702 00:45:24,282 --> 00:45:30,048 So the first black and white slide is this one. 703 00:45:30,048 --> 00:45:37,695 I hope we will all agree that this is a black and white slide. 704 00:45:37,695 --> 00:45:44,84 And the second black and white slide is of the same scene. 705 00:45:44,84 --> 00:45:52,989 This, by the way, was taken through a red filter. 706 00:45:52,989 --> 00:45:56,735 But it is black and white. The next one was not taken 707 00:45:56,735 --> 00:46:00,049 through a red filter, but, I hope we all agree, 708 00:46:00,049 --> 00:46:03,579 is black and white. If I put a red filter in front 709 00:46:03,579 --> 00:46:07,902 of this black and white slide, you see exactly what you would 710 00:46:07,902 --> 00:46:09,847 have predicted, namely that, 711 00:46:09,847 --> 00:46:13,521 yes, it's like looking through a red piece of glass, 712 00:46:13,521 --> 00:46:16,259 the whole world turns a little reddish. 713 00:46:16,259 --> 00:46:19,213 Very boring. Although some kids like that. 714 00:46:19,213 --> 00:46:23,032 So this is what you're going to see. 715 00:46:23,032 --> 00:46:27,344 I can do the same with the other one, this is the one that 716 00:46:27,344 --> 00:46:30,673 Edwin Land photographed through a red filter. 717 00:46:30,673 --> 00:46:35,289 If I put a red filter in front of it, you're going to see what 718 00:46:35,289 --> 00:46:37,937 you expect, reddish, pinkish colors. 719 00:46:37,937 --> 00:46:40,434 OK. What do you think you're going 720 00:46:40,434 --> 00:46:44,898 to see if we project one black and white slide on top of the 721 00:46:44,898 --> 00:46:48,53 other black and white slide? Well, let's face it. 722 00:46:48,53 --> 00:46:52,54 Let's be down-to-earth. Black and white plus black and 723 00:46:52,54 --> 00:46:56,398 white will remain black and white, 724 00:46:56,398 --> 00:47:00,839 and that's what you see now. One is now on top of the other. 725 00:47:00,839 --> 00:47:04,527 You may not notice that, but I will take one away, 726 00:47:04,527 --> 00:47:08,064 and add it again. Black and white plus black and 727 00:47:08,064 --> 00:47:12,279 white gives black and white. Now, I'm going to ask you to 728 00:47:12,279 --> 00:47:16,569 sit very firm in your chairs, because you're going to fall 729 00:47:16,569 --> 00:47:19,353 off your chairs if you're not careful. 730 00:47:19,353 --> 00:47:23,643 I'm now going to put in front of the slide that Edwin Land 731 00:47:23,643 --> 00:47:27,482 took through a red filter, I'm going to put that red 732 00:47:27,482 --> 00:47:33,652 filter in front of my projector, only through that slide. 733 00:47:33,652 --> 00:47:36,859 The other one remains as it was. 734 00:47:36,859 --> 00:47:40,996 And there we go. And now what do you see? 735 00:47:40,996 --> 00:47:44,41 You see colors. Is this a miracle? 736 00:47:44,41 --> 00:47:48,134 Well, maybe it is. I see yellow here, 737 00:47:48,134 --> 00:47:52,065 I see green here, I see some dark blue. 738 00:47:52,065 --> 00:47:55,581 Who also sees colors? Just say yes. 739 00:47:55,581 --> 00:47:58,685 [Chorus of yeses]. Who doesn't? 740 00:47:58,685 --> 00:48:03 Good for you. Isn't this amazing? 741 00:48:03 --> 00:48:06,808 Two black and white slides. That's all you're seeing and 742 00:48:06,808 --> 00:48:10,615 then you see this silly red filter, which normally would 743 00:48:10,615 --> 00:48:14,215 give you only a little bit of pinkish, reddish light. 744 00:48:14,215 --> 00:48:18,439 But when you put one on top of the other, something bizarre is 745 00:48:18,439 --> 00:48:22,177 happening in your brains. Your brains are so incredibly 746 00:48:22,177 --> 00:48:26,193 mixed up that they really think you're seeing yellow there. 747 00:48:26,193 --> 00:48:30,416 And they really make you think that you're seeing green there. 748 00:48:30,416 --> 00:48:35,302 A reasonable question now, is to ask, if we took a picture 749 00:48:35,302 --> 00:48:38,173 of this, you take your camera with color film, 750 00:48:38,173 --> 00:48:40,598 what will you see? Will you see colors, 751 00:48:40,598 --> 00:48:44,107 or will it be black and white? Yes, you will see colors, 752 00:48:44,107 --> 00:48:47,489 but the colors will be different from the way that you 753 00:48:47,489 --> 00:48:51,381 and I perceive them right now. So now you can ask yourself the 754 00:48:51,381 --> 00:48:54,253 question, well, "What are not the real colors? 755 00:48:54,253 --> 00:48:57,826 The ones that you and I see, or the ones that our picture 756 00:48:57,826 --> 00:49:00,825 will record?" Well, I think that's a meaningless 757 00:49:00,825 --> 00:49:03,377 question. There is no such thing as right 758 00:49:03,377 --> 00:49:07,976 or wrong in these matters. Our brains are very 759 00:49:07,976 --> 00:49:13,229 complicated, and whatever they show us, that's the real thing 760 00:49:13,229 --> 00:49:16,031 for us. Reality is very relative. 761 00:49:16,031 --> 00:49:20,934 And if you're color-blind, which quite a few people in my 762 00:49:20,934 --> 00:49:25,662 audience must be -- just a matter of statistics -- then 763 00:49:25,662 --> 00:49:29,165 they have a different reality altogether. 764 00:49:29,165 --> 00:49:32,93 Reality is only in the mind of the beholder, 765 00:49:32,93 --> 00:49:38,27 and it all depends on how your brains are processing messages. 766 00:49:38,27 --> 00:49:43,089 The message that I'm giving you for this 767 00:49:43,089 --> 00:49:47,122 weekend is, have a good time, but by all means, 768 00:49:47,122 --> 00:49:52,206 start working on your exam three, which certainly is not an 769 00:49:52,206 --> 49:57 illusion. [applause]