WEBVTT 00:00:02.490 --> 00:00:04.830 The following content is provided under a Creative 00:00:04.830 --> 00:00:06.250 Commons license. 00:00:06.250 --> 00:00:08.460 Your support will help MIT OpenCourseWare 00:00:08.460 --> 00:00:12.550 continue to offer high quality educational resources for free. 00:00:12.550 --> 00:00:15.090 To make a donation or to view additional materials 00:00:15.090 --> 00:00:19.020 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:19.020 --> 00:00:20.280 at ocw.mit.edu. 00:00:24.010 --> 00:00:27.400 PROFESSOR: Today we are going to continue discussion about two 00:00:27.400 --> 00:00:29.420 very important issues. 00:00:29.420 --> 00:00:31.780 The first one is the understanding 00:00:31.780 --> 00:00:34.700 of so-called quarter wave plate. 00:00:34.700 --> 00:00:38.170 That may not mean anything to you in the beginning, 00:00:38.170 --> 00:00:40.590 but I hope after this lecture, you 00:00:40.590 --> 00:00:43.810 will know what does that mean and why that is actually 00:00:43.810 --> 00:00:46.010 interesting. 00:00:46.010 --> 00:00:49.630 The second thing is that-- 00:00:49.630 --> 00:00:52.600 the second topic we want to talk about in the lecture today 00:00:52.600 --> 00:00:56.620 is, OK, we have been talking about electromagnetic waves 00:00:56.620 --> 00:01:01.130 for a long time already, since the last few lectures. 00:01:01.130 --> 00:01:04.250 But we have never touched the topic, 00:01:04.250 --> 00:01:09.180 how do we actually create electromagnetic wave, right? 00:01:09.180 --> 00:01:12.530 And we are going to answer that in the lecture today. 00:01:12.530 --> 00:01:15.560 So that's my plan about these two topics. 00:01:15.560 --> 00:01:18.940 OK, so before we start, it's a reminder 00:01:18.940 --> 00:01:21.370 about why we have learned last time. 00:01:21.370 --> 00:01:24.790 So we have learned several situations 00:01:24.790 --> 00:01:27.280 related to polarization. 00:01:27.280 --> 00:01:30.520 So we have learned linearly polarized wave. 00:01:30.520 --> 00:01:32.080 What is linearly polarized wave? 00:01:32.080 --> 00:01:37.060 If you plot the wave amplitude as a function of time 00:01:37.060 --> 00:01:40.750 as a function of space, it's going up and down, up and down, 00:01:40.750 --> 00:01:43.150 up and down. 00:01:43.150 --> 00:01:45.580 And the direction of the field doesn't 00:01:45.580 --> 00:01:47.410 change as a function of time. 00:01:47.410 --> 00:01:51.640 So that is actually called linearly polarized light. 00:01:51.640 --> 00:01:56.110 And we also learned circularly polarized light, right? 00:01:56.110 --> 00:02:00.500 When you have two components, one is in the x direction, 00:02:00.500 --> 00:02:03.520 the other one is in the y direction, if the two 00:02:03.520 --> 00:02:08.560 components are out of phase, say, they differ 00:02:08.560 --> 00:02:17.290 by 90 degrees, for example, and they the same amplitude, 00:02:17.290 --> 00:02:20.770 then the superposition of these two waves 00:02:20.770 --> 00:02:23.500 will be a circularly polarized wave. 00:02:23.500 --> 00:02:27.530 So basically, the wave propagation looks like this. 00:02:27.530 --> 00:02:31.390 So basically, the pointy angle of the electric field 00:02:31.390 --> 00:02:34.060 is rotating as a function over time 00:02:34.060 --> 00:02:37.060 as a function of the distance it travels. 00:02:37.060 --> 00:02:40.300 And the other case, which is also interesting, 00:02:40.300 --> 00:02:42.205 is that when you have-- 00:02:42.205 --> 00:02:45.760 OK, for example, different phase difference. 00:02:45.760 --> 00:02:49.912 Like delta phi different from 90 degree, or say 00:02:49.912 --> 00:02:52.370 you have different amplitude, although the phase difference 00:02:52.370 --> 00:02:55.220 is 90 degree but you have different amplitude 00:02:55.220 --> 00:02:58.210 in the x and the y direction. 00:02:58.210 --> 00:03:04.540 If that's the case, then you have a situation which not only 00:03:04.540 --> 00:03:06.820 the direction is changing, but also the amplitude 00:03:06.820 --> 00:03:09.220 is changing as a function of time. 00:03:09.220 --> 00:03:12.520 And that we call it elliptically polarized. 00:03:12.520 --> 00:03:16.120 So that's actually the three situations we learned. 00:03:16.120 --> 00:03:22.460 And also we learned about how to make polarized light 00:03:22.460 --> 00:03:23.630 during the class. 00:03:23.630 --> 00:03:27.540 So usually, the light source we are talking about, 00:03:27.540 --> 00:03:31.750 or even present in this room, like the light 00:03:31.750 --> 00:03:34.880 from the light bulb, et cetera, those 00:03:34.880 --> 00:03:36.410 are unpolarized light, right? 00:03:36.410 --> 00:03:42.790 So that means you have a lot of electromagnetic wave emitted 00:03:42.790 --> 00:03:47.740 from the light with different initial time, emission time. 00:03:47.740 --> 00:03:51.940 And those are in slightly different angular frequency, 00:03:51.940 --> 00:03:55.200 slightly different pointing direction. 00:03:55.200 --> 00:03:58.780 So you can have all kinds of different emissions. 00:03:58.780 --> 00:04:01.660 And the sum of all those emissions 00:04:01.660 --> 00:04:04.830 is unpolarized light, which is actually 00:04:04.830 --> 00:04:08.180 the light source I have here. 00:04:08.180 --> 00:04:11.440 And you can use so-called polarizer. 00:04:11.440 --> 00:04:18.910 So the polarizer can actually kill one of the direction, 00:04:18.910 --> 00:04:23.500 and only keep all the projection to the easy axis. 00:04:23.500 --> 00:04:25.630 And in this presentation, the easy axis 00:04:25.630 --> 00:04:27.320 is in the x direction. 00:04:27.320 --> 00:04:30.750 And you can see that if you start with unpolarized light, 00:04:30.750 --> 00:04:34.870 and basically, you have that pass through a polarizer, 00:04:34.870 --> 00:04:37.180 then the resulting electric field 00:04:37.180 --> 00:04:41.340 will be pointing toward the so-called easy axis. 00:04:41.340 --> 00:04:43.990 So the easier axis to pass, right? 00:04:43.990 --> 00:04:48.730 So therefore, all the electric field perpendicular 00:04:48.730 --> 00:04:52.360 to the easy axis is illuminated. 00:04:52.360 --> 00:04:55.360 And what is left over is the electric field, 00:04:55.360 --> 00:05:00.520 which is actually parallel to the easy axis. 00:05:00.520 --> 00:05:06.200 And of course, you can rotate this polarizer 00:05:06.200 --> 00:05:09.070 and you would see that, OK, if you 00:05:09.070 --> 00:05:13.800 have a linearly polarized wave passing through polarizer, 00:05:13.800 --> 00:05:15.940 because easy axis is actually now 00:05:15.940 --> 00:05:19.630 in line with the polarization, what is going to happen 00:05:19.630 --> 00:05:24.940 is, as I said, still only the component which is actually 00:05:24.940 --> 00:05:27.730 parallel to the easy axis will passed through. 00:05:27.730 --> 00:05:30.165 And the resulting electric field will still 00:05:30.165 --> 00:05:33.520 be pointing to the direction of the easy axis. 00:05:33.520 --> 00:05:36.920 So that's actually what we have learned last time. 00:05:36.920 --> 00:05:40.370 OK, so that means we know how to generate 00:05:40.370 --> 00:05:42.490 linearly polarized wave, right? 00:05:42.490 --> 00:05:45.070 Because you just need a polarizer 00:05:45.070 --> 00:05:47.200 and put it in front of your light source, 00:05:47.200 --> 00:05:50.230 then you produce a linearly polarized save. 00:05:50.230 --> 00:05:54.400 But we didn't talk about how to produce a circularly 00:05:54.400 --> 00:05:56.200 polarized wave, right? 00:05:56.200 --> 00:05:58.150 OK, so that is actually the topic which 00:05:58.150 --> 00:06:01.510 I would like to talk about. 00:06:01.510 --> 00:06:05.700 So let's take a look at the diagram here. 00:06:05.700 --> 00:06:12.560 So assuming that I have a single layer of sheet, 00:06:12.560 --> 00:06:14.750 which I call wave plate. 00:06:14.750 --> 00:06:18.420 This is actually the zoom in and zoom in of that sheet. 00:06:18.420 --> 00:06:24.410 And the interesting property of this wave plate sheet 00:06:24.410 --> 00:06:31.280 is that the refraction index in the x direction 00:06:31.280 --> 00:06:35.930 and the refraction index for the linearly 00:06:35.930 --> 00:06:40.390 polarized wave in the y direction, they are different. 00:06:40.390 --> 00:06:41.360 That can happen, right? 00:06:41.360 --> 00:06:44.450 Because when we were discussing two-dimensional and 00:06:44.450 --> 00:06:49.490 three-dimensional waves, the dispersion relation 00:06:49.490 --> 00:06:53.930 can be dependent on the k vector, right? 00:06:53.930 --> 00:06:56.660 So that should not surprise you by now. 00:06:56.660 --> 00:07:02.390 And it depends on the structure of the material you 00:07:02.390 --> 00:07:04.940 use to make this wave plate. 00:07:04.940 --> 00:07:09.830 So therefore, you can have different velocity 00:07:09.830 --> 00:07:13.400 when you have an incident where pointing in the x direction, 00:07:13.400 --> 00:07:15.530 and compared to an incident where 00:07:15.530 --> 00:07:17.840 pointing in the y direction. 00:07:17.840 --> 00:07:21.390 So in short, we can actually summarize 00:07:21.390 --> 00:07:24.760 this kind of information, the dispersion relation, 00:07:24.760 --> 00:07:25.840 into two components. 00:07:25.840 --> 00:07:29.460 One is the velocity, the phase velocity in the x direction, 00:07:29.460 --> 00:07:32.270 which is denoted as nx. 00:07:32.270 --> 00:07:35.810 Just a reminder, the speed of the light 00:07:35.810 --> 00:07:39.260 will be equal to c divided by nx, right? 00:07:39.260 --> 00:07:45.230 So larger n means smaller speed of light in material. 00:07:45.230 --> 00:07:50.060 And if that happens, if nx is different from ny, what 00:07:50.060 --> 00:07:56.570 is going to happen is that if you have an incident wave, when 00:07:56.570 --> 00:08:00.440 it passes through this wave plate, what is going to happen 00:08:00.440 --> 00:08:04.070 is that the x component, the delay in phase 00:08:04.070 --> 00:08:07.910 in the x component, would be different from the delay 00:08:07.910 --> 00:08:11.480 in phase in the y component. 00:08:11.480 --> 00:08:14.210 And that is, essentially, how we can actually 00:08:14.210 --> 00:08:16.990 make use of that to create elliptically 00:08:16.990 --> 00:08:21.410 polarized wave or circularly polarized wave, OK? 00:08:21.410 --> 00:08:23.970 So let's take a look at this example together. 00:08:23.970 --> 00:08:29.840 So suppose I have incident light with angular frequency omega, 00:08:29.840 --> 00:08:30.830 OK? 00:08:30.830 --> 00:08:34.880 Since I give you already the omega, what I really need 00:08:34.880 --> 00:08:38.030 is the speed of light, then I can calculate the resulting 00:08:38.030 --> 00:08:40.250 wave number and wave lengths. 00:08:40.250 --> 00:08:44.570 So this is actually the incident wave angular frequency. 00:08:44.570 --> 00:08:49.970 And the lens of the-- or say the thickness of the wave plate 00:08:49.970 --> 00:08:52.070 is called little l. 00:08:52.070 --> 00:08:54.860 And we can actually check immediately 00:08:54.860 --> 00:08:57.380 what would be the corresponding wave 00:08:57.380 --> 00:09:04.580 number in the median for the linearly polarized wave 00:09:04.580 --> 00:09:07.640 in the x direction and linearly polarized wave in the y 00:09:07.640 --> 00:09:08.460 direction. 00:09:08.460 --> 00:09:10.770 So we can actually calculate Kx will 00:09:10.770 --> 00:09:15.965 be equal to nx over c omega, because this is actually 00:09:15.965 --> 00:09:18.800 just omega divided by v, which is 00:09:18.800 --> 00:09:24.950 the phase velocity in the median for waves in the x direction. 00:09:24.950 --> 00:09:29.080 And that would be equal to 2 pi over lambda x. 00:09:29.080 --> 00:09:32.180 Similarly, you can also conclude that Ky 00:09:32.180 --> 00:09:37.260 can be written as ny divided by c times omega, 00:09:37.260 --> 00:09:39.783 which is 2 pi over lambda u. 00:09:39.783 --> 00:09:45.050 Kx and Ky are the wave numbers inside 00:09:45.050 --> 00:09:50.510 for the progressing harmonic waves inside the median, OK? 00:09:50.510 --> 00:09:51.700 One is in the x direction. 00:09:51.700 --> 00:09:54.290 The other one's in the y direction. 00:09:54.290 --> 00:09:58.140 So if we keep those in mind, you will see that, 00:09:58.140 --> 00:10:04.820 huh, if I have different nx and ny, when the same frequency 00:10:04.820 --> 00:10:10.010 light goes through this median, its x component 00:10:10.010 --> 00:10:13.650 will travel through different amount of period, 00:10:13.650 --> 00:10:17.150 where is a different amount of phase difference. 00:10:17.150 --> 00:10:20.180 Compared to the light polarized-- 00:10:20.180 --> 00:10:24.000 compared to the component in the y direction, 00:10:24.000 --> 00:10:26.210 as you can see from this demonstration. 00:10:26.210 --> 00:10:29.240 Therefore, we can actually conclude 00:10:29.240 --> 00:10:31.730 that there must be a phase difference 00:10:31.730 --> 00:10:33.860 between the x component and y component. 00:10:33.860 --> 00:10:35.570 And we can calculate that-- 00:10:35.570 --> 00:10:38.390 this is actually delta phi, the phase difference 00:10:38.390 --> 00:10:42.740 between the x direction and y direction will be equal to 2 pi 00:10:42.740 --> 00:10:46.070 times l divided by lambda x. 00:10:46.070 --> 00:10:50.680 So basically, it's the number of waves times 2 pi. 00:10:50.680 --> 00:10:54.770 l over lambda x is number of periods past. 00:10:54.770 --> 00:11:00.110 And the times 2 pi translates that to phase. 00:11:00.110 --> 00:11:02.840 And we are taking the difference between the x 00:11:02.840 --> 00:11:05.090 and the y direction. 00:11:05.090 --> 00:11:09.480 And we can conclude that based on what we have written here. 00:11:09.480 --> 00:11:12.920 As you see that this is just nx minus ny 00:11:12.920 --> 00:11:19.380 divided by c times omega times l, OK? 00:11:19.380 --> 00:11:23.790 So this is actually how the wave plate works. 00:11:23.790 --> 00:11:29.320 Suppose I have a linearly polarizer 00:11:29.320 --> 00:11:32.580 wave coming into this plate. 00:11:32.580 --> 00:11:37.080 And the direction of the polarization 00:11:37.080 --> 00:11:39.050 is not in the x direction or y direction. 00:11:39.050 --> 00:11:41.140 So they are positioned-- 00:11:41.140 --> 00:11:44.820 they are components in the x direction and y direction. 00:11:44.820 --> 00:11:50.100 For example, I can have an incoming polarizer like this. 00:11:50.100 --> 00:11:52.400 And this is actually the x direction. 00:11:52.400 --> 00:11:54.290 This is actually the y direction. 00:11:54.290 --> 00:11:59.580 And I can now decompose this kind of linearly polarized wave 00:11:59.580 --> 00:12:00.900 into two components. 00:12:00.900 --> 00:12:07.160 And after this wave passes through the wave plate, 00:12:07.160 --> 00:12:10.200 x component will be-- 00:12:10.200 --> 00:12:13.210 the phase difference between x and y 00:12:13.210 --> 00:12:16.320 will be increased by delta phi. 00:12:16.320 --> 00:12:19.320 So if originally there were no phase difference 00:12:19.320 --> 00:12:22.410 because this is actually a linearly polarized wave, 00:12:22.410 --> 00:12:24.990 and after it passes through the wave plate, 00:12:24.990 --> 00:12:26.220 it will be increased. 00:12:26.220 --> 00:12:28.500 And then the phase difference between x and y 00:12:28.500 --> 00:12:31.560 will be delta phi. 00:12:31.560 --> 00:12:35.420 All right, so that's really nice tour. 00:12:35.420 --> 00:12:39.120 And the so-called quarter wave plate 00:12:39.120 --> 00:12:45.450 is a device which we intentionally set the delta phi 00:12:45.450 --> 00:12:48.090 to be pi over 2. 00:12:48.090 --> 00:12:49.580 Why is that interesting? 00:12:49.580 --> 00:12:52.140 That is because initially you have 00:12:52.140 --> 00:13:05.420 Ex equal to E0 cosine omega t minus Kz, 00:13:05.420 --> 00:13:10.230 and this is actually the y component. 00:13:10.230 --> 00:13:14.720 If initially you have this kind of incident wave, 00:13:14.720 --> 00:13:19.170 now it corresponds to a polarization 00:13:19.170 --> 00:13:25.189 which is actually 45 degree with respect to the x-axis. 00:13:25.189 --> 00:13:26.480 So this is actually the x-axis. 00:13:29.190 --> 00:13:31.000 And this is actually the y-axis. 00:13:33.540 --> 00:13:39.030 When I have this kind of linearly polarized wave pass 00:13:39.030 --> 00:13:43.680 through the quarter wave plate, what is going to happen? 00:13:43.680 --> 00:13:46.440 What is going to happen is that one of the components 00:13:46.440 --> 00:13:50.100 will be delayed by delta phi or pi over 2. 00:13:50.100 --> 00:13:54.360 That will make you a circularly polarized wave. 00:13:54.360 --> 00:13:58.030 Because that will become sine and cosine. 00:13:58.030 --> 00:14:02.510 Therefore, if you plot the locus of the electric field 00:14:02.510 --> 00:14:07.410 in two-dimensional xy plane, you will see a circle. 00:14:07.410 --> 00:14:10.740 So that is actually why we want are 00:14:10.740 --> 00:14:14.130 interested in a special setup which delta phi is 00:14:14.130 --> 00:14:17.460 equal to pi over 2, OK? 00:14:17.460 --> 00:14:20.550 So let me go through a few examples 00:14:20.550 --> 00:14:24.990 so that actually you get some feelings about what is actually 00:14:24.990 --> 00:14:27.780 a quarter wave plate. 00:14:27.780 --> 00:14:32.910 Usually, instead of drawing this complicated diagram, 00:14:32.910 --> 00:14:35.670 we actually simplify the presentation 00:14:35.670 --> 00:14:38.280 into a diagram like this. 00:14:38.280 --> 00:14:42.160 So basically, you have a fast axis, 00:14:42.160 --> 00:14:47.160 which is the axis with smaller phase shift. 00:14:47.160 --> 00:14:53.490 And you have slow axis, which is actually the axis with larger 00:14:53.490 --> 00:14:54.990 phase shift. 00:14:54.990 --> 00:14:58.670 So basically, we just reduce the whole complicated setup 00:14:58.670 --> 00:15:02.520 into a simple diagram like that. 00:15:02.520 --> 00:15:10.060 So suppose I have an incident wave which is actually linearly 00:15:10.060 --> 00:15:14.140 polarized in this direction. 00:15:14.140 --> 00:15:17.570 In this direction, which I can call it x direction. 00:15:17.570 --> 00:15:21.000 And this is actually y direction. 00:15:21.000 --> 00:15:26.190 And I have that pass through a quarter wave plate, 00:15:26.190 --> 00:15:30.350 where the fast axis is in the x direction, 00:15:30.350 --> 00:15:33.465 and there's a slow axis in the y direction. 00:15:36.080 --> 00:15:41.660 Can somebody tell me, what would be the resulting polarization 00:15:41.660 --> 00:15:45.620 after this electromagnetic wave passes through this quarter 00:15:45.620 --> 00:15:47.240 wave plate? 00:15:47.240 --> 00:15:49.550 Somebody want to try it? 00:15:49.550 --> 00:15:50.417 Yes. 00:15:50.417 --> 00:15:53.550 STUDENT: It would be polarized in the y direction. 00:15:53.550 --> 00:15:55.178 PROFESSOR: Polarized in what? 00:15:55.178 --> 00:15:58.507 STUDENT: In the y direction. 00:15:58.507 --> 00:15:59.090 PROFESSOR: No. 00:15:59.090 --> 00:16:04.390 Basically-- OK, maybe I didn't explain that clearly. 00:16:04.390 --> 00:16:10.810 So initially, in this example, all the electric field 00:16:10.810 --> 00:16:13.320 is in the x direction. 00:16:13.320 --> 00:16:17.140 Therefore, in the y direction, there's nothing there. 00:16:17.140 --> 00:16:20.252 So that's actually a linearly polarized wave. 00:16:20.252 --> 00:16:22.480 The direction in actually in the x direction. 00:16:22.480 --> 00:16:25.030 And this quarter wave plate is going 00:16:25.030 --> 00:16:31.900 to slow down the y component by a phase of pi over 2. 00:16:31.900 --> 00:16:34.831 So what would be the resulting polarization? 00:16:34.831 --> 00:16:35.330 Yes. 00:16:35.330 --> 00:16:39.160 STUDENT: Very similar to [INAUDIBLE].. 00:16:39.160 --> 00:16:40.450 PROFESSOR: Yes, that's right. 00:16:40.450 --> 00:16:44.780 So because we are dividing something which is zero. 00:16:44.780 --> 00:16:46.660 But zero is zero. 00:16:46.660 --> 00:16:49.730 So zero is zero is zero, right? 00:16:49.730 --> 00:16:54.060 So therefore, what you are going to get is this. 00:16:54.060 --> 00:16:57.100 It's still a linearly polarized wave, right? 00:16:57.100 --> 00:17:01.420 OK, doesn't surprise you after I explain to you more clearly. 00:17:01.420 --> 00:17:05.609 And then you can see that if you have this-- 00:17:05.609 --> 00:17:08.750 OK, now I change the situation. 00:17:08.750 --> 00:17:10.500 So this is the x direction. 00:17:10.500 --> 00:17:12.099 This is the y direction. 00:17:12.099 --> 00:17:14.230 And I have something which is 45 degrees. 00:17:17.450 --> 00:17:21.870 And I have that pass through the same setup. 00:17:21.870 --> 00:17:25.840 Slow axis is in the y direction and the fast axis 00:17:25.840 --> 00:17:27.980 is in the x direction. 00:17:27.980 --> 00:17:29.300 What will we get? 00:17:29.300 --> 00:17:32.000 What kind of polarized light will we 00:17:32.000 --> 00:17:38.240 get after it passed through this quarter wave plate? 00:17:38.240 --> 00:17:39.676 Somebody can help me? 00:17:39.676 --> 00:17:40.509 STUDENT: Circular. 00:17:40.509 --> 00:17:41.550 PROFESSOR: Circular, yes. 00:17:41.550 --> 00:17:42.660 Thank you very much. 00:17:42.660 --> 00:17:44.610 So that's actually exactly what I was 00:17:44.610 --> 00:17:46.470 talking about in the beginning. 00:17:46.470 --> 00:17:50.610 The y component will be delayed by pi over 2. 00:17:50.610 --> 00:17:55.230 Therefore, it would become a circularly polarized wave. 00:17:55.230 --> 00:17:59.520 How about I change this to 30 degrees? 00:17:59.520 --> 00:18:00.950 What is going to happen? 00:18:00.950 --> 00:18:02.024 STUDENT: [INAUDIBLE]. 00:18:02.024 --> 00:18:04.440 PROFESSOR: Yeah, it will be elliptically polarized, right? 00:18:04.440 --> 00:18:08.190 Because now the projection to a different component 00:18:08.190 --> 00:18:09.050 is different. 00:18:09.050 --> 00:18:12.870 So therefore, it would be elliptically polarized wave. 00:18:12.870 --> 00:18:13.680 Very good. 00:18:13.680 --> 00:18:15.900 It seems to me that most of you actually 00:18:15.900 --> 00:18:17.880 understand what we are doing. 00:18:17.880 --> 00:18:23.641 And now it's time to do some experiment to actually show you 00:18:23.641 --> 00:18:24.390 what we have done. 00:18:24.390 --> 00:18:25.147 Yes. 00:18:25.147 --> 00:18:26.772 STUDENT: It's a little more complicated 00:18:26.772 --> 00:18:29.123 than that because the slope the refraction 00:18:29.123 --> 00:18:42.050 is [INAUDIBLE] be much, much slower than the fast axis. 00:18:42.050 --> 00:18:43.925 PROFESSOR: Yeah. 00:18:43.925 --> 00:18:47.050 Yeah, that's right. 00:18:47.050 --> 00:18:48.570 You are absolutely right. 00:18:48.570 --> 00:18:51.150 So it depends on the delta phi, right? 00:18:51.150 --> 00:18:54.740 So if delta phi is not pi over 2, 00:18:54.740 --> 00:18:58.430 then it can be elliptically polarized. 00:18:58.430 --> 00:19:01.610 And in this setup, I say that this is actually a quarter wave 00:19:01.610 --> 00:19:03.800 plate, therefore, the delay is always 00:19:03.800 --> 00:19:05.570 delta phi equal to pi over 2. 00:19:05.570 --> 00:19:07.120 Yeah. 00:19:07.120 --> 00:19:09.410 So then-- thank you for that. 00:19:09.410 --> 00:19:11.480 This is what we have been discussing 00:19:11.480 --> 00:19:13.610 is always quarter wave plate. 00:19:13.610 --> 00:19:17.120 Therefore, the delta phi between the slow and fast axis 00:19:17.120 --> 00:19:18.800 is always pi over 2, OK? 00:19:18.800 --> 00:19:21.900 So that everybody is on the same page. 00:19:21.900 --> 00:19:22.568 Yes. 00:19:22.568 --> 00:19:24.480 STUDENT: How can you have a material 00:19:24.480 --> 00:19:28.310 that has a different refraction index for different directions? 00:19:28.310 --> 00:19:33.170 PROFESSOR: For example, we were talking about materials-- 00:19:33.170 --> 00:19:36.950 or say the two-dimensional discrete case, right? 00:19:36.950 --> 00:19:41.690 So we can have little mass arranged 00:19:41.690 --> 00:19:43.370 in the x and y direction. 00:19:43.370 --> 00:19:50.450 But the space between mass in the x direction and y direction 00:19:50.450 --> 00:19:53.690 are different, then you have a dispersion relation 00:19:53.690 --> 00:19:56.840 which is actually different for the harmonic 00:19:56.840 --> 00:19:59.780 wave in the x direction compared to y direction. 00:19:59.780 --> 00:20:01.440 And that's just some random example. 00:20:01.440 --> 00:20:04.700 And that can be achieved by engineering 00:20:04.700 --> 00:20:09.150 the material we will use for the wave plate, OK? 00:20:09.150 --> 00:20:10.580 Good question. 00:20:10.580 --> 00:20:12.460 All right, so we will go ahead and I'll 00:20:12.460 --> 00:20:15.440 show you some demonstration. 00:20:15.440 --> 00:20:17.360 We prepare. 00:20:17.360 --> 00:20:22.840 The first thing I have to do is to turn off the light 00:20:22.840 --> 00:20:24.630 to have some more excitement. 00:20:27.810 --> 00:20:31.050 I cannot even see where is my experiment now. 00:20:31.050 --> 00:20:33.060 Oh, right here, yeah. 00:20:33.060 --> 00:20:34.910 OK, woo. 00:20:34.910 --> 00:20:38.190 OK, so look at what we have here. 00:20:38.190 --> 00:20:41.820 This is a projector. 00:20:41.820 --> 00:20:44.095 So what is the polarization of that light? 00:20:44.095 --> 00:20:44.970 STUDENT: Unpolarized. 00:20:44.970 --> 00:20:46.190 PROFESSOR: Unpolarized. 00:20:46.190 --> 00:20:47.480 Yeah, very good. 00:20:47.480 --> 00:20:50.900 OK, I'm very happy to hear that. 00:20:50.900 --> 00:20:55.520 All right, so now I have the polarizer and I put it on it. 00:20:55.520 --> 00:20:58.184 What is the polarization of this light? 00:20:58.184 --> 00:21:01.490 STUDENT: [INAUDIBLE]. 00:21:01.490 --> 00:21:03.003 PROFESSOR: I couldn't hear you. 00:21:03.003 --> 00:21:04.160 STUDENT: It's linear. 00:21:04.160 --> 00:21:04.670 PROFESSOR: Linear, yeah. 00:21:04.670 --> 00:21:06.410 Linearly of-- don't be afraid. 00:21:06.410 --> 00:21:07.400 OK, you can say that. 00:21:07.400 --> 00:21:08.570 No, this is not linear. 00:21:08.570 --> 00:21:10.310 The edge is not linear, right? 00:21:10.310 --> 00:21:11.430 But it's OK. 00:21:11.430 --> 00:21:15.830 I'm talking about everything inside of this material. 00:21:15.830 --> 00:21:17.000 Very good. 00:21:17.000 --> 00:21:22.070 So now what I'm going to do is to put two polarizers 00:21:22.070 --> 00:21:24.380 on top of each other. 00:21:24.380 --> 00:21:29.960 And of course, I can rotate such that the polarizer, the easy 00:21:29.960 --> 00:21:33.170 axis is perpendicular to each other, OK? 00:21:33.170 --> 00:21:37.700 So you see that ha, I almost black most of that light. 00:21:37.700 --> 00:21:41.120 So the first thing which I have been doing 00:21:41.120 --> 00:21:46.820 is that I first turn this unpolarized light polarized. 00:21:46.820 --> 00:21:49.760 And it's actually oscillating in one direction. 00:21:49.760 --> 00:21:53.340 And I block it again with the second one. 00:21:53.340 --> 00:21:55.220 And then you see that it's black. 00:21:55.220 --> 00:21:57.900 It's consistent with what we expect. 00:21:57.900 --> 00:22:00.032 So we are happy. 00:22:00.032 --> 00:22:00.740 We are not happy? 00:22:00.740 --> 00:22:01.400 No? 00:22:01.400 --> 00:22:03.530 Yes, we are happy. 00:22:03.530 --> 00:22:08.100 All right, so remember the discussion we had before. 00:22:08.100 --> 00:22:15.440 So what I could do is to add a third one, a third polarizer. 00:22:15.440 --> 00:22:18.430 So I can have the first polarizer 00:22:18.430 --> 00:22:21.920 which actually makes the direction of the oscillation 00:22:21.920 --> 00:22:24.330 in this direction. 00:22:24.330 --> 00:22:28.760 Then I put a second polarizer, where the easy axis 00:22:28.760 --> 00:22:30.380 is in this direction. 00:22:30.380 --> 00:22:35.840 Then I actually-- I'm going to extract all the components 00:22:35.840 --> 00:22:37.950 which projected to this axis. 00:22:37.950 --> 00:22:44.270 Therefore, after passing the second polarizer, 00:22:44.270 --> 00:22:48.860 the oscillation of the wave will be in this direction. 00:22:48.860 --> 00:22:55.130 Therefore, aha, now I put the third polarizer on, 00:22:55.130 --> 00:23:00.050 you can see that in the middle, because it changed 00:23:00.050 --> 00:23:03.110 the direction of the polarization by 45 degrees 00:23:03.110 --> 00:23:06.610 already by this polarizer, therefore 00:23:06.610 --> 00:23:11.372 you can see that there's some residual light survived. 00:23:11.372 --> 00:23:12.830 And then you can actually calculate 00:23:12.830 --> 00:23:20.100 what will be the intensity of the light surviving these three 00:23:20.100 --> 00:23:21.020 polarizers. 00:23:21.020 --> 00:23:22.610 And you can see that the ones which 00:23:22.610 --> 00:23:29.450 didn't pass the second polarizer is actually completely blocked 00:23:29.450 --> 00:23:33.410 by the two polarizers, which their easy axes are 00:23:33.410 --> 00:23:35.880 perpendicular to each other. 00:23:35.880 --> 00:23:38.420 So now, the interesting thing is that now I 00:23:38.420 --> 00:23:41.360 have a quarter wave plate here. 00:23:41.360 --> 00:23:42.270 OK, it's here. 00:23:42.270 --> 00:23:44.010 Hope you can see it. 00:23:44.010 --> 00:23:48.220 And I'm going to insert this into this experiment 00:23:48.220 --> 00:23:50.830 and see what is going to happen. 00:23:50.830 --> 00:23:53.660 Look at what we have here. 00:23:53.660 --> 00:23:57.920 Oh, this is actually much brighter, right? 00:23:57.920 --> 00:24:01.860 So basically, this water-- 00:24:01.860 --> 00:24:04.690 this quarter wave plate-- sorry, it's not water-- 00:24:04.690 --> 00:24:07.320 quarter wave plate, OK? 00:24:07.320 --> 00:24:10.390 Quarter wave plate actually turned the polarized light 00:24:10.390 --> 00:24:14.170 into a circularly polarized light. 00:24:14.170 --> 00:24:20.100 And after this circularly polarized light 00:24:20.100 --> 00:24:25.180 continued and passed through the third polarizer, 00:24:25.180 --> 00:24:27.760 you can see that, huh, the light passed 00:24:27.760 --> 00:24:31.510 through this kind of combination is 00:24:31.510 --> 00:24:39.310 a lot more than this experiment which was three polarizers. 00:24:39.310 --> 00:24:41.320 And we can also calculate what would 00:24:41.320 --> 00:24:43.330 be the expected intensity. 00:24:43.330 --> 00:24:46.360 And the good news is that we are not going to calculate that 00:24:46.360 --> 00:24:48.820 now, but in your P set. 00:24:48.820 --> 00:24:52.840 So you will be able to show that, indeed, the intensity you 00:24:52.840 --> 00:24:57.690 expect with quarter wave plate will be higher than why you 00:24:57.690 --> 00:25:01.630 expect with three polarizers. 00:25:01.630 --> 00:25:03.650 So that's actually the first experiment 00:25:03.650 --> 00:25:04.700 I would like to show you. 00:25:07.460 --> 00:25:11.270 The second experiment is also very interesting. 00:25:11.270 --> 00:25:13.810 So I have here-- 00:25:13.810 --> 00:25:20.370 OK, first I need to see if I can turn on the light. 00:25:20.370 --> 00:25:22.890 I have to turn on this light. 00:25:22.890 --> 00:25:25.130 Very good. 00:25:25.130 --> 00:25:27.060 So look at this tube. 00:25:27.060 --> 00:25:33.140 This tube is made of water and sugar. 00:25:33.140 --> 00:25:35.440 So we all love sugar. 00:25:35.440 --> 00:25:39.980 And I love it too much, so I add too much into this tube. 00:25:39.980 --> 00:25:45.070 So it's actually oversaturated sugar water. 00:25:45.070 --> 00:25:50.270 And so there is sugar inside and there are some animal 00:25:50.270 --> 00:25:52.610 or whatever living inside. 00:25:52.610 --> 00:25:54.540 But we don't care. 00:25:54.540 --> 00:25:57.500 We are not studying biology. 00:25:57.500 --> 00:26:02.510 But what is actually interesting is that, OK, now I 00:26:02.510 --> 00:26:06.350 have a light source from the lamp inside emitting 00:26:06.350 --> 00:26:09.040 what kind of polarized light? 00:26:09.040 --> 00:26:10.310 Unpolarized light, right? 00:26:10.310 --> 00:26:15.590 And I have that pass through a polarizer, which is here. 00:26:15.590 --> 00:26:17.120 There's a polarizer here. 00:26:17.120 --> 00:26:19.400 And therefore, what I want to say 00:26:19.400 --> 00:26:26.720 is that the incident light into this tube is polarized. 00:26:26.720 --> 00:26:28.790 That's the first thing I want to say. 00:26:28.790 --> 00:26:32.090 The second thing I want to say is that, OK, 00:26:32.090 --> 00:26:36.880 a linearly polarized light, due to superposition principle, 00:26:36.880 --> 00:26:41.300 actually you can decompose that into two 00:26:41.300 --> 00:26:44.630 circularly polarized light. 00:26:44.630 --> 00:26:46.970 Both of them are actually rotating 00:26:46.970 --> 00:26:49.100 in different directions. 00:26:49.100 --> 00:26:50.540 You can actually work on the mass 00:26:50.540 --> 00:26:53.060 and you will see that, ha, indeed, it works. 00:26:53.060 --> 00:26:57.220 So our linearly polarized light you can always rewrite it 00:26:57.220 --> 00:27:00.010 as a superposition of two circularly 00:27:00.010 --> 00:27:04.810 polarized light, but rotating in different directions. 00:27:04.810 --> 00:27:07.400 The interesting thing is the material 00:27:07.400 --> 00:27:12.830 which we use in this demonstration is oversaturated 00:27:12.830 --> 00:27:13.910 sugar. 00:27:13.910 --> 00:27:19.610 And we know that the molecule for the sugar and those kind 00:27:19.610 --> 00:27:26.630 of material is asymmetric under mirror transformation. 00:27:26.630 --> 00:27:27.860 It's asymmetric. 00:27:27.860 --> 00:27:30.050 It's a chiral material. 00:27:30.050 --> 00:27:31.850 OK, chiral is actually just some name, 00:27:31.850 --> 00:27:33.470 but it doesn't mean anything to you. 00:27:33.470 --> 00:27:37.640 But what is actually interesting is that this material 00:27:37.640 --> 00:27:39.470 is asymmetric. 00:27:39.470 --> 00:27:41.750 If you have a mirror and this material 00:27:41.750 --> 00:27:45.390 is looking at the mirror, in the other side of the mirror, 00:27:45.390 --> 00:27:47.480 it looks different. 00:27:47.480 --> 00:27:52.150 It's like your hand, right? 00:27:52.150 --> 00:27:56.300 So in a mirror, it's asymmetric. 00:27:56.300 --> 00:27:59.960 So what is interesting is that due to this kind of structure 00:27:59.960 --> 00:28:04.860 in the material that the light passed through, 00:28:04.860 --> 00:28:09.530 the circularly polarized light, counterclockwise polarized 00:28:09.530 --> 00:28:13.070 light, will have different refractive index 00:28:13.070 --> 00:28:15.680 compared to clockwise. 00:28:15.680 --> 00:28:18.800 Clockwise and counterclockwise light 00:28:18.800 --> 00:28:21.860 will have different refractive index. 00:28:21.860 --> 00:28:29.420 Therefore, you see that now you can see some kind of rotation 00:28:29.420 --> 00:28:32.840 or some kind of change in the polarization 00:28:32.840 --> 00:28:36.830 as a function of distance the light travels through. 00:28:36.830 --> 00:28:39.320 So basically, this material would 00:28:39.320 --> 00:28:42.530 rotate the linearly polarized light, 00:28:42.530 --> 00:28:46.280 because the refractive index for the clockwise and 00:28:46.280 --> 00:28:49.920 counterclockwise are different. 00:28:49.920 --> 00:28:51.830 So if you accept that, I would like 00:28:51.830 --> 00:28:54.200 to add another complication. 00:28:54.200 --> 00:28:58.520 In addition to that, the refractive index 00:28:58.520 --> 00:29:04.250 also depends on the frequency of the incident light. 00:29:04.250 --> 00:29:09.020 Therefore, you will have different amount of rotation 00:29:09.020 --> 00:29:11.330 for different color. 00:29:11.330 --> 00:29:13.760 So therefore, you can see that once I 00:29:13.760 --> 00:29:16.670 have incident light which is linearly polarized, 00:29:16.670 --> 00:29:19.370 all the colors are lined up. 00:29:19.370 --> 00:29:21.410 You can see that here. 00:29:21.410 --> 00:29:24.160 What is the color here? 00:29:24.160 --> 00:29:27.760 It's kind of bluish or white, essentially, right? 00:29:27.760 --> 00:29:32.030 But if you move slightly more, then it becomes pretty blue. 00:29:32.030 --> 00:29:35.800 And then if you move more, because of the dependence 00:29:35.800 --> 00:29:40.360 of the refractive index as a function of wavelength, 00:29:40.360 --> 00:29:42.790 therefore, you can see that this whole thing is actually 00:29:42.790 --> 00:29:44.260 changing color. 00:29:44.260 --> 00:29:48.700 And in the end, I have another polarizer which 00:29:48.700 --> 00:29:51.980 filter one of the directions. 00:29:51.980 --> 00:29:54.010 And I can change the direction, and you 00:29:54.010 --> 00:29:59.320 will see that I can filter out different colors. 00:29:59.320 --> 00:30:02.130 Which color do you like? 00:30:02.130 --> 00:30:02.990 Now it's red. 00:30:05.900 --> 00:30:09.770 And of course, I can rotate this polarizer, 00:30:09.770 --> 00:30:12.080 and I am sampling different color. 00:30:12.080 --> 00:30:16.070 Because at the time different color of light 00:30:16.070 --> 00:30:18.170 passes through this material, they 00:30:18.170 --> 00:30:21.650 are rotated by different amount of degree. 00:30:21.650 --> 00:30:25.370 Therefore, I can filter out and create all kinds 00:30:25.370 --> 00:30:27.820 of different color on the wall. 00:30:27.820 --> 00:30:31.120 The other thing which is interesting which I can do 00:30:31.120 --> 00:30:36.200 is that I can now change that direction of the incident 00:30:36.200 --> 00:30:39.950 light, or the direction of the polarization of the incident 00:30:39.950 --> 00:30:41.960 light, by rotating this one. 00:30:44.720 --> 00:30:51.350 You can see that the whole tube is changing color, like why you 00:30:51.350 --> 00:30:54.190 see in the barber shop, right? 00:30:57.400 --> 00:31:02.700 OK, so maybe this is a fancy way to make that kind of tube. 00:31:02.700 --> 00:31:03.200 No? 00:31:03.200 --> 00:31:06.330 A physics barber shop. 00:31:06.330 --> 00:31:07.910 Maybe we should do that. 00:31:07.910 --> 00:31:10.335 OK, so I hope you enjoyed this demonstration. 00:31:10.335 --> 00:31:13.420 And we will take a five minute break to take questions. 00:31:13.420 --> 00:31:15.430 And the next topic we are going to talk about 00:31:15.430 --> 00:31:21.620 is how do we actually create electromagnetic wave at all. 00:31:21.620 --> 00:31:24.670 So let's come back in 15. 00:31:31.070 --> 00:31:35.030 OK, so I hope you can hear me. 00:31:35.030 --> 00:31:39.140 All right, so welcome back from the break. 00:31:39.140 --> 00:31:42.440 So we are going to talk about the second topic we would like 00:31:42.440 --> 00:31:45.150 to cover in the lecture today. 00:31:45.150 --> 00:31:48.640 The question we are asking is, how do we actually 00:31:48.640 --> 00:31:54.680 create electromagnetic waves and so-called radiation? 00:31:54.680 --> 00:31:59.300 So this is actually a picture from Hubble telescope. 00:31:59.300 --> 00:32:02.540 And you can see that light can travel 00:32:02.540 --> 00:32:07.280 through billions, or tens of billions, of light years 00:32:07.280 --> 00:32:09.260 and arrive at Earth. 00:32:09.260 --> 00:32:11.790 And you can actually measure them 00:32:11.790 --> 00:32:16.770 and see you what is actually going on in the past. 00:32:16.770 --> 00:32:20.300 And that means if you have a source 00:32:20.300 --> 00:32:22.890 and you have some kind of radiation, 00:32:22.890 --> 00:32:29.360 and this source is going to emit energy towards somewhere, which 00:32:29.360 --> 00:32:32.960 is actually really, really far away toward the edge 00:32:32.960 --> 00:32:34.730 of the universe. 00:32:34.730 --> 00:32:39.980 So that is actually what we call electromagnetic wave 00:32:39.980 --> 00:32:44.090 and radiation. 00:32:44.090 --> 00:32:47.290 But the what is actually requirement for that to happen? 00:32:47.290 --> 00:32:49.730 What is the requirement for us to be 00:32:49.730 --> 00:32:53.390 able to see the stars which are so far away? 00:32:53.390 --> 00:32:55.460 That's the question. 00:32:55.460 --> 00:33:00.670 So let me actually make a simple argument here. 00:33:00.670 --> 00:33:03.410 Suppose I have some kind of a light source. 00:33:03.410 --> 00:33:06.180 It's a source in the center. 00:33:06.180 --> 00:33:09.420 And we have learned about pointing vector, right? 00:33:09.420 --> 00:33:11.610 So what this actually pointing vector? 00:33:11.610 --> 00:33:13.800 It's not really the pointing vector, right? 00:33:13.800 --> 00:33:20.730 So it's rate of energy transfer per unit area. 00:33:20.730 --> 00:33:22.530 So it's kind of pointing, but it's 00:33:22.530 --> 00:33:27.660 pointing to the direction of the energy transfer. 00:33:27.660 --> 00:33:29.420 So this is a vector. 00:33:29.420 --> 00:33:32.280 And it's actually highly related to the direction 00:33:32.280 --> 00:33:36.220 of the electric field and the magnetic field. 00:33:36.220 --> 00:33:38.540 And now, if I-- 00:33:38.540 --> 00:33:42.690 since this is essentially the energy transfer per area, 00:33:42.690 --> 00:33:50.820 I can now capture the average pointing vector times area. 00:33:50.820 --> 00:33:55.820 And what is going to happen is that if I do this calculation 00:33:55.820 --> 00:33:56.760 at this surface-- 00:33:56.760 --> 00:34:02.740 this is actually a sphere which is covering this source. 00:34:02.740 --> 00:34:05.990 I can do this at sphere number 1. 00:34:05.990 --> 00:34:10.739 And I can actually also do that in the sphere number 2. 00:34:10.739 --> 00:34:13.949 Since there are absolutely no other source-- 00:34:13.949 --> 00:34:16.530 I'm assuming that there's only one source here. 00:34:16.530 --> 00:34:19.889 There's only one light source in the universe, 00:34:19.889 --> 00:34:21.870 which is kind of lonely. 00:34:21.870 --> 00:34:26.370 Apparently it's not my universe, but somebody else's problem. 00:34:26.370 --> 00:34:31.770 And then I will conclude that since there's nothing outside, 00:34:31.770 --> 00:34:36.880 I will conclude that S times A, if I evaluate that 00:34:36.880 --> 00:34:40.199 in the first surface, will be equal to S 00:34:40.199 --> 00:34:42.199 times A in the second surface. 00:34:42.199 --> 00:34:44.639 That's equal to power, OK? 00:34:44.639 --> 00:34:48.260 So that should not surprise anybody. 00:34:48.260 --> 00:34:51.440 So that means the pointing vector 00:34:51.440 --> 00:34:57.620 will be proportional to 1/A, which is the surface area. 00:34:57.620 --> 00:35:01.250 And that means, based on simple mathematics, that 00:35:01.250 --> 00:35:03.810 would be proportional to 1 over r 00:35:03.810 --> 00:35:10.760 squared for this constant power transfer to happen. 00:35:10.760 --> 00:35:13.640 So this means that there's a source. 00:35:13.640 --> 00:35:18.050 And if I integrate all the energy transfer 00:35:18.050 --> 00:35:20.270 from some kind of surface, it's going 00:35:20.270 --> 00:35:26.000 to be a constant, no matter what surface you are choosing. 00:35:26.000 --> 00:35:29.630 So that means if I look at the structure of the S 00:35:29.630 --> 00:35:32.300 vector, the pointing vector, we can 00:35:32.300 --> 00:35:36.010 conclude that at least the electric field 00:35:36.010 --> 00:35:41.610 and magnetic field has to be proportional to 1/r, 00:35:41.610 --> 00:35:44.600 which is the distance with respect to the source. 00:35:44.600 --> 00:35:49.790 Otherwise, it's going to be decaying faster, or reducing 00:35:49.790 --> 00:35:56.720 faster than 1/r, then the total power will approach zero 00:35:56.720 --> 00:35:58.760 when you increase r enough. 00:35:58.760 --> 00:36:01.910 Then that means if you have that happen, 00:36:01.910 --> 00:36:06.710 you will not see anything if you are far enough. 00:36:06.710 --> 00:36:10.390 So if that's actually the case, we 00:36:10.390 --> 00:36:16.670 can now come back and discuss two situations which 00:36:16.670 --> 00:36:18.980 we are very familiar with. 00:36:18.980 --> 00:36:22.070 For example, you can say, how about I 00:36:22.070 --> 00:36:23.420 have a stationary charge? 00:36:27.220 --> 00:36:28.710 So I can have a stationary charge 00:36:28.710 --> 00:36:30.330 and see what will happen. 00:36:30.330 --> 00:36:33.390 And apparently, if I have a charge here 00:36:33.390 --> 00:36:37.250 without actually moving it, it's going to emit-- 00:36:37.250 --> 00:36:42.750 basically, it is going to have an electric field around this. 00:36:42.750 --> 00:36:46.980 But electric field, based on what we learned from 8.02, 00:36:46.980 --> 00:36:54.690 is going to be 2 divided by 4 pi epsilon zero r squared r hat. 00:36:54.690 --> 00:36:59.090 It's going to be proportional to 1 over r squared. 00:36:59.090 --> 00:37:02.130 It's already not very good news, because it's proportional to 1 00:37:02.130 --> 00:37:03.330 over r squared. 00:37:03.330 --> 00:37:05.530 And it's hitted by this. 00:37:05.530 --> 00:37:07.365 The magnetic field is zero. 00:37:10.551 --> 00:37:14.360 If I have something times zero it's zero. 00:37:14.360 --> 00:37:16.650 Then there will be no energy transfer 00:37:16.650 --> 00:37:20.970 if you have a stationary charge just sitting there. 00:37:20.970 --> 00:37:22.830 So apparently, this is not a good way 00:37:22.830 --> 00:37:27.320 to create electromagnetic wave, based on our argument. 00:37:27.320 --> 00:37:32.050 The pointing vector is actually equal to zero. 00:37:32.050 --> 00:37:34.940 So now you can say, OK, this is actually too boring, 00:37:34.940 --> 00:37:36.760 so let's introduce some excitement. 00:37:36.760 --> 00:37:42.780 How about we make this charge moving at a constant speed? 00:37:42.780 --> 00:37:44.380 What we can do is like this. 00:37:44.380 --> 00:37:47.950 Basically, if you have a positively charged particle, 00:37:47.950 --> 00:37:51.780 you can actually make it move at a constant speed, 00:37:51.780 --> 00:37:56.060 velocity equal to v. And what you are going to see is that, 00:37:56.060 --> 00:37:59.560 oh, indeed, there will be some changes in the electric field 00:37:59.560 --> 00:38:00.940 and the magnetic field. 00:38:00.940 --> 00:38:03.880 And I'm not going to go through the calculation 00:38:03.880 --> 00:38:05.590 of this kind of situation. 00:38:05.590 --> 00:38:07.390 And I will leave that as an exercise. 00:38:07.390 --> 00:38:11.230 But I would like to tell you what would be the conclusion. 00:38:11.230 --> 00:38:15.190 So if you have a single charge, which is essentially 00:38:15.190 --> 00:38:19.900 moving at a constant speed, and what is going to happen 00:38:19.900 --> 00:38:26.860 is that the electric field density, or the field line 00:38:26.860 --> 00:38:28.720 density will change. 00:38:28.720 --> 00:38:32.180 And you will be more concentrated in the direction, 00:38:32.180 --> 00:38:34.890 which is essentially perpendicular to the direction 00:38:34.890 --> 00:38:40.450 of the motion of this charge. 00:38:40.450 --> 00:38:42.830 And we can actually calculate what 00:38:42.830 --> 00:38:44.980 would be the electric field. 00:38:44.980 --> 00:38:52.360 The electric field will be equal to q divided by 4 pi epsilon0 r 00:38:52.360 --> 00:38:55.540 squared, 1 minus beta squared. 00:38:55.540 --> 00:38:57.580 I will define bet in a moment. 00:38:57.580 --> 00:39:00.870 1 minus beta squared sine squared 00:39:00.870 --> 00:39:07.270 theta 3/2 in the r direction. 00:39:07.270 --> 00:39:15.030 And where the beta is actually defined as u/c, which is u 00:39:15.030 --> 00:39:22.070 is actually the velocity of this little charge. 00:39:22.070 --> 00:39:24.740 And of course, you can also calculate 00:39:24.740 --> 00:39:27.710 what would be the corresponding B, right? 00:39:27.710 --> 00:39:33.445 The magnetic field will be actually equal to u plus E 00:39:33.445 --> 00:39:36.430 divided by c squared. 00:39:36.430 --> 00:39:39.080 And that is actually proportional to 1 00:39:39.080 --> 00:39:42.830 over r squared. 00:39:42.830 --> 00:39:46.100 As you can see from here, the bad news 00:39:46.100 --> 00:39:50.420 is that, OK, you indeed now have both electric field 00:39:50.420 --> 00:39:51.540 and the magnetic field. 00:39:51.540 --> 00:39:52.940 There is some improvement. 00:39:52.940 --> 00:39:57.497 But the problem is that the reduction 00:39:57.497 --> 00:39:59.330 of the electric field and the magnetic field 00:39:59.330 --> 00:40:00.970 is a function of distance. 00:40:00.970 --> 00:40:02.450 It's too large. 00:40:02.450 --> 00:40:06.920 Both of them are proportional to 1 over r squared, 00:40:06.920 --> 00:40:09.020 proportional to 1 over r squared. 00:40:09.020 --> 00:40:13.150 Therefore, the magnitude of S will be proportional 1 00:40:13.150 --> 00:40:16.510 over r to the fourth. 00:40:16.510 --> 00:40:20.140 So if you are far enough, you can 00:40:20.140 --> 00:40:26.200 conclude that the total power will approach zero, 00:40:26.200 --> 00:40:30.780 even if you integrate over the whole surface 00:40:30.780 --> 00:40:34.570 surrounding this moving charge. 00:40:34.570 --> 00:40:38.380 So apparently, that's actually not the solution 00:40:38.380 --> 00:40:42.600 we are seeking. 00:40:42.600 --> 00:40:45.060 Therefore, we have to do something 00:40:45.060 --> 00:40:50.230 more aggressive to accelerate the charge. 00:40:50.230 --> 00:40:53.810 So you can now have a charge moving at a constant speed. 00:40:53.810 --> 00:40:55.520 We see that it didn't do anything. 00:40:55.520 --> 00:40:59.890 Therefore, we have to make the velocity increase 00:40:59.890 --> 00:41:02.080 and see what'll happen. 00:41:02.080 --> 00:41:06.870 So what I am going to do now requires concentration. 00:41:06.870 --> 00:41:09.890 So I will hope that you don't take notes. 00:41:09.890 --> 00:41:14.920 Just follow me so that you get what I am trying to argue. 00:41:14.920 --> 00:41:18.190 And of course, if you are really good in mathematics, 00:41:18.190 --> 00:41:23.470 you can actually also go through page 356 to 360 00:41:23.470 --> 00:41:24.730 in George's book. 00:41:24.730 --> 00:41:27.180 There are some really mathematical deviations 00:41:27.180 --> 00:41:30.460 of the radiation from an accelerated charge. 00:41:33.100 --> 00:41:40.160 So let's try to see how can we actually understand 00:41:40.160 --> 00:41:42.560 an accelerated charge and what is actually 00:41:42.560 --> 00:41:47.150 the associated electromagnetic field. 00:41:47.150 --> 00:41:52.590 So my goal is to have some kind of acceleration. 00:41:52.590 --> 00:41:54.830 So I would like to set up the stage. 00:41:54.830 --> 00:41:58.210 So let's take a look at the slide here. 00:41:58.210 --> 00:42:01.970 At t equal to zero, time equal to zero, 00:42:01.970 --> 00:42:05.510 before I introduce any excitement, 00:42:05.510 --> 00:42:11.270 I have a charged particle initially at rest. 00:42:11.270 --> 00:42:13.890 And it's sitting there. 00:42:13.890 --> 00:42:17.360 What I'm going to do is that at some point, at t equal to zero, 00:42:17.360 --> 00:42:24.170 I try to accelerate this charge until t equal to delta t. 00:42:24.170 --> 00:42:30.770 The original position of that charged particle is at a. 00:42:30.770 --> 00:42:38.490 And I try to accelerate this charge by acceleration a. 00:42:38.490 --> 00:42:42.440 And that only happened in a very small amount of time, 00:42:42.440 --> 00:42:44.720 which is delta t. 00:42:44.720 --> 00:42:46.810 So what is going to happen is that this charge 00:42:46.810 --> 00:42:48.680 will get accelerated. 00:42:48.680 --> 00:42:52.640 And you can see that the velocity of the charge-- 00:42:52.640 --> 00:42:55.450 you can see velocity as a function of time here-- 00:42:55.450 --> 00:42:59.590 is increasing linearly in this period, and reaching 00:42:59.590 --> 00:43:04.030 maxima, which is a delta t. 00:43:04.030 --> 00:43:08.350 So after that, I stop the acceleration. 00:43:08.350 --> 00:43:11.210 So originally, the charge is at rest. 00:43:11.210 --> 00:43:14.170 Then I accelerate it for some period of time. 00:43:14.170 --> 00:43:19.690 And I stop the acceleration at A prime, or t equal to delta t. 00:43:19.690 --> 00:43:23.840 And what is going to happen afterwards to the charge? 00:43:23.840 --> 00:43:25.210 Everybody is following? 00:43:25.210 --> 00:43:28.420 You will be moving at constant velocity. 00:43:28.420 --> 00:43:30.030 Very good. 00:43:30.030 --> 00:43:32.090 So that's actually what you see here. 00:43:32.090 --> 00:43:36.860 And the wave can actually-- this information can propagate 00:43:36.860 --> 00:43:38.290 as a function of time. 00:43:38.290 --> 00:43:40.600 So that's actually the whole setup, 00:43:40.600 --> 00:43:43.840 which I would like to discuss. 00:43:43.840 --> 00:43:46.930 Before that, I would like to bring your attention 00:43:46.930 --> 00:43:50.790 to the graph I was trying to draw here. 00:43:50.790 --> 00:43:52.290 So you can see that originally there 00:43:52.290 --> 00:43:57.560 is a line which is pointing up, like 45 degree with respect 00:43:57.560 --> 00:44:00.040 to this charge. 00:44:00.040 --> 00:44:04.360 So that's one of the field lines I was drawing here. 00:44:04.360 --> 00:44:08.380 That's actually the electric field line. 00:44:08.380 --> 00:44:12.970 And as you can see that as I manipulate this charged 00:44:12.970 --> 00:44:16.180 particle, this is a sphere-- 00:44:16.180 --> 00:44:18.300 or a circle I should-- 00:44:18.300 --> 00:44:23.500 on this slide, which is actually telling you 00:44:23.500 --> 00:44:28.930 where this information already propagated in the space. 00:44:28.930 --> 00:44:32.740 So for example, if I am sitting here 00:44:32.740 --> 00:44:35.122 in the position of my little mouse here. 00:44:35.122 --> 00:44:35.830 Can you see that? 00:44:35.830 --> 00:44:37.990 No, you cannot see it. 00:44:37.990 --> 00:44:46.060 If I'm sitting in the upper right corner of the slide, 00:44:46.060 --> 00:44:48.340 and I try to-- 00:44:48.340 --> 00:44:54.030 then the experiment starts and I move the charge, 00:44:54.030 --> 00:45:00.240 the observer at the upper right corner would not feel anything. 00:45:00.240 --> 00:45:05.070 Because it takes time for the field, or for the changes, 00:45:05.070 --> 00:45:11.430 or for the information to be sent from the position A 00:45:11.430 --> 00:45:17.580 to the observer, which are far away from the charged particle. 00:45:17.580 --> 00:45:21.060 And the surface which-- 00:45:21.060 --> 00:45:26.520 the surface is actually where the information has propagated. 00:45:26.520 --> 00:45:32.100 So this information that my charge is accelerated, 00:45:32.100 --> 00:45:34.740 this information has already propagated 00:45:34.740 --> 00:45:40.950 to a sphere, which is actually far away by c times delta t 00:45:40.950 --> 00:45:46.550 away from the center, which is the location 00:45:46.550 --> 00:45:47.820 of the charged particle. 00:45:47.820 --> 00:45:50.640 And you can see that as time goes on, 00:45:50.640 --> 00:45:56.290 this black circle is actually becoming larger and larger, 00:45:56.290 --> 00:45:58.070 which contains the information that, 00:45:58.070 --> 00:46:01.520 OK, I accelerated the charge. 00:46:01.520 --> 00:46:04.620 This is actually where you can see that out of this circle 00:46:04.620 --> 00:46:08.340 is as if the charge is stationary. 00:46:08.340 --> 00:46:11.380 So you can see the field line is still linear. 00:46:11.380 --> 00:46:16.280 And passing through this line, or say, this surface, 00:46:16.280 --> 00:46:18.640 the information is already propagated. 00:46:18.640 --> 00:46:22.840 If you standing inside this line, like for example, 00:46:22.840 --> 00:46:26.380 next to the question mark, if you are there, 00:46:26.380 --> 00:46:30.700 you feel, aha, now I observe the acceleration 00:46:30.700 --> 00:46:33.610 to the charged particle. 00:46:33.610 --> 00:46:39.940 Finally, if I go toward the charged particle even more, 00:46:39.940 --> 00:46:44.560 and I will see, aha, if I am now inside the green circle, 00:46:44.560 --> 00:46:46.660 I know that this charged particle already 00:46:46.660 --> 00:46:48.430 stopped the acceleration. 00:46:48.430 --> 00:46:50.920 It's now moving at constant speed. 00:46:50.920 --> 00:46:54.760 So that's the meaning of these two little circles. 00:46:54.760 --> 00:47:00.570 And now I am looking at the situation at time 00:47:00.570 --> 00:47:07.920 equal to t where the charge is at position B. 00:47:07.920 --> 00:47:12.550 And I should see something really interesting. 00:47:12.550 --> 00:47:17.400 As I mentioned before, if you have a constantly propagating 00:47:17.400 --> 00:47:24.830 charge, the field line is actually still 00:47:24.830 --> 00:47:29.500 a straight line, actually, right there in the equation. 00:47:29.500 --> 00:47:31.510 If you have a stationary charge, it's 00:47:31.510 --> 00:47:34.780 also a linear straight line. 00:47:34.780 --> 00:47:38.080 And you can see that you have two straight lines, 00:47:38.080 --> 00:47:44.850 but in between, there's a kink which connects these two lines. 00:47:44.850 --> 00:47:49.680 So between these two lines, basically this 00:47:49.680 --> 00:47:51.360 is actually what we have here. 00:47:51.360 --> 00:47:54.200 So we have the original particle. 00:47:54.200 --> 00:47:58.370 And this is actually where the particle have the field 00:47:58.370 --> 00:48:01.220 line as a moving charge. 00:48:01.220 --> 00:48:04.890 And there's another surface, which 00:48:04.890 --> 00:48:07.250 actually out of the surface, it's 00:48:07.250 --> 00:48:11.930 like there is no acceleration at all. 00:48:11.930 --> 00:48:15.320 The charge is still stationary at A. 00:48:15.320 --> 00:48:20.840 You can see that these two field lines are linear, 00:48:20.840 --> 00:48:25.020 and also essentially in the radial direction. 00:48:25.020 --> 00:48:28.220 But the excitement is that since the field line has 00:48:28.220 --> 00:48:34.760 to be continuous, the excitement is that I have successfully 00:48:34.760 --> 00:48:39.210 created a kink, which is actually propagating 00:48:39.210 --> 00:48:42.210 in the radial direction. 00:48:42.210 --> 00:48:48.390 And this kink is going to be our electromagnetic wave because it 00:48:48.390 --> 00:48:53.760 has a component which is perpendicular to the direction 00:48:53.760 --> 00:48:54.600 of propagation. 00:48:54.600 --> 00:48:56.670 Just a reminder, what is actually 00:48:56.670 --> 00:48:59.010 an electromagnetic field looks like, it 00:48:59.010 --> 00:49:01.350 looks like this, right? 00:49:01.350 --> 00:49:03.120 So basically, you have the electric field 00:49:03.120 --> 00:49:07.920 oscillating up and down in one of the directions, 00:49:07.920 --> 00:49:09.690 the polarization-- 00:49:09.690 --> 00:49:12.780 linearly polarized electromagnetic wave. 00:49:12.780 --> 00:49:15.000 And the whole wave is actually propagating 00:49:15.000 --> 00:49:17.010 toward the right-hand side of the board. 00:49:17.010 --> 00:49:20.490 And the electric field is in the perpendicular direction 00:49:20.490 --> 00:49:22.120 of the direction of propagation. 00:49:22.120 --> 00:49:26.550 And this kink is actually what we are looking for, OK? 00:49:26.550 --> 00:49:32.600 And that really becomes the electromagnetic wave 00:49:32.600 --> 00:49:37.130 right there from the point source. 00:49:37.130 --> 00:49:40.080 Any questions so far? 00:49:40.080 --> 00:49:42.090 Everybody's following? 00:49:42.090 --> 00:49:45.060 OK, so now, that's good. 00:49:45.060 --> 00:49:49.260 We have managed to create this situation. 00:49:49.260 --> 00:49:51.660 And I would like to be more concrete 00:49:51.660 --> 00:49:53.740 about several settings. 00:49:53.740 --> 00:49:57.630 The first one is actually we have a constant acceleration a, 00:49:57.630 --> 00:50:01.140 and this delta t is really small. 00:50:01.140 --> 00:50:05.000 Very small delta t, very small acceleration. 00:50:05.000 --> 00:50:11.700 Therefore, I would assume that u defined as delta t, 00:50:11.700 --> 00:50:15.450 the resulting velocity is much, much smaller 00:50:15.450 --> 00:50:17.700 than the speed of light. 00:50:17.700 --> 00:50:23.100 So that's actually the setup which I would like to use. 00:50:23.100 --> 00:50:26.280 Then the question now is, how do we actually 00:50:26.280 --> 00:50:29.490 evaluate what will be the magnitude 00:50:29.490 --> 00:50:33.750 of this so-called kink electric field? 00:50:33.750 --> 00:50:38.640 So for this, it's actually also pretty easy. 00:50:38.640 --> 00:50:43.770 So now I would like to copy the geometry which I have there. 00:50:43.770 --> 00:50:50.040 I am trying to draw a copy of that to my board here. 00:50:50.040 --> 00:50:55.140 So basically, originally the charge is stationary at A. 00:50:55.140 --> 00:51:02.580 And it's emitting an electric field, which is actually only 00:51:02.580 --> 00:51:05.520 in the radial direction. 00:51:05.520 --> 00:51:09.930 And it got accelerated by a really small time. 00:51:09.930 --> 00:51:12.720 I'm exaggerating in that figure, OK? 00:51:12.720 --> 00:51:18.210 So it got accelerated a really small amount of time. 00:51:18.210 --> 00:51:21.960 And after that, it reached a prime, 00:51:21.960 --> 00:51:25.580 which is the exaggerated version is actually probably there. 00:51:25.580 --> 00:51:31.110 And A and A prime is, in fact, very, very close to each other, 00:51:31.110 --> 00:51:35.040 because this is actually just a very, very small delta t. 00:51:35.040 --> 00:51:38.190 I can have delta t goes to zero. 00:51:38.190 --> 00:51:42.510 Then A and A prime would be very, very similar. 00:51:42.510 --> 00:51:49.130 And now I let the time go on, and now this 00:51:49.130 --> 00:51:55.650 charged particle is now at point B. It's moved to point B. 00:51:55.650 --> 00:51:59.670 And I can connect B to A and A prime. 00:51:59.670 --> 00:52:01.860 And I can actually conclude that, OK, 00:52:01.860 --> 00:52:06.160 since the resulting velocity of the charged particle 00:52:06.160 --> 00:52:11.100 up to a prime is actually equal to u, defined as a times delta 00:52:11.100 --> 00:52:17.490 t, and we are now at time equal to t. 00:52:17.490 --> 00:52:20.160 Therefore, the distance these charged 00:52:20.160 --> 00:52:24.090 particles pass through, or travel through, 00:52:24.090 --> 00:52:27.740 is actually u times t. 00:52:27.740 --> 00:52:29.100 Doesn't surprise you, right? 00:52:29.100 --> 00:52:30.550 So that's velocity times t. 00:52:33.630 --> 00:52:39.020 And also, we can actually calculate this lens. 00:52:39.020 --> 00:52:40.390 This lens is actually-- 00:52:40.390 --> 00:52:43.500 I call it this point D here, which 00:52:43.500 --> 00:52:46.570 is the intersection between the second surface 00:52:46.570 --> 00:52:49.350 and the original field line. 00:52:49.350 --> 00:52:54.430 And I call this one E, which is the intersection of the field 00:52:54.430 --> 00:53:00.310 line from the moving charge and the second surface. 00:53:00.310 --> 00:53:04.300 And finally, I also have the intersection, 00:53:04.300 --> 00:53:06.910 which I call it F, which is actually 00:53:06.910 --> 00:53:10.330 where the field line and the surface actually join, 00:53:10.330 --> 00:53:13.270 which is actually the information about the charge 00:53:13.270 --> 00:53:18.910 has moved is actually the surface, which 00:53:18.910 --> 00:53:22.900 within that surface, people know the charge is actually 00:53:22.900 --> 00:53:24.320 already moved. 00:53:24.320 --> 00:53:29.070 So once I have all these, I can now evaluate what will be at D 00:53:29.070 --> 00:53:33.970 and F. D and F are actually pretty straightforward as well, 00:53:33.970 --> 00:53:38.460 because all those surfaces are traveling at the speed of what? 00:53:38.460 --> 00:53:40.190 Light, right. 00:53:40.190 --> 00:53:44.230 So what is actually the delta t between these two surfaces? 00:53:44.230 --> 00:53:46.630 It's delta t, right? 00:53:46.630 --> 00:53:51.550 Because I actually stopped the acceleration at delta t, 00:53:51.550 --> 00:53:55.840 therefore, the distance between D point and F 00:53:55.840 --> 00:53:57.812 is actually just c times delta t. 00:54:01.260 --> 00:54:04.500 And of course, now I have this. 00:54:04.500 --> 00:54:11.160 I can connect E and D. And roughly, because a and a prime 00:54:11.160 --> 00:54:14.700 are very, very close to each other, 00:54:14.700 --> 00:54:22.290 and also t is very large, therefore the BE, this line, 00:54:22.290 --> 00:54:27.480 is roughly parallel to these AF line. 00:54:27.480 --> 00:54:32.760 So these two lines are actually roughly parallel to each other. 00:54:32.760 --> 00:54:35.370 Therefore, I can now evaluate what 00:54:35.370 --> 00:54:39.510 will be this line, D and E-- 00:54:39.510 --> 00:54:43.800 what would be the size of the distance between D and E. 00:54:43.800 --> 00:54:45.190 And that can be evaluated. 00:54:45.190 --> 00:54:49.920 And it's actually just u perpendicular times t-- 00:54:49.920 --> 00:54:55.410 perpendicular to the direction of the field. 00:54:55.410 --> 00:54:58.560 And I can copy that here. 00:54:58.560 --> 00:55:06.880 The distance between D and E is just u perpendicular times t. 00:55:06.880 --> 00:55:10.780 And of course, I can approximate that is actually just a line. 00:55:10.780 --> 00:55:13.930 And I have a theta angle which is actually DEF. 00:55:17.840 --> 00:55:23.960 So now I can actually try to use this information, 00:55:23.960 --> 00:55:28.010 this geometrical argument information, 00:55:28.010 --> 00:55:33.620 to figure out what will be the electric field, this kink. 00:55:33.620 --> 00:55:41.430 So now I can have the electric field, the same triangle here, 00:55:41.430 --> 00:55:43.850 this is angle theta. 00:55:43.850 --> 00:55:52.790 And this is the electric field parallel to the AF line. 00:55:52.790 --> 00:55:56.970 And I can have also E perp, which 00:55:56.970 --> 00:56:01.340 is actually the perpendicular to AF, this line. 00:56:01.340 --> 00:56:05.480 And the kink, E kink, is actually 00:56:05.480 --> 00:56:10.010 what we would like to figure out as well. 00:56:10.010 --> 00:56:14.210 And basically, this E kink is what we want to figure out. 00:56:14.210 --> 00:56:18.480 And the E has the following two components. 00:56:18.480 --> 00:56:20.060 One is the E parallel. 00:56:20.060 --> 00:56:22.070 The other one is the E perp, which 00:56:22.070 --> 00:56:25.940 is the perpendicular and the parallel components to the AF 00:56:25.940 --> 00:56:28.010 line. 00:56:28.010 --> 00:56:31.640 And we can already make use of the similarity of these two 00:56:31.640 --> 00:56:32.990 triangles, right? 00:56:32.990 --> 00:56:36.920 Basically, this field line is actually pure geometrical, 00:56:36.920 --> 00:56:38.870 therefore, I know what is actually 00:56:38.870 --> 00:56:41.600 theta from this geometrical argument. 00:56:41.600 --> 00:56:46.880 So what is actually theta, basically, you 00:56:46.880 --> 00:56:50.470 can get that from the information of c delta t. 00:56:50.470 --> 00:56:54.140 And then u perp times t. 00:56:54.140 --> 00:56:56.730 So therefore, I can conclude that the magnitude 00:56:56.730 --> 00:57:01.810 of E perp divided by magnitude of E parallel 00:57:01.810 --> 00:57:11.610 will be equal to u perp t divided by c delta t. 00:57:11.610 --> 00:57:15.110 And this E kink is like this. 00:57:15.110 --> 00:57:18.290 It actually has a direction. 00:57:18.290 --> 00:57:21.710 However, you can see that, wait a second, 00:57:21.710 --> 00:57:23.390 you have this ratio, right? 00:57:23.390 --> 00:57:28.430 But the E kink is actually pointing to this direction. 00:57:28.430 --> 00:57:33.980 And this ut is pointing up to upward direction. 00:57:33.980 --> 00:57:37.820 Therefore, if you take this ratio, 00:57:37.820 --> 00:57:41.360 the E kink will be pointing to the upper left direction. 00:57:41.360 --> 00:57:44.350 Therefore, you really need a minus sign here, right? 00:57:44.350 --> 00:57:49.370 Therefore, the E perp would be pointing downward. 00:57:49.370 --> 00:57:53.640 Therefore, that's actually how you get this minus sign there. 00:57:53.640 --> 00:57:56.210 From this pure geometrical argument, 00:57:56.210 --> 00:57:57.780 you can actually conclude what would 00:57:57.780 --> 00:58:01.980 be the ratio between E perp and the E parallel, which 00:58:01.980 --> 00:58:03.770 is actually equal to that. 00:58:03.770 --> 00:58:06.190 And I can write it down explicitly. 00:58:06.190 --> 00:58:11.276 Basically, that's going to be equal to a delta t times 00:58:11.276 --> 00:58:14.760 t divided by c delta t. 00:58:14.760 --> 00:58:21.350 Remember, u is equal to a times delta t. 00:58:21.350 --> 00:58:24.350 Therefore, I can now cancel delta t. 00:58:24.350 --> 00:58:29.145 Then basically, what I get is minus a perp t divided by c. 00:58:32.380 --> 00:58:34.730 And now this is actually equal to minus 00:58:34.730 --> 00:58:39.050 a perp r divided by c squared, where 00:58:39.050 --> 00:58:42.980 r is actually just c times t. 00:58:42.980 --> 00:58:46.640 r is actually the distance between the position 00:58:46.640 --> 00:58:56.220 you are evaluating this field and the origin, which is A, OK? 00:58:56.220 --> 00:58:58.770 So you can now conclude that-- based 00:58:58.770 --> 00:59:01.080 on this geometrical argument, you 00:59:01.080 --> 00:59:04.050 can conclude that E perp is highly related 00:59:04.050 --> 00:59:06.630 to the E parallel. 00:59:06.630 --> 00:59:11.400 The E perp is equal to minus a perp r divided 00:59:11.400 --> 00:59:16.462 by c squared E parallel. 00:59:16.462 --> 00:59:18.458 Any questions so far? 00:59:21.951 --> 00:59:22.949 Yes. 00:59:22.949 --> 00:59:24.960 STUDENT: How'd you get r real quick? 00:59:24.960 --> 00:59:27.710 PROFESSOR: R is actually-- yeah, so r is actually 00:59:27.710 --> 00:59:29.610 just c times t. 00:59:29.610 --> 00:59:36.028 So it's the whole distance is the r. 00:59:36.028 --> 00:59:37.020 Cool. 00:59:37.020 --> 00:59:41.590 All right, so you can see that right now all of those things 00:59:41.590 --> 00:59:44.620 are purely geometrical, right? 00:59:44.620 --> 00:59:46.200 So this is really no magic. 00:59:46.200 --> 00:59:48.790 And no even integration. 00:59:48.790 --> 00:59:52.720 So now we are going to do some integration. 00:59:52.720 --> 00:59:55.320 So now we are almost there. 00:59:55.320 --> 00:59:58.320 I would like to figure out what would be the E kink. 00:59:58.320 --> 01:00:02.760 And I am especially interested in E perp, 01:00:02.760 --> 01:00:05.070 because E perp is the direction which 01:00:05.070 --> 01:00:08.130 is actually perpendicular to the direction of propagation. 01:00:08.130 --> 01:00:09.210 It's really cool. 01:00:09.210 --> 01:00:11.820 So that's actually related to the magnitude 01:00:11.820 --> 01:00:14.490 of the electromagnetic field radiating. 01:00:14.490 --> 01:00:16.920 So I would like to know E perp, but I 01:00:16.920 --> 01:00:19.470 don't know what is E parallel. 01:00:19.470 --> 01:00:25.650 So what we could do is to use Gauss' law in this example. 01:00:25.650 --> 01:00:28.770 So now what I could do is that I can 01:00:28.770 --> 01:00:35.140 draw a pillbox, which is actually 01:00:35.140 --> 01:00:38.350 through the surface number 1. 01:00:38.350 --> 01:00:40.780 This is actually surface number 1. 01:00:40.780 --> 01:00:45.060 What I could do is I can draw a pillbox which is actually 01:00:45.060 --> 01:00:48.930 passing through the surface number 1. 01:00:48.930 --> 01:00:53.320 Out of surface number 1, we know the physics very well, 01:00:53.320 --> 01:00:55.860 which is actually the electric field 01:00:55.860 --> 01:00:59.310 of a single stationary charge. 01:00:59.310 --> 01:01:02.470 So therefore, I know what is actually the electric field 01:01:02.470 --> 01:01:02.970 outside. 01:01:08.550 --> 01:01:12.010 Which is actually pointing outward 01:01:12.010 --> 01:01:14.640 in the radial direction. 01:01:14.640 --> 01:01:18.870 And the E parallel is actually what we are stuck with. 01:01:18.870 --> 01:01:20.445 So we don't know what is actually 01:01:20.445 --> 01:01:23.060 the magnitude of E parallel. 01:01:23.060 --> 01:01:26.950 That's the electric field inside the surface number 1. 01:01:29.590 --> 01:01:32.250 Makes sense? 01:01:32.250 --> 01:01:36.660 So now we also have the component 01:01:36.660 --> 01:01:41.130 which is actually perpendicular to the direction 01:01:41.130 --> 01:01:42.330 of propagation. 01:01:42.330 --> 01:01:46.140 So this is actually the contribution of the E perp 01:01:46.140 --> 01:01:50.910 and the contribution of E perp, which they go from the side 01:01:50.910 --> 01:01:52.200 to the site. 01:01:52.200 --> 01:01:58.110 Go in from the side, go out from the side of this pillbox. 01:01:58.110 --> 01:02:00.720 So I can now immediately conclude 01:02:00.720 --> 01:02:07.650 that the total contribution of this surface integral 01:02:07.650 --> 01:02:10.750 will be equal to 0, because of Gauss' law. 01:02:10.750 --> 01:02:15.060 There's no charge in my pillbox. 01:02:15.060 --> 01:02:18.180 Therefore, all those things should cancel. 01:02:18.180 --> 01:02:23.720 Apparently, these will cancel, because side 01:02:23.720 --> 01:02:29.050 in, side out, the same magnitude, which is E perp. 01:02:29.050 --> 01:02:31.740 Therefore, that cancel is trivial. 01:02:31.740 --> 01:02:34.650 And the interesting thing is that we can also 01:02:34.650 --> 01:02:41.610 figure out that e parallel will have to be equal to E out. 01:02:45.060 --> 01:02:51.180 So that the sum of all the integral will be equal to 0, 01:02:51.180 --> 01:02:52.970 because of Gauss' law. 01:02:52.970 --> 01:02:55.650 That's actually a very big amount of information, 01:02:55.650 --> 01:03:01.560 because I know how to write down E out. 01:03:01.560 --> 01:03:06.210 So E parallel will be equal to E out. 01:03:06.210 --> 01:03:10.510 We learned from 8.02 this is actually just q divided 01:03:10.510 --> 01:03:14.605 by 4 pi epsilon0 r squared. 01:03:17.550 --> 01:03:19.110 Does that surprise you? 01:03:19.110 --> 01:03:22.920 Should not, right, because out of the surface, 01:03:22.920 --> 01:03:25.200 people think nothing actually really 01:03:25.200 --> 01:03:27.930 happened to the charged particle. 01:03:27.930 --> 01:03:31.500 So it's actually still stationary sitting there. 01:03:31.500 --> 01:03:34.590 So therefore, I have the information of E parallel, 01:03:34.590 --> 01:03:39.660 therefore, I can now conclude what would be the E perp. 01:03:39.660 --> 01:03:47.700 Now, E perp will be equal to minus q a perp divided by 4 pi 01:03:47.700 --> 01:03:52.710 epsilon0 c squared r, because this is actually 01:03:52.710 --> 01:03:55.980 just a perp minus a perp r divided 01:03:55.980 --> 01:04:00.010 by c squared times E parallel. 01:04:00.010 --> 01:04:02.740 Look at what we have achieved. 01:04:02.740 --> 01:04:04.430 Look at this. 01:04:04.430 --> 01:04:08.060 This is actually proportional to what? 01:04:08.060 --> 01:04:10.230 1/r, right? 01:04:10.230 --> 01:04:19.020 So that means the decaying speed of this E perp 01:04:19.020 --> 01:04:23.970 is really slow compared to the electric field 01:04:23.970 --> 01:04:25.890 from a stationary charge. 01:04:25.890 --> 01:04:27.930 So that's actually very encouraging. 01:04:27.930 --> 01:04:31.050 And of course, you can also write down 01:04:31.050 --> 01:04:36.210 what will be the resulting magnetic field. 01:04:36.210 --> 01:04:39.930 And it's going to be also proportional to 1/r. 01:04:39.930 --> 01:04:41.970 So what we can actually conclude is 01:04:41.970 --> 01:04:50.510 that the E rad is a function of direction of the-- 01:04:50.510 --> 01:04:54.450 evaluating this E radiated electric field is 01:04:54.450 --> 01:04:56.370 a function of t. 01:04:56.370 --> 01:04:58.830 And we can actually-- based on this exercise, 01:04:58.830 --> 01:05:02.640 this will be minus q. 01:05:02.640 --> 01:05:05.390 a is a vector, but now I only take 01:05:05.390 --> 01:05:08.300 the perpendicular direction. 01:05:08.300 --> 01:05:11.350 And this thing is actually evaluated 01:05:11.350 --> 01:05:22.570 at t minus r over c divided by 4 pi epsilon0 c squared r. 01:05:22.570 --> 01:05:24.190 Let's take a look at this formula 01:05:24.190 --> 01:05:27.880 closely together, since we have spent a lot of time 01:05:27.880 --> 01:05:29.500 trying to get this result. 01:05:29.500 --> 01:05:31.370 So look at this structure. 01:05:31.370 --> 01:05:35.230 So basically, the radiated energy 01:05:35.230 --> 01:05:40.000 has a minus sign in front of q and a perp, 01:05:40.000 --> 01:05:43.960 because the E kink is actually pointing 01:05:43.960 --> 01:05:45.580 in the opposite direction compared 01:05:45.580 --> 01:05:49.390 to the directional acceleration, as you can see from here. 01:05:49.390 --> 01:05:54.280 The E kink and the E perpendicular 01:05:54.280 --> 01:06:03.640 is pointing to the opposite direction of the acceleration. 01:06:03.640 --> 01:06:07.450 Therefore, we have this minus sign there. 01:06:07.450 --> 01:06:11.680 And only the perpendicular direction motion, acceleration, 01:06:11.680 --> 01:06:14.020 works. 01:06:14.020 --> 01:06:18.670 And there's this little component here, t minus r/c. 01:06:18.670 --> 01:06:20.510 This is actually-- now multiplying 01:06:20.510 --> 01:06:26.690 this factor is evaluated at the t equal to t minus r/c. 01:06:26.690 --> 01:06:28.900 It's evaluated at that time. 01:06:28.900 --> 01:06:34.160 So this is actually evaluated at retarded time. 01:06:34.160 --> 01:06:39.050 So that means I am really slow. 01:06:39.050 --> 01:06:41.150 I need to wait for the information 01:06:41.150 --> 01:06:46.910 to arrive my detector so that I know there are acceleration 01:06:46.910 --> 01:06:49.780 happening. 01:06:49.780 --> 01:06:53.750 Finally, I can now also conclude what 01:06:53.750 --> 01:06:56.060 will be the magnetic field. 01:06:56.060 --> 01:06:59.270 The magnetic field rad, as I mentioned, 01:06:59.270 --> 01:07:01.660 would be proportional to 1/r. 01:07:01.660 --> 01:07:06.610 And of course, I also give you the explicit formula 01:07:06.610 --> 01:07:10.330 in the lecture notes. 01:07:10.330 --> 01:07:14.980 And now we can actually conclude that s will be proportional 01:07:14.980 --> 01:07:17.350 to 1 over r squared. 01:07:17.350 --> 01:07:20.800 So that means I can now send energy 01:07:20.800 --> 01:07:25.600 to the edge of the universe, because of all this hard work 01:07:25.600 --> 01:07:28.000 we have been doing here. 01:07:28.000 --> 01:07:31.520 Any questions? 01:07:31.520 --> 01:07:34.760 All right, before the end of the lecture 01:07:34.760 --> 01:07:38.550 today, I'm going to show you an experiment here. 01:07:38.550 --> 01:07:41.840 So here I have an antenna, which you 01:07:41.840 --> 01:07:46.250 can have electron going back and forth, 01:07:46.250 --> 01:07:52.730 oscillating harmonically really, really fast like this. 01:07:52.730 --> 01:07:55.910 Therefore, there will be acceleration, because 01:07:55.910 --> 01:07:57.950 of this harmonic oscillation. 01:07:57.950 --> 01:07:59.952 And I'm going to turn off the light. 01:08:06.900 --> 01:08:10.620 Also probably hide the image. 01:08:10.620 --> 01:08:14.180 OK, this is good. 01:08:14.180 --> 01:08:21.500 But I have to be able to see the button. 01:08:21.500 --> 01:08:22.450 Can I see it? 01:08:22.450 --> 01:08:24.390 No. 01:08:24.390 --> 01:08:26.206 Oh, I'm in trouble. 01:08:26.206 --> 01:08:28.290 Ah, here. 01:08:28.290 --> 01:08:31.200 OK, here I have a receiver. 01:08:31.200 --> 01:08:35.100 It's also a metal rod. 01:08:35.100 --> 01:08:38.700 And I have a light bulb in between, 01:08:38.700 --> 01:08:43.830 which is actually trying to receive the information from-- 01:08:43.830 --> 01:08:47.340 or say that it receives the electromagnetic wave emitted 01:08:47.340 --> 01:08:49.290 from that source. 01:08:49.290 --> 01:08:51.930 Which you have electrons going back and forth 01:08:51.930 --> 01:08:53.399 in that direction. 01:08:53.399 --> 01:08:57.810 So now, first, I am trying to align 01:08:57.810 --> 01:09:01.649 my setup in this direction so that it's really-- 01:09:01.649 --> 01:09:04.972 what would be the polarization of an electromagnetic wave? 01:09:04.972 --> 01:09:08.689 The polarization is going to be in a horizontal direction. 01:09:08.689 --> 01:09:10.220 Yes, very good. 01:09:10.220 --> 01:09:14.670 Therefore, if I have this set up like this, 01:09:14.670 --> 01:09:17.120 it's actually perpendicular to the direction 01:09:17.120 --> 01:09:21.220 of the polarization, therefore, I see nothing here, 01:09:21.220 --> 01:09:24.350 It is also possible that the light bulb is actually broken, 01:09:24.350 --> 01:09:25.970 but let's see. 01:09:25.970 --> 01:09:30.250 So now what I'm going to do is to change the direction. 01:09:30.250 --> 01:09:31.279 You see that? 01:09:31.279 --> 01:09:35.180 I am moving also closer really carefully. 01:09:35.180 --> 01:09:37.160 Now you can see what happened. 01:09:37.160 --> 01:09:43.470 You can see that now I receive the signal from this machine. 01:09:43.470 --> 01:09:47.630 The emitted light is actually polarized 01:09:47.630 --> 01:09:49.430 in the horizontal direction. 01:09:49.430 --> 01:09:52.470 And now I have also the electron going back and forth, 01:09:52.470 --> 01:09:56.330 and that actually can light up the light bulb. 01:09:56.330 --> 01:09:58.926 Now, if I change the direction, you 01:09:58.926 --> 01:10:01.060 can see that this is actually gone. 01:10:04.850 --> 01:10:06.460 And I can do this again. 01:10:06.460 --> 01:10:09.410 And I can go farther away from the source. 01:10:09.410 --> 01:10:13.450 You can see that now the light is actually disappearing. 01:10:13.450 --> 01:10:14.320 Why? 01:10:14.320 --> 01:10:18.030 That is because you get the 1/r term. 01:10:18.030 --> 01:10:20.310 Therefore, it's actually disappearing. 01:10:20.310 --> 01:10:24.030 And if I move closer to the source, it's reappearing. 01:10:24.030 --> 01:10:29.550 So now I need an assistant to hold this thing for me. 01:10:29.550 --> 01:10:30.600 Who can volunteer? 01:10:30.600 --> 01:10:33.270 And I would like to rotate that. 01:10:33.270 --> 01:10:35.880 I can actually also rotate my setup. 01:10:35.880 --> 01:10:36.660 Can you help? 01:10:36.660 --> 01:10:37.550 Yes. 01:10:37.550 --> 01:10:39.710 OK, be careful. 01:10:39.710 --> 01:10:42.160 And I hope you can survive this. 01:10:44.710 --> 01:10:47.230 So now what am I going to do-- 01:10:47.230 --> 01:10:48.870 OK, so stay there. 01:10:48.870 --> 01:10:53.040 And what I'm going to do is I can rotate the whole setup, 01:10:53.040 --> 01:10:56.270 the same concept. 01:10:56.270 --> 01:10:59.690 If I rotate the setup, I have to be careful so that I am not 01:10:59.690 --> 01:11:01.670 touching this more. 01:11:01.670 --> 01:11:03.690 I want to survive. 01:11:03.690 --> 01:11:05.740 And you can see now what is actually 01:11:05.740 --> 01:11:07.000 the direction of the emission. 01:11:07.000 --> 01:11:09.590 It's actually in this direction, right? 01:11:09.590 --> 01:11:13.410 The direction of the polarization 01:11:13.410 --> 01:11:15.860 is in the back and forth direction. 01:11:15.860 --> 01:11:19.500 And you see that that the light bulb is actually turned off. 01:11:19.500 --> 01:11:23.060 And now I can turn it back on. 01:11:23.060 --> 01:11:24.900 And you see that it's still there. 01:11:24.900 --> 01:11:26.180 OK, thank you very much. 01:11:26.180 --> 01:11:27.050 You survived. 01:11:27.050 --> 01:11:29.030 Not everybody actually survives this. 01:11:29.030 --> 01:11:31.070 [LAUGHTER] 01:11:31.070 --> 01:11:35.780 So you can see it now I can move really close to this thing. 01:11:35.780 --> 01:11:37.920 And what is going to happen? 01:11:37.920 --> 01:11:40.490 The amount of energy will be too high, 01:11:40.490 --> 01:11:44.620 and probably this light bulb will explode or broken. 01:11:44.620 --> 01:11:46.126 Do you want to see that? 01:11:46.126 --> 01:11:47.100 STUDENT: [INAUDIBLE]. 01:11:47.100 --> 01:11:49.540 PROFESSOR: Oh, my god. 01:11:49.540 --> 01:11:50.830 Let's see. 01:11:50.830 --> 01:11:52.288 Ooh, [INAUDIBLE]. 01:11:52.288 --> 01:11:54.760 [LAUGHTER] 01:11:54.760 --> 01:11:56.390 OK, very good. 01:11:56.390 --> 01:11:59.210 So now this experiment is dead. 01:11:59.210 --> 01:12:02.610 And then we can-- it's a very good time 01:12:02.610 --> 01:12:04.660 to close the lecture today. 01:12:04.660 --> 01:12:07.530 And thank you very much for attending the lecture today. 01:12:07.530 --> 01:12:14.130 And I hope now you understand how we actually create light. 01:12:14.130 --> 01:12:19.860 And enjoy the homework, because you 01:12:19.860 --> 01:12:27.270 will be able to figure out why the quarter wave plate 01:12:27.270 --> 01:12:31.500 combination will give you a higher light intensity. 01:12:31.500 --> 01:12:32.940 OK, so if you have any questions, 01:12:32.940 --> 01:12:35.460 I will be here and just standing up here. 01:12:42.732 --> 01:12:44.940 OK, hello everybody. 01:12:44.940 --> 01:12:50.760 Today I'm going to show you a demonstration, which actually 01:12:50.760 --> 01:12:56.370 demonstrates the effect of polarizer and quarter wave 01:12:56.370 --> 01:12:58.470 plate. 01:12:58.470 --> 01:12:59.850 Here is the setup. 01:12:59.850 --> 01:13:07.180 I have a projector here, which emits our polarizer light. 01:13:07.180 --> 01:13:13.810 And if I put a sheet of polarizer on top of it 01:13:13.810 --> 01:13:21.750 with easy axis in the vertical direction, 01:13:21.750 --> 01:13:23.630 like what my finger-- 01:13:23.630 --> 01:13:27.900 in the direction oscillation along the direction 01:13:27.900 --> 01:13:29.600 of my finger, then basically, you 01:13:29.600 --> 01:13:34.710 will see that the intensity of the light is reduced. 01:13:34.710 --> 01:13:39.830 Because for the unpolarized light, 01:13:39.830 --> 01:13:41.340 light component which is actually 01:13:41.340 --> 01:13:46.170 oscillating along the easy axis can pass through the polarizer, 01:13:46.170 --> 01:13:48.600 but the component which is actually 01:13:48.600 --> 01:13:54.250 oscillating perpendicular to the easy axis, like this, 01:13:54.250 --> 01:13:56.190 is not going to pass the polarizer. 01:13:56.190 --> 01:14:00.340 Therefore, a large fraction of unpolarized light 01:14:00.340 --> 01:14:04.230 is actually filtered out, and you will see a reduction 01:14:04.230 --> 01:14:08.440 in the intensity on the screen. 01:14:08.440 --> 01:14:12.990 So what I'm going to do now is to place another polarizer 01:14:12.990 --> 01:14:16.290 on top of the first one. 01:14:16.290 --> 01:14:18.150 So now we have two sheets. 01:14:18.150 --> 01:14:25.290 And you can see that after adding the second sheet, 01:14:25.290 --> 01:14:28.550 you see some change in the intensity. 01:14:28.550 --> 01:14:32.630 But if I rotate this sheet so that now 01:14:32.630 --> 01:14:36.960 the easy axis of the first and the second sheet 01:14:36.960 --> 01:14:40.770 are perpendicular to each other, you can see on the screen 01:14:40.770 --> 01:14:47.520 that all the light which are emitted from the projector 01:14:47.520 --> 01:14:50.660 is actually filtered out. 01:14:50.660 --> 01:14:51.480 Why is that? 01:14:51.480 --> 01:14:56.870 That is because now the first sheet actually filters out 01:14:56.870 --> 01:15:02.310 all that light which is actually oscillating in the direction 01:15:02.310 --> 01:15:05.100 perpendicular to the easy axis. 01:15:05.100 --> 01:15:10.830 If I actually introduce another filter which has easy axis 01:15:10.830 --> 01:15:16.920 now perpendicular to the one from the first sheet, 01:15:16.920 --> 01:15:20.250 then I'm going to filter out both directions. 01:15:20.250 --> 01:15:23.786 Therefore, all the light are filtered out 01:15:23.786 --> 01:15:28.686 due to this putting perpendicular setup. 01:15:28.686 --> 01:15:33.420 Now, if I introduce a third sheet, 01:15:33.420 --> 01:15:36.990 insert that between the two existing sheets, 01:15:36.990 --> 01:15:39.180 but now I am trying to actually insert 01:15:39.180 --> 01:15:44.760 that such that the direction of the easy axis 01:15:44.760 --> 01:15:47.440 is actually 45 degrees with respect 01:15:47.440 --> 01:15:52.230 to the easy axis of the first sheet. 01:15:52.230 --> 01:15:57.180 According to our calculation in class, also in your homework, 01:15:57.180 --> 01:16:02.260 you should see some light which will pass through this setup. 01:16:02.260 --> 01:16:05.130 And let's take a look at the experimental result. 01:16:05.130 --> 01:16:11.070 You can see that, indeed, after you insert a third sheet, 01:16:11.070 --> 01:16:14.970 you see that now the easy axis is actually 01:16:14.970 --> 01:16:18.300 45 degrees with respect to the first sheet. 01:16:18.300 --> 01:16:25.410 And you do see the intensity of the light becomes larger, 01:16:25.410 --> 01:16:29.340 or you see a brighter light output passing 01:16:29.340 --> 01:16:33.250 through these three polarizers. 01:16:33.250 --> 01:16:39.450 And if I rotate it so that actually 01:16:39.450 --> 01:16:43.380 the easy axis of the second sheet is actually changing, 01:16:43.380 --> 01:16:45.700 you can see that it reached maxima 01:16:45.700 --> 01:16:48.360 at roughly 45 degrees, which is actually 01:16:48.360 --> 01:16:54.150 consistent with what we predicted from your homework. 01:16:54.150 --> 01:16:57.510 And then the other thing which you predicted from the homework 01:16:57.510 --> 01:17:03.230 is that if we insert a quarter wave plate between these two 01:17:03.230 --> 01:17:08.250 sheets, you are going to see a brighter light passing 01:17:08.250 --> 01:17:10.440 through this setup. 01:17:10.440 --> 01:17:12.170 So let's actually take a look at what 01:17:12.170 --> 01:17:15.330 will happen by inserting the quarter wave 01:17:15.330 --> 01:17:18.900 plate between these two sheets. 01:17:18.900 --> 01:17:22.230 And this is actually the result. You 01:17:22.230 --> 01:17:29.610 can see that, indeed, the intensity is higher 01:17:29.610 --> 01:17:35.030 compared to the three polarizer experiment. 01:17:35.030 --> 01:17:40.410 And also, the intensity actually reached maxima 01:17:40.410 --> 01:17:45.030 when the fast axis of the polarizer 01:17:45.030 --> 01:17:49.200 is 45 degrees with respect to the easy axis, 01:17:49.200 --> 01:17:51.850 as we predicted from your homework. 01:17:51.850 --> 01:17:55.720 And we can actually put both experimental results side 01:17:55.720 --> 01:17:56.910 by side. 01:17:56.910 --> 01:17:59.430 Indeed, the results from the-- 01:17:59.430 --> 01:18:02.170 so now I am inserting the polarizer also 01:18:02.170 --> 01:18:04.300 between the two sheets. 01:18:04.300 --> 01:18:08.620 And you can see that, indeed, the light passing 01:18:08.620 --> 01:18:12.160 through three polarizers, the intensity 01:18:12.160 --> 01:18:16.980 is actually lower than two polarizers and the one quarter 01:18:16.980 --> 01:18:18.109 wave plate setup. 01:18:25.100 --> 01:18:27.030 Hello, everybody. 01:18:27.030 --> 01:18:29.520 So today, we are going to show you a demonstration 01:18:29.520 --> 01:18:32.250 of dipole radiation. 01:18:32.250 --> 01:18:33.550 Here is the setup. 01:18:33.550 --> 01:18:38.480 So we have a radiator here with two antenna. 01:18:38.480 --> 01:18:41.720 And when I turn it down, there will be current 01:18:41.720 --> 01:18:46.940 going back and forth through these two antenna. 01:18:46.940 --> 01:18:49.070 And therefore, this setup is going 01:18:49.070 --> 01:18:55.610 to emit polarized electromagnetic wave. 01:18:55.610 --> 01:19:00.530 And we are able to detect those electromagnetic waves 01:19:00.530 --> 01:19:08.600 by using a detector here, which consists of two antenna and one 01:19:08.600 --> 01:19:09.590 light bulb here. 01:19:09.590 --> 01:19:18.180 When there are current on this antenna, 01:19:18.180 --> 01:19:21.230 you will see the light emitting from the light bulb. 01:19:21.230 --> 01:19:24.020 And the intensity of the light bulb 01:19:24.020 --> 01:19:26.510 actually can help us to understand 01:19:26.510 --> 01:19:32.510 the structure of the radiation from the dipole radiator. 01:19:32.510 --> 01:19:39.260 So what I am going to do now is to turn this setup on. 01:19:39.260 --> 01:19:43.640 You can see now, the setup is on and the light is on. 01:19:43.640 --> 01:19:49.170 And there will be current going back and forth 01:19:49.170 --> 01:19:52.340 through these two antenna. 01:19:52.340 --> 01:19:57.170 So since the oscillation of the charge will 01:19:57.170 --> 01:19:59.540 generate electromagnetic wave-- 01:19:59.540 --> 01:20:01.670 since the direction of oscillation 01:20:01.670 --> 01:20:06.140 is in the horizontal direction, therefore, the electric field 01:20:06.140 --> 01:20:08.300 of the electromagnetic wave is going 01:20:08.300 --> 01:20:11.550 to be in the horizontal direction. 01:20:11.550 --> 01:20:15.890 So this can be actually verified by using the detector here. 01:20:15.890 --> 01:20:19.610 When my detector-- the direction of the antenna 01:20:19.610 --> 01:20:24.250 is actually perpendicular to the direction of the oscillation, 01:20:24.250 --> 01:20:27.140 you basically don't see any light emitting 01:20:27.140 --> 01:20:29.060 from the light bulb. 01:20:29.060 --> 01:20:32.290 Now I'm going to rotate my detector. 01:20:32.290 --> 01:20:40.070 You can see that as we actually rotate so that the antenna is 01:20:40.070 --> 01:20:43.700 parallel to the direction of the oscillation, 01:20:43.700 --> 01:20:45.260 then you will see that, huh, we will 01:20:45.260 --> 01:20:50.270 see a large intensity of light emitted from the light bulb. 01:20:50.270 --> 01:20:53.680 But on the other hand, if we actually rotate such 01:20:53.680 --> 01:20:57.260 that the direction of the antenna 01:20:57.260 --> 01:21:00.440 is perpendicular to the direction of oscillation 01:21:00.440 --> 01:21:03.020 of the charges, then you will not 01:21:03.020 --> 01:21:07.460 see any light emitted from the light bulb. 01:21:07.460 --> 01:21:10.640 This can also be demonstrated from on the other side 01:21:10.640 --> 01:21:12.150 of the experiment. 01:21:12.150 --> 01:21:15.640 So now, instead of standing in front of the setup, 01:21:15.640 --> 01:21:22.660 I'm going to go to the side of this dipole radiator. 01:21:22.660 --> 01:21:28.040 So here is actually roughly 90 degrees with respect 01:21:28.040 --> 01:21:30.010 to where I was standing. 01:21:30.010 --> 01:21:32.180 And you can see that no matter which angle-- 01:21:35.375 --> 01:21:42.575 no matter which angle of my detector is in, basically, 01:21:42.575 --> 01:21:48.810 you will never see light emitted from the light bulb. 01:21:48.810 --> 01:21:53.230 That is because the direction of the oscillation 01:21:53.230 --> 01:21:54.910 is in this direction. 01:21:54.910 --> 01:21:58.390 And according to our formula, our prediction 01:21:58.390 --> 01:22:04.420 is that there will be no electromagnetic wave traveling 01:22:04.420 --> 01:22:06.870 in this direction. 01:22:06.870 --> 01:22:10.630 And therefore, no matter which angle you are actually 01:22:10.630 --> 01:22:14.380 trying to detect the emitted light, 01:22:14.380 --> 01:22:18.970 the light bulb will never light up. 01:22:18.970 --> 01:22:22.690 So that's essentially consistent with our declaration. 01:22:22.690 --> 01:22:26.800 The second thing which I would like to actually show you 01:22:26.800 --> 01:22:31.720 is that we can also detect the nodal point 01:22:31.720 --> 01:22:36.470 of the emitted electromagnetic wave 01:22:36.470 --> 01:22:43.910 by moving this detector around in the classroom. 01:22:43.910 --> 01:22:51.640 For example, if now I move farther away from the dipole, 01:22:51.640 --> 01:22:56.530 now I am here and you can see that the intensity goes 01:22:56.530 --> 01:23:00.600 to zero at this point, because we are actually 01:23:00.600 --> 01:23:06.980 in one of the nodes of the electromagnetic radiation. 01:23:06.980 --> 01:23:11.080 And if I now move further away from the setup, 01:23:11.080 --> 01:23:17.090 you can see now the light is actually emitting again. 01:23:17.090 --> 01:23:20.210 And also, the intensity increases. 01:23:20.210 --> 01:23:26.935 And again, if I move farther and farther away from the setup, 01:23:26.935 --> 01:23:30.580 you can see that the light becomes dimmer and dimmer, 01:23:30.580 --> 01:23:32.370 and disappears again. 01:23:32.370 --> 01:23:35.840 Here is actually another node in the classroom. 01:23:35.840 --> 01:23:41.390 And also, you can see that as a function of distance, 01:23:41.390 --> 01:23:46.000 the maxima intensity emitted by the light bulb 01:23:46.000 --> 01:23:50.200 is also decreasing because of the larger and larger distance 01:23:50.200 --> 01:23:53.770 with respect to the source. 01:23:53.770 --> 01:23:57.760 So this demonstration actually shows 01:23:57.760 --> 01:24:01.750 that we can understand the dipole radiation. 01:24:01.750 --> 01:24:03.700 And the other experimental results 01:24:03.700 --> 01:24:05.870 are consistent with the calculation 01:24:05.870 --> 01:24:08.390 we have done in class.