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. 00:00:23.784 --> 00:00:24.450 YEN-JIE LEE: OK. 00:00:24.450 --> 00:00:29.010 So welcome back, everybody, to 8.03. 00:00:29.010 --> 00:00:31.200 So before we start the lecture today, 00:00:31.200 --> 00:00:34.710 we will give you, as usual, a short review on what we 00:00:34.710 --> 00:00:39.600 have learned, and also, an introduction about what we 00:00:39.600 --> 00:00:42.490 are going to learn today. 00:00:42.490 --> 00:00:45.410 So last lecture, we were discussing 00:00:45.410 --> 00:00:50.760 an interesting phenomenon, which is seeing film interference 00:00:50.760 --> 00:00:51.660 pattern. 00:00:51.660 --> 00:00:54.120 As you can see from this slide, we 00:00:54.120 --> 00:00:59.690 were wondering why the soap bubbles are colorful. 00:00:59.690 --> 00:01:02.160 And in the end of the class, we actually 00:01:02.160 --> 00:01:07.080 recognized that the reason why the soap bubbles are colorful 00:01:07.080 --> 00:01:10.130 is because of the interference phenomenon 00:01:10.130 --> 00:01:16.470 between the refracted light on the bubble. 00:01:16.470 --> 00:01:20.210 One puzzle path is that the light goes into the-- 00:01:20.210 --> 00:01:25.330 goes refracted directly from the surface of the soap film. 00:01:25.330 --> 00:01:29.250 The other possible optical path is 00:01:29.250 --> 00:01:34.290 to get refracted by the inner surface of the film. 00:01:34.290 --> 00:01:37.410 Therefore, the interference between these two paths 00:01:37.410 --> 00:01:44.390 actually created a colorful pattern on the bubble. 00:01:44.390 --> 00:01:51.790 So we also learned about how thick is the soap film. 00:01:51.790 --> 00:01:54.670 And I think just a quick reminder, actually, 00:01:54.670 --> 00:02:01.300 we concluded that in order to see a colorful pattern, 00:02:01.300 --> 00:02:05.020 the thickness of the wall or, say, the film, 00:02:05.020 --> 00:02:09.269 should be something like in the order of 100 nanometer. 00:02:09.269 --> 00:02:10.810 So that's actually pretty remarkable, 00:02:10.810 --> 00:02:14.970 because that's already in the order of the size of a virus. 00:02:14.970 --> 00:02:15.540 OK. 00:02:15.540 --> 00:02:19.120 OK that's actually pretty cool. 00:02:19.120 --> 00:02:22.210 So what are we going to do today? 00:02:22.210 --> 00:02:24.940 What we are going to do today is to continue the discussion 00:02:24.940 --> 00:02:28.300 that all kinds of different phenomenons, 00:02:28.300 --> 00:02:31.810 which can be explained by interference. 00:02:31.810 --> 00:02:36.580 We will learn interference phenomenon with a double slit 00:02:36.580 --> 00:02:42.820 experiment and using, for example, laser or water, 00:02:42.820 --> 00:02:46.040 and which I have a water tank here, 00:02:46.040 --> 00:02:48.740 which I will show you the interference pattern. 00:02:48.740 --> 00:02:51.820 And also, the second thing we are going to learn today 00:02:51.820 --> 00:02:58.650 is how does a phased radar actually works. 00:02:58.650 --> 00:02:59.520 OK? 00:02:59.520 --> 00:03:03.470 So by the end of the lecture today, you 00:03:03.470 --> 00:03:07.200 should be able to learn why we should construct 00:03:07.200 --> 00:03:13.420 the radar in the way and how to actually 00:03:13.420 --> 00:03:17.140 focus on the electromagnetic wave 00:03:17.140 --> 00:03:19.390 to work one specific direction. 00:03:19.390 --> 00:03:21.760 So that's essentially what we are going to learn today. 00:03:21.760 --> 00:03:24.130 The third goal is that we are going 00:03:24.130 --> 00:03:29.590 to make a connection to quantum mechanics from the lecture 00:03:29.590 --> 00:03:31.250 today. 00:03:31.250 --> 00:03:31.750 All right. 00:03:31.750 --> 00:03:34.570 So let's immediately get started. 00:03:34.570 --> 00:03:39.520 So before we start the discussion of a double slit 00:03:39.520 --> 00:03:42.580 experiment, I would like to remind everybody 00:03:42.580 --> 00:03:46.510 about Huygens' Principle, which you may already learned it 00:03:46.510 --> 00:03:49.970 from 8.02 or in the high school days. 00:03:49.970 --> 00:03:52.490 So what essentially is this principle? 00:03:52.490 --> 00:03:55.630 So this principle is saying that if I 00:03:55.630 --> 00:04:02.980 take a look at all the points in the wavefront, basically, 00:04:02.980 --> 00:04:08.080 you can treat all those points on the wavefront a point 00:04:08.080 --> 00:04:09.040 source. 00:04:09.040 --> 00:04:11.770 And this point source, essentially, a point source 00:04:11.770 --> 00:04:14.830 of a spherical wave. 00:04:14.830 --> 00:04:19.390 And it's immediate from all the points on the wavefront. 00:04:19.390 --> 00:04:23.130 So you can see from this slide, basically, 00:04:23.130 --> 00:04:28.240 if we choose to focus on the yellow point on the wavefront, 00:04:28.240 --> 00:04:30.670 you can see that from each yellow point, 00:04:30.670 --> 00:04:37.900 you can actually treat that as a spherical wave point source. 00:04:37.900 --> 00:04:41.500 And then what you actually need to do in order 00:04:41.500 --> 00:04:45.610 to calculate what would be the total electric field, 00:04:45.610 --> 00:04:49.240 for example, is to add up all those contribution 00:04:49.240 --> 00:04:50.590 from each point. 00:04:50.590 --> 00:04:53.610 And then you will be able to actually explain 00:04:53.610 --> 00:04:59.530 the interference pattern, which we see in the experiment. 00:04:59.530 --> 00:05:05.200 You may wonder where is this Huygens' Principle coming from? 00:05:05.200 --> 00:05:08.130 And although we are not going to derive that directly 00:05:08.130 --> 00:05:11.380 in the lecture today, but I can actually safely 00:05:11.380 --> 00:05:14.530 tell you that essentially, it can be derived 00:05:14.530 --> 00:05:16.290 from Maxwell's equation. 00:05:16.290 --> 00:05:16.870 OK? 00:05:16.870 --> 00:05:19.300 I will link some document, which actually 00:05:19.300 --> 00:05:23.060 shows the proof of the principle on the website 00:05:23.060 --> 00:05:25.870 and for your reference. 00:05:25.870 --> 00:05:29.450 The other thing which you may or you may not know 00:05:29.450 --> 00:05:38.050 is that we are really lucky so that we can use this Huygens' 00:05:38.050 --> 00:05:40.890 Principle in our universe. 00:05:40.890 --> 00:05:42.220 Why is that? 00:05:42.220 --> 00:05:45.280 Because if you look at the mathematical proof 00:05:45.280 --> 00:05:51.310 of this principle, it is because the number of dimension, number 00:05:51.310 --> 00:05:54.880 of spatial dimension is odd, which 00:05:54.880 --> 00:05:56.830 is three in our universe-- 00:05:56.830 --> 00:05:59.610 Or in my universe also is yours, OK, 00:05:59.610 --> 00:06:02.300 [LAUGHS] happened to be yours, as well-- 00:06:02.300 --> 00:06:06.280 such that the Huygens' principle actually works. 00:06:06.280 --> 00:06:11.680 On the other hand, if the number of dimension is even, 00:06:11.680 --> 00:06:13.720 there's no Huygens' principle, actually. 00:06:13.720 --> 00:06:15.700 So that's pretty interesting in that we 00:06:15.700 --> 00:06:19.780 are really lucky that it actually works in our universe. 00:06:19.780 --> 00:06:24.580 But I will not go into detail in 8.03. 00:06:24.580 --> 00:06:28.180 So let's get started with a concrete example, which 00:06:28.180 --> 00:06:31.630 we would like to further investigate to understand 00:06:31.630 --> 00:06:34.120 the interference phenomena. 00:06:34.120 --> 00:06:36.370 And those will prepare ourselves to the understanding 00:06:36.370 --> 00:06:40.000 of the design of the radar, for example. 00:06:40.000 --> 00:06:40.630 All right. 00:06:40.630 --> 00:06:44.440 So suppose I have experimental set 00:06:44.440 --> 00:06:50.350 up here which contain a wall where on the wall, 00:06:50.350 --> 00:06:55.450 there are two slit, A and a B. The upper one is A. The lower 00:06:55.450 --> 00:06:58.120 one is B, as designed here. 00:06:58.120 --> 00:07:04.570 And from the left inside there's an insert plane wave 00:07:04.570 --> 00:07:08.460 with a wavelength lambda, which is showing here. 00:07:08.460 --> 00:07:11.780 And this plane wave, plane electromagnetic wave, 00:07:11.780 --> 00:07:15.760 or can be water wave, et cetera, essentially 00:07:15.760 --> 00:07:20.020 approaching the wall with these two slits there. 00:07:20.020 --> 00:07:24.040 And we were wondering what would be the resulting 00:07:24.040 --> 00:07:26.750 pattern on the screen. 00:07:26.750 --> 00:07:30.250 This screen is actually pretty far away 00:07:30.250 --> 00:07:34.720 from the experimental setup, the wall on the left-hand side. 00:07:34.720 --> 00:07:37.030 How far is that? 00:07:37.030 --> 00:07:41.700 The distance between the screen, which shows the resulting 00:07:41.700 --> 00:07:46.710 interference pattern, and that the wall is actually defined. 00:07:46.710 --> 00:07:48.260 It's actually given here. 00:07:48.260 --> 00:07:51.720 It's actually called L, capital L. 00:07:51.720 --> 00:07:56.660 And in this experimental setup L essentially pretty, pretty 00:07:56.660 --> 00:08:01.960 large and is much, much larger than the d, where d, small d, 00:08:01.960 --> 00:08:05.180 is the distance between the two slits. 00:08:05.180 --> 00:08:06.700 OK? 00:08:06.700 --> 00:08:10.810 So our job now is to understand what will be-- 00:08:10.810 --> 00:08:13.660 and to predict what is going to be the interference 00:08:13.660 --> 00:08:19.390 pattern coming from the electromagnetic wave which 00:08:19.390 --> 00:08:23.170 pass through point A and point B, 00:08:23.170 --> 00:08:26.030 and what is going to happen over, say, 00:08:26.030 --> 00:08:29.790 what would be the result which we will observe on the screen. 00:08:29.790 --> 00:08:30.600 OK? 00:08:30.600 --> 00:08:32.100 So the first thing which we can do 00:08:32.100 --> 00:08:36.190 is that we can now assign observer, 00:08:36.190 --> 00:08:39.809 which is called P, one of the point of interest 00:08:39.809 --> 00:08:42.840 on the screen, which is located here. 00:08:42.840 --> 00:08:45.160 And then we can link or, say, the 00:08:45.160 --> 00:08:49.530 connect the point A, which is the location of the first slit 00:08:49.530 --> 00:08:53.310 and the location of the second slit, which 00:08:53.310 --> 00:08:58.260 is called B. We can link those points together by a line. 00:08:58.260 --> 00:09:03.550 And that is actually denoted by AP and the BP, these two lines. 00:09:03.550 --> 00:09:08.080 Since we are talking about L, which is essentially very, very 00:09:08.080 --> 00:09:12.270 large, assuming that the distance, the length 00:09:12.270 --> 00:09:15.250 scale of the distance between the wall and the screen 00:09:15.250 --> 00:09:17.650 is much, much larger than the length 00:09:17.650 --> 00:09:21.490 scale of the distance between the two slit, which is d. 00:09:21.490 --> 00:09:28.495 Therefore, I can safely assume that AP and the BP 00:09:28.495 --> 00:09:31.260 are almost parallel to each other. 00:09:31.260 --> 00:09:32.960 Right? 00:09:32.960 --> 00:09:38.620 And I can also try to express the location of the P point 00:09:38.620 --> 00:09:44.140 by using the angle between BP and the horizontal direction. 00:09:44.140 --> 00:09:45.160 OK? 00:09:45.160 --> 00:09:47.070 And the horizontal direction is actually 00:09:47.070 --> 00:09:49.330 showing there's a dash line here. 00:09:49.330 --> 00:09:52.300 And the angle between BP and the horizontal direction 00:09:52.300 --> 00:09:54.990 it's called theta here. 00:09:54.990 --> 00:09:55.660 OK. 00:09:55.660 --> 00:10:01.380 So since AP and the BP are almost parallel to each other, 00:10:01.380 --> 00:10:05.850 I can now calculate what would be the optical path length 00:10:05.850 --> 00:10:09.600 difference between AP and the BP. 00:10:09.600 --> 00:10:10.440 Right? 00:10:10.440 --> 00:10:13.590 So in order to actually calculate 00:10:13.590 --> 00:10:19.170 the phase difference between the electromagnetic wave coming 00:10:19.170 --> 00:10:25.320 from slit A compared to slit B, I need to calculate-- 00:10:25.320 --> 00:10:33.865 again, like what we did last time-- optical path length 00:10:33.865 --> 00:10:34.811 difference. 00:10:37.500 --> 00:10:38.000 OK? 00:10:38.000 --> 00:10:44.150 In this case, I can call the distance between A and P, rA. 00:10:44.150 --> 00:10:47.930 And then I can also call the distance between B 00:10:47.930 --> 00:10:50.570 and the P, rB. 00:10:50.570 --> 00:10:53.270 Then the optical path length difference 00:10:53.270 --> 00:10:57.405 is called rB minus rA. 00:10:57.405 --> 00:10:58.970 And then we can actually calculate 00:10:58.970 --> 00:11:04.400 that because we have already given you the angle between BP 00:11:04.400 --> 00:11:06.380 and the horizontal direction. 00:11:06.380 --> 00:11:08.900 And basically, we can safely conclude 00:11:08.900 --> 00:11:14.780 that the path length difference is actually this line here. 00:11:14.780 --> 00:11:17.900 Therefore, I can actually calculate and get 00:11:17.900 --> 00:11:19.780 the optical path length difference, 00:11:19.780 --> 00:11:25.850 the difference between rB and the rA to be d sine theta. 00:11:25.850 --> 00:11:27.310 OK? 00:11:27.310 --> 00:11:30.650 Once we have that, it's actually pretty straightforward 00:11:30.650 --> 00:11:33.666 to calculate what would be the phase difference. 00:11:37.560 --> 00:11:44.940 The phase difference between the field coming from slit A, which 00:11:44.940 --> 00:11:48.640 I will call it EA here, and the field 00:11:48.640 --> 00:11:55.790 coming from the slit B, which I will call it EB here. 00:11:55.790 --> 00:12:00.750 The phase difference, as you define a lot of time 00:12:00.750 --> 00:12:06.390 to be delta, delta can be calculated by the optical path 00:12:06.390 --> 00:12:10.460 length difference, d sin theta, divided 00:12:10.460 --> 00:12:16.170 by lambda, which essentially telling you how many period 00:12:16.170 --> 00:12:23.130 have passed when the light have to actually overcome this-- 00:12:23.130 --> 00:12:27.396 or say have to pass through this optical path length difference. 00:12:27.396 --> 00:12:28.770 And, of course, these things need 00:12:28.770 --> 00:12:32.930 to be modified by 2 pi in order to translate 00:12:32.930 --> 00:12:35.970 from a number of period to a phase difference. 00:12:35.970 --> 00:12:41.220 Therefore, you get the phase difference between AP and BP 00:12:41.220 --> 00:12:44.280 to be delta equal to d sine theta 00:12:44.280 --> 00:12:48.520 divided by lambda times 2 pi. 00:12:48.520 --> 00:12:49.020 OK. 00:12:49.020 --> 00:12:52.020 So you can see that all those calculations 00:12:52.020 --> 00:12:53.290 are pretty straightforward. 00:12:53.290 --> 00:12:57.885 Maybe you have already seen that before in an earlier class. 00:12:57.885 --> 00:13:01.110 But what I want to say is that it is actually 00:13:01.110 --> 00:13:04.560 because of Huygens' Principle, such 00:13:04.560 --> 00:13:09.000 that you can't expect something which will show up at point P, 00:13:09.000 --> 00:13:11.790 right? 00:13:11.790 --> 00:13:13.920 If you don't have Huygens' Principle 00:13:13.920 --> 00:13:15.690 what is going to happen? 00:13:15.690 --> 00:13:19.380 What is going to happen is that the light 00:13:19.380 --> 00:13:23.100 passing through this slit will just go straight. 00:13:23.100 --> 00:13:25.510 And they will never overlap each other. 00:13:25.510 --> 00:13:26.010 OK? 00:13:26.010 --> 00:13:33.920 So that's actually why, because of the Huygens' principle, 00:13:33.920 --> 00:13:38.820 all the points on the wavefront are treated as a point 00:13:38.820 --> 00:13:41.570 source of a spherical wave. 00:13:41.570 --> 00:13:42.090 OK? 00:13:42.090 --> 00:13:46.140 So that is essentially why you can expect that something will 00:13:46.140 --> 00:13:51.720 hit the P point, which is because, in this case, 00:13:51.720 --> 00:13:54.810 we have two points, two point source. 00:13:54.810 --> 00:14:00.420 And they are emitting spherical waves 00:14:00.420 --> 00:14:02.390 coming from these two points. 00:14:02.390 --> 00:14:02.970 OK? 00:14:02.970 --> 00:14:06.600 So it is really because of Huygens' Principle, which 00:14:06.600 --> 00:14:13.380 applies here, such that we can actually observe the phenomenon 00:14:13.380 --> 00:14:15.510 at the P. And now, we have managed 00:14:15.510 --> 00:14:17.550 to calculate the phase difference, 00:14:17.550 --> 00:14:20.670 which is delta, presented here. 00:14:20.670 --> 00:14:26.620 So what the next question is, what would be the intensity? 00:14:26.620 --> 00:14:32.200 Since we have already calculated the phase difference delta, 00:14:32.200 --> 00:14:35.720 what would be the intensity observed at P? 00:14:35.720 --> 00:14:40.370 So for that, we have already prepared ourselves 00:14:40.370 --> 00:14:42.580 from the last few lectures. 00:14:42.580 --> 00:14:44.320 So now, we can actually calculate 00:14:44.320 --> 00:14:47.610 what would be the total E. The total E will 00:14:47.610 --> 00:14:54.130 be equal to EA plus EB. 00:14:54.130 --> 00:14:57.350 And here, I'm going to use complex notation just 00:14:57.350 --> 00:14:59.010 for simplicity. 00:14:59.010 --> 00:15:01.940 And basically, you can rewrite EA 00:15:01.940 --> 00:15:14.650 and the EB as E0 exponential i omega t minus k times rA 00:15:14.650 --> 00:15:25.160 plus E0 exponential i omega t minus k rB. 00:15:25.160 --> 00:15:29.120 The first term is actually telling you the contribution 00:15:29.120 --> 00:15:34.610 from the first slit, slit A. And the second term is actually 00:15:34.610 --> 00:15:39.832 telling you the contribution coming from slit B. 00:15:39.832 --> 00:15:43.910 In this set up, I'm telling you that I have the plane 00:15:43.910 --> 00:15:48.080 wave coming from the left hand side of the experiment 00:15:48.080 --> 00:15:50.330 and actually hitting the wall. 00:15:50.330 --> 00:15:52.420 And you can see that from the drawing. 00:15:52.420 --> 00:15:57.525 Actually, the wavefront, essentially, 00:15:57.525 --> 00:16:02.450 actually telling you that the direction of the electric field 00:16:02.450 --> 00:16:08.960 is actually in the Z direction in my coordinate system shown 00:16:08.960 --> 00:16:09.980 on the board. 00:16:09.980 --> 00:16:14.180 So basically, the Z direction is actually pointing to you guys. 00:16:14.180 --> 00:16:18.020 And that means the electric field is actually 00:16:18.020 --> 00:16:20.120 oscillating in this direction. 00:16:20.120 --> 00:16:20.720 OK? 00:16:20.720 --> 00:16:24.140 So therefore, I have to be careful of those vectors. 00:16:24.140 --> 00:16:26.990 So therefore, I need to give it other direction. 00:16:26.990 --> 00:16:31.360 And in this case, it's actually the Z direction. 00:16:31.360 --> 00:16:34.280 And also, you can see that the amplitude is actually 00:16:34.280 --> 00:16:41.620 denoted by E0 because I always assuming that both slit have 00:16:41.620 --> 00:16:44.120 the same finite width. 00:16:44.120 --> 00:16:47.060 For the moment, ignore the width of the slit. 00:16:47.060 --> 00:16:49.740 And also, they are coming from the same plane wave. 00:16:49.740 --> 00:16:54.980 Therefore, the amplitude is all denoted by E0. 00:16:54.980 --> 00:16:55.820 OK? 00:16:55.820 --> 00:16:58.060 So now, I have the expression here. 00:16:58.060 --> 00:17:01.610 And I can now go ahead and simplify this expression 00:17:01.610 --> 00:17:04.020 and rewrite that in this form. 00:17:04.020 --> 00:17:06.190 So I can now extract the E0. 00:17:06.190 --> 00:17:09.349 And also, I extract the common factors here, 00:17:09.349 --> 00:17:15.950 which essentially the exponential i omega t 00:17:15.950 --> 00:17:19.235 and also, minus k rA. 00:17:19.235 --> 00:17:22.310 I can actually factorize some part 00:17:22.310 --> 00:17:25.220 of the exponential function out. 00:17:25.220 --> 00:17:27.869 So the choice I made is that I actually 00:17:27.869 --> 00:17:33.320 could factorize out exponential i omega t minus k times r. 00:17:33.320 --> 00:17:34.670 Basically, I take these out. 00:17:34.670 --> 00:17:41.900 And I get this term showing here, omega t minus k rA. 00:17:41.900 --> 00:17:43.860 I take this out. 00:17:43.860 --> 00:17:46.760 Then basically, what you are doing to get inside 00:17:46.760 --> 00:17:52.770 will be 1 plus exponential minus i delta, actually. 00:17:55.656 --> 00:17:57.100 times z. 00:17:57.100 --> 00:17:57.920 OK? 00:17:57.920 --> 00:17:59.240 Why is that delta? 00:17:59.240 --> 00:18:04.010 Because once you factorize out or take out exponential i omega 00:18:04.010 --> 00:18:07.310 t minus k rA, basically, you are left 00:18:07.310 --> 00:18:13.200 with something proportional to exponential i minus k 00:18:13.200 --> 00:18:15.600 rB minus rA, right? 00:18:15.600 --> 00:18:20.310 And that is actually the optical path length difference here. 00:18:20.310 --> 00:18:25.650 And also, of course, you can always rewrite lambda 00:18:25.650 --> 00:18:27.560 over 2 pi, right? 00:18:27.560 --> 00:18:34.800 Basically, you write this to be k times d times theta. 00:18:34.800 --> 00:18:35.300 Right? 00:18:35.300 --> 00:18:39.740 So therefore, you can actually immediately identify 00:18:39.740 --> 00:18:43.830 the second term is to essentially exponential 00:18:43.830 --> 00:18:45.670 minus i delta. 00:18:45.670 --> 00:18:47.270 OK? 00:18:47.270 --> 00:18:49.330 Any questions here? 00:18:49.330 --> 00:18:50.280 OK. 00:18:50.280 --> 00:18:54.810 Because d sine theta essentially is just rB minus rA, 00:18:54.810 --> 00:18:58.530 therefore, I safely replace that by delta here. 00:18:58.530 --> 00:18:59.361 OK? 00:18:59.361 --> 00:18:59.860 All right. 00:18:59.860 --> 00:19:02.430 So since everybody's on the same page, 00:19:02.430 --> 00:19:07.440 I can now, again, factorize out not only the omega t 00:19:07.440 --> 00:19:11.320 minus kA term, but I can actually 00:19:11.320 --> 00:19:14.960 do a trick to factorize out, also, exponential 00:19:14.960 --> 00:19:18.200 minus i delta divided by 2 out. 00:19:18.200 --> 00:19:19.830 And basically, what I'm going to get 00:19:19.830 --> 00:19:26.480 is exponential i delta over 2 plus exponential minus i delta 00:19:26.480 --> 00:19:29.910 over 2. 00:19:29.910 --> 00:19:33.360 This reason why I'm doing this is because, huh, now, 00:19:33.360 --> 00:19:36.180 I have this term identified. 00:19:36.180 --> 00:19:40.210 And this is actually just 2 times cosine delta 00:19:40.210 --> 00:19:41.210 divided by 2. 00:19:41.210 --> 00:19:43.860 All right? 00:19:43.860 --> 00:19:45.240 OK? 00:19:45.240 --> 00:19:50.320 So now, I'm really pretty close to the intensity. 00:19:50.320 --> 00:19:52.590 So what would be the intensity coming out 00:19:52.590 --> 00:19:55.200 of this electric field? 00:19:55.200 --> 00:20:00.090 That is actually going to be average intensity, 00:20:00.090 --> 00:20:03.450 as we discussed last time in the lecture. 00:20:03.450 --> 00:20:08.220 The average intensity is proportional to square 00:20:08.220 --> 00:20:09.740 of E vector. 00:20:09.740 --> 00:20:10.650 Right? 00:20:10.650 --> 00:20:12.810 In the complex notation, how do we 00:20:12.810 --> 00:20:17.940 evaluate the absolute value of E vector square? 00:20:17.940 --> 00:20:20.260 In the complex notation, basically, you 00:20:20.260 --> 00:20:28.530 get basically, E times E star, where E is actually 00:20:28.530 --> 00:20:33.790 the amplitude, which is the size of the E vector, the magnitude 00:20:33.790 --> 00:20:35.560 of the E vector. 00:20:35.560 --> 00:20:37.800 Then, basically, you will see that this 00:20:37.800 --> 00:20:45.035 will be proportional to cosine square delta divided by 2. 00:20:45.035 --> 00:20:46.510 Right? 00:20:46.510 --> 00:20:51.010 Because you can see that if I calculate EE star, 00:20:51.010 --> 00:20:56.380 then all the terms with related to exponential i something 00:20:56.380 --> 00:20:57.730 actually got cancelled. 00:20:57.730 --> 00:20:58.480 Right? 00:20:58.480 --> 00:21:01.470 So therefore, you can see the "aha" very, very quickly. 00:21:01.470 --> 00:21:04.180 We can show that the intensity will 00:21:04.180 --> 00:21:08.590 be proportional to cosine square delta divided by 2, 00:21:08.590 --> 00:21:12.280 where delta is the phase difference 00:21:12.280 --> 00:21:15.160 between the first path and the second path. 00:21:15.160 --> 00:21:16.090 OK? 00:21:16.090 --> 00:21:17.080 Any questions so far? 00:21:20.890 --> 00:21:22.580 OK. 00:21:22.580 --> 00:21:30.050 So we can see that the intensity essentially changing really 00:21:30.050 --> 00:21:34.266 rapidly as a function of delta. 00:21:34.266 --> 00:21:35.040 Right? 00:21:35.040 --> 00:21:41.210 So when I have a situation where delta is equal to 0-- 00:21:41.210 --> 00:21:47.420 let's actually stop here a bit and enjoy what we have 00:21:47.420 --> 00:21:48.800 as you learn from here. 00:21:48.800 --> 00:21:49.310 All right? 00:21:49.310 --> 00:21:53.310 So if you have delta equal to 0, what does that mean? 00:21:53.310 --> 00:21:56.630 That means there's no phase difference 00:21:56.630 --> 00:21:58.810 between the first and second electric field. 00:21:58.810 --> 00:22:02.580 Therefore, when you add them together-- 00:22:02.580 --> 00:22:06.050 just a reminder about the notation we were using before. 00:22:06.050 --> 00:22:10.130 So if you draw the vector in a complex frame, what 00:22:10.130 --> 00:22:13.790 you are doing is that you are actually adding EA 00:22:13.790 --> 00:22:20.180 and the EB together in the most efficient way, right? 00:22:20.180 --> 00:22:23.270 Because the delta is equal to 0, the phase differences 00:22:23.270 --> 00:22:24.470 is equal to 0. 00:22:24.470 --> 00:22:27.610 Therefore, you are actually adding them in a straight line. 00:22:27.610 --> 00:22:28.430 OK? 00:22:28.430 --> 00:22:32.400 So that actually will give you the maxima intensity. 00:22:32.400 --> 00:22:37.111 Because when delta is equal to 0, cosine 0 is 1. 00:22:37.111 --> 00:22:37.610 Right? 00:22:37.610 --> 00:22:42.210 Therefore, you are reaching the maxima in the intensity. 00:22:42.210 --> 00:22:45.940 So now, I can always increase my delta 00:22:45.940 --> 00:22:49.940 until a number which is actually pi. 00:22:49.940 --> 00:22:52.610 What is going to happen is that if I still 00:22:52.610 --> 00:22:56.870 use the notation which I was using for the complex frame, 00:22:56.870 --> 00:22:58.650 what it does this is that, huh. 00:22:58.650 --> 00:23:04.670 Now, I am actually completely cancel the electric field, 00:23:04.670 --> 00:23:08.670 because the phase difference now is pi, right? 00:23:08.670 --> 00:23:11.480 So therefore, in the complex frame, 00:23:11.480 --> 00:23:15.710 you are adding the two vectors in way such 00:23:15.710 --> 00:23:18.140 that they completely cancel each other. 00:23:18.140 --> 00:23:20.300 The magnitude of the two vectors are 00:23:20.300 --> 00:23:24.020 the same, as shown here, which is actually E0, right? 00:23:24.020 --> 00:23:27.440 Therefore, what you are going to get, as you expect, 00:23:27.440 --> 00:23:32.030 is going to be 0, because they completely cancel. 00:23:32.030 --> 00:23:32.880 OK? 00:23:32.880 --> 00:23:36.770 You can also see that from this formula we did right here. 00:23:36.770 --> 00:23:41.000 When delta is equal to pi, then essentially, cosine pi over 2. 00:23:41.000 --> 00:23:44.210 Then you get intensity equal to 0. 00:23:44.210 --> 00:23:44.990 OK? 00:23:44.990 --> 00:23:47.330 Everybody accept this? 00:23:47.330 --> 00:23:48.790 All right. 00:23:48.790 --> 00:23:53.380 Now, I can still continue and increase the delta, 00:23:53.380 --> 00:23:56.750 for example, until delta is equal to 2 pi. 00:23:56.750 --> 00:23:58.370 Then you are getting this again. 00:23:58.370 --> 00:24:04.210 Basically, you have EA and the EB, again, line up each other. 00:24:04.210 --> 00:24:08.530 And the difference is that this EB actually 00:24:08.530 --> 00:24:14.890 rotated maybe 360 degree. 00:24:14.890 --> 00:24:20.540 And basically, you will see that, again, the intensity 00:24:20.540 --> 00:24:22.200 become the maxima again. 00:24:22.200 --> 00:24:23.350 OK? 00:24:23.350 --> 00:24:26.110 So that is actually how we can actually 00:24:26.110 --> 00:24:30.190 understand this result. And, of course, you 00:24:30.190 --> 00:24:34.450 can also go ahead and plot or simulate 00:24:34.450 --> 00:24:42.670 this result in the computer and really draw the amplitude, 00:24:42.670 --> 00:24:47.560 really draw the intensity as a function of angle here, 00:24:47.560 --> 00:24:49.630 or, say, the delta here. 00:24:49.630 --> 00:24:52.520 As you can see from here, that the intensity 00:24:52.520 --> 00:24:58.450 is actually reaching the maximum in the center. 00:24:58.450 --> 00:24:59.470 Why is that? 00:24:59.470 --> 00:25:04.500 In the center, if I have observer here 00:25:04.500 --> 00:25:07.270 in the center, what is going to happen 00:25:07.270 --> 00:25:10.210 is that the path length, optical path 00:25:10.210 --> 00:25:14.860 length between AP prong and the BP prong 00:25:14.860 --> 00:25:18.520 is going to be the same by symmetry, 00:25:18.520 --> 00:25:21.010 because it's actually in the optical center. 00:25:21.010 --> 00:25:26.900 Therefore, you will expect that delta is actually equal to 0. 00:25:26.900 --> 00:25:27.400 OK? 00:25:27.400 --> 00:25:31.170 So that's essentially why you see the maxima there. 00:25:31.170 --> 00:25:34.210 And if you start to move away from there, 00:25:34.210 --> 00:25:37.730 you will see that the delta start to increase. 00:25:37.730 --> 00:25:41.170 And at some point, you'll reach a minima, which 00:25:41.170 --> 00:25:44.630 you can see that on the plot. 00:25:44.630 --> 00:25:47.670 And that is actually because now, 00:25:47.670 --> 00:25:50.320 due to the increasing optical path length 00:25:50.320 --> 00:25:52.310 difference and the phase difference, 00:25:52.310 --> 00:25:54.550 the two electric field is starting 00:25:54.550 --> 00:25:57.640 to cancel each other, which actually produce 00:25:57.640 --> 00:26:00.220 the black pattern there. 00:26:00.220 --> 00:26:06.790 And finally, after it pass delta equal to pi, 00:26:06.790 --> 00:26:10.210 then these two electric fields start to work together again. 00:26:10.210 --> 00:26:10.910 All right? 00:26:10.910 --> 00:26:12.610 They're collaborating again. 00:26:12.610 --> 00:26:14.050 And you can see that again. 00:26:14.050 --> 00:26:18.010 You would get another maxima afterward. 00:26:18.010 --> 00:26:18.850 OK? 00:26:18.850 --> 00:26:23.260 And here, you can see that is actually my calculation. 00:26:23.260 --> 00:26:28.000 And, of course, I can do a demonstration to you 00:26:28.000 --> 00:26:29.560 to really show that this is actually 00:26:29.560 --> 00:26:35.760 what we are going to see based on the demonstration we 00:26:35.760 --> 00:26:37.060 are going to show here. 00:26:37.060 --> 00:26:39.260 So now, I am going to turn the light off. 00:26:44.630 --> 00:26:49.790 And here, I have a device which actually contain a water tank. 00:26:49.790 --> 00:26:53.210 And I need to actually turn this thing up. 00:26:59.310 --> 00:27:04.310 On the water tank I have two vibrator, which is actually 00:27:04.310 --> 00:27:07.090 acting as a point source. 00:27:07.090 --> 00:27:10.540 So basically, those vibrator vibrating up and down 00:27:10.540 --> 00:27:15.640 to create waves in this tank. 00:27:15.640 --> 00:27:16.240 OK? 00:27:16.240 --> 00:27:18.910 So basically, you can see that, huh, really, 00:27:18.910 --> 00:27:21.350 you have two point-like source. 00:27:21.350 --> 00:27:26.350 And you can see spherical waves is actually really generated 00:27:26.350 --> 00:27:30.220 and is really propagating away from the point source. 00:27:30.220 --> 00:27:31.540 OK? 00:27:31.540 --> 00:27:34.930 And what I can do now, you can see 00:27:34.930 --> 00:27:38.380 that this picture is really dynamic, because we 00:27:38.380 --> 00:27:40.510 can see that wavefront essentially moving 00:27:40.510 --> 00:27:41.900 as a function of time. 00:27:41.900 --> 00:27:45.700 So what I'm going to do is to really change 00:27:45.700 --> 00:27:48.730 the frequency of the light, which is actually 00:27:48.730 --> 00:27:52.280 shining on this water, so that you can actually 00:27:52.280 --> 00:27:55.150 see the fixed pattern here. 00:27:55.150 --> 00:28:01.520 And now, I am going to change the light frequency. 00:28:01.520 --> 00:28:05.870 You can see now I only shine the water tank 00:28:05.870 --> 00:28:10.460 at the specific time which match the speed of the propagation 00:28:10.460 --> 00:28:11.840 of the water wave. 00:28:11.840 --> 00:28:13.790 And you can see, aha, I've actually managed 00:28:13.790 --> 00:28:16.370 to freeze the wavefront. 00:28:16.370 --> 00:28:16.951 We see? 00:28:16.951 --> 00:28:17.450 OK. 00:28:17.450 --> 00:28:23.610 So you can see, now, really, you can see coming from the source, 00:28:23.610 --> 00:28:28.210 they are circular wavefront, which 00:28:28.210 --> 00:28:32.840 actually mimicking the result from Huygens' Principle. 00:28:32.840 --> 00:28:35.810 And you can see that they are complicated 00:28:35.810 --> 00:28:39.240 interference pattern forming. 00:28:39.240 --> 00:28:41.600 You can see that at some point they 00:28:41.600 --> 00:28:43.520 have constructive interference. 00:28:43.520 --> 00:28:46.100 If you focus on the central part, 00:28:46.100 --> 00:28:50.840 you can see that the maxima is actually reach there. 00:28:50.840 --> 00:28:53.720 On the other hand, if you move away, a little bit 00:28:53.720 --> 00:28:57.770 away from the center, you can see that really, the intensity 00:28:57.770 --> 00:28:58.550 drop. 00:28:58.550 --> 00:29:03.885 And at some point, you will also see that, OK, again, I 00:29:03.885 --> 00:29:06.190 am changing the procedure in such 00:29:06.190 --> 00:29:10.250 that the phase difference between the contribution 00:29:10.250 --> 00:29:14.320 of our source A and the B essentially equal to 2 pi. 00:29:14.320 --> 00:29:21.340 In that case, you will be able to see that another maxima is 00:29:21.340 --> 00:29:22.660 actually created again. 00:29:28.600 --> 00:29:30.660 So now, we can actually also show you 00:29:30.660 --> 00:29:37.890 that a lot, in fact, based on this glorious pattern, 00:29:37.890 --> 00:29:40.630 let's actually take a look at the projector here. 00:29:40.630 --> 00:29:47.280 So if I look at on the individual slide, which 00:29:47.280 --> 00:29:51.160 I have here, you can see that those are actually 00:29:51.160 --> 00:29:55.450 a point-light source and is creating a circular pattern. 00:29:55.450 --> 00:29:59.130 And now, I can actually overlap with two patterns together. 00:29:59.130 --> 00:30:09.270 And you can see that when I have the center of the two circles 00:30:09.270 --> 00:30:12.850 pretty close to each other, you can see that really, you 00:30:12.850 --> 00:30:14.610 have very small d. 00:30:14.610 --> 00:30:17.520 In this case, you have very small distance 00:30:17.520 --> 00:30:20.610 between source number one and number two. 00:30:20.610 --> 00:30:25.350 Then basically, based on our expression, 00:30:25.350 --> 00:30:30.390 so you can see that delta is equal to d sine theta divided 00:30:30.390 --> 00:30:32.820 by lambda times two pi, right? 00:30:32.820 --> 00:30:36.120 And you can actually calculate sine theta 00:30:36.120 --> 00:30:42.051 will be equal to delta divided by k times t. 00:30:42.051 --> 00:30:42.550 OK? 00:30:53.060 --> 00:30:56.890 When delta is equal to pi, that is going to give you 00:30:56.890 --> 00:31:01.030 a minima where, essentially, also showing here, 00:31:01.030 --> 00:31:04.510 the minima is shown as the black pattern here. 00:31:04.510 --> 00:31:05.240 OK? 00:31:05.240 --> 00:31:07.660 You can see from on here. 00:31:07.660 --> 00:31:10.270 So what this says, your formula is showing you 00:31:10.270 --> 00:31:15.280 that when I have d, which is very small, 00:31:15.280 --> 00:31:16.840 what is going to happen is that I'm 00:31:16.840 --> 00:31:22.870 going to get sine theta to be very large when d is actually 00:31:22.870 --> 00:31:23.770 very small. 00:31:23.770 --> 00:31:25.370 And that can be shown here. 00:31:25.370 --> 00:31:28.930 When I have d, which is the distance between the center 00:31:28.930 --> 00:31:32.510 of these two point source, very small, 00:31:32.510 --> 00:31:38.140 you can see that the place you get the minima 00:31:38.140 --> 00:31:44.710 is really far away from the center, which is actually here. 00:31:44.710 --> 00:31:45.550 OK? 00:31:45.550 --> 00:31:48.910 Now, what I'm going to do is to increase the distance 00:31:48.910 --> 00:31:50.200 between these two source. 00:31:50.200 --> 00:31:53.410 According to our position, what is going to happen 00:31:53.410 --> 00:32:00.220 is that the central maxima will decrease. 00:32:00.220 --> 00:32:04.810 The position where you get a minima will be moving closer 00:32:04.810 --> 00:32:07.870 to the center, according to that formula, 00:32:07.870 --> 00:32:10.210 because it's proportional to 1 over d. 00:32:10.210 --> 00:32:12.400 And we can do this really carefully 00:32:12.400 --> 00:32:14.900 to see if I can succeed. 00:32:14.900 --> 00:32:19.900 And you can see that really, when I am moving 00:32:19.900 --> 00:32:22.960 these two slides away from each other, 00:32:22.960 --> 00:32:25.590 you can see that the pattern is changing, right? 00:32:25.590 --> 00:32:34.390 And the center maxima, or, say, this Gaussian-like curve there 00:32:34.390 --> 00:32:37.020 becoming narrower and narrower. 00:32:37.020 --> 00:32:37.600 OK? 00:32:37.600 --> 00:32:40.058 So that essentially what we can actually observe form here. 00:32:40.058 --> 00:32:45.822 And our calculation really works very well here. 00:32:48.720 --> 00:32:49.500 Very good. 00:32:49.500 --> 00:32:53.480 So do we have any questions regarding 00:32:53.480 --> 00:32:55.030 the demonstration we have here? 00:32:59.360 --> 00:33:00.300 OK. 00:33:00.300 --> 00:33:04.560 So all those things seems to be pretty straightforward to you. 00:33:04.560 --> 00:33:08.700 And what we are actually now is seeing a position 00:33:08.700 --> 00:33:13.030 where we can actually discuss how we actually 00:33:13.030 --> 00:33:22.570 can understand the radar, which is how actually radar works. 00:33:22.570 --> 00:33:25.090 So here is actually how radar works. 00:33:25.090 --> 00:33:28.860 Suppose you have some unknown object, 00:33:28.860 --> 00:33:31.350 which is like an airplane, OK? 00:33:31.350 --> 00:33:35.220 And you would like to know where is this object. 00:33:35.220 --> 00:33:41.550 What you do, actually, is to shoot whatever radio waves 00:33:41.550 --> 00:33:43.840 toward some direction and see if there 00:33:43.840 --> 00:33:45.300 are something coming back. 00:33:45.300 --> 00:33:45.960 Right? 00:33:45.960 --> 00:33:49.290 Then you know there's something on the sky 00:33:49.290 --> 00:33:51.770 because you can detect the refracted wave. 00:33:51.770 --> 00:33:52.760 Right? 00:33:52.760 --> 00:33:56.070 So we shoot this airplane. 00:33:56.070 --> 00:33:59.050 And then something is going to come back. 00:33:59.050 --> 00:34:01.630 And now, we can say OK. 00:34:01.630 --> 00:34:03.870 In that direction I have something coming back. 00:34:03.870 --> 00:34:06.370 That means there's something there. 00:34:06.370 --> 00:34:09.090 And I can also measure the time it takes 00:34:09.090 --> 00:34:10.590 for the wave to come back. 00:34:10.590 --> 00:34:13.211 Then I know where it's actually that object. 00:34:13.211 --> 00:34:13.710 Right? 00:34:13.710 --> 00:34:18.750 So that's actually a pretty straightforward thing to do. 00:34:18.750 --> 00:34:23.170 However, there's one difficulty. 00:34:23.170 --> 00:34:27.790 So this is actually the radiation pattern 00:34:27.790 --> 00:34:32.920 of oscillating dipole which we actually learned before. 00:34:32.920 --> 00:34:36.280 So the problem is that, OK, what we really 00:34:36.280 --> 00:34:40.600 need is electromagnetic wave, which is actually very, very 00:34:40.600 --> 00:34:44.920 narrow in angle and pointing to some specific direction. 00:34:44.920 --> 00:34:46.449 And then I would like to see if I 00:34:46.449 --> 00:34:49.920 can get some refractive wave coming from that direction. 00:34:49.920 --> 00:34:50.710 OK? 00:34:50.710 --> 00:34:53.770 The problem is that, look! 00:34:53.770 --> 00:34:57.040 if I oscillate some charge up and down, 00:34:57.040 --> 00:35:00.590 the radiation I'm getting is really, really broad. 00:35:00.590 --> 00:35:01.090 Right? 00:35:01.090 --> 00:35:04.090 So it's going toward all kinds of different direction. 00:35:04.090 --> 00:35:07.240 So if you use this to detect things, 00:35:07.240 --> 00:35:10.810 you are always going to get something coming back, 00:35:10.810 --> 00:35:14.080 because it's actually shooting the electromagnetic wave 00:35:14.080 --> 00:35:16.450 into random direction. 00:35:16.450 --> 00:35:20.530 And you are not sure any more where 00:35:20.530 --> 00:35:23.570 is actually this object you are trying to detect. 00:35:23.570 --> 00:35:24.070 OK? 00:35:24.070 --> 00:35:27.890 So that's actually apparently a problem. 00:35:27.890 --> 00:35:33.520 And what we can actually do is to make use of the interference 00:35:33.520 --> 00:35:35.440 phenomenon, which we can actually 00:35:35.440 --> 00:35:39.400 learn from here to actually try to make sure 00:35:39.400 --> 00:35:41.470 that the electromagnetic wave is actually 00:35:41.470 --> 00:35:46.130 pointing to some specific direction we want. 00:35:46.130 --> 00:35:51.100 So let's actually go ahead consider a three slit 00:35:51.100 --> 00:35:52.099 experiment. 00:35:56.230 --> 00:35:59.130 I have this setup changed. 00:35:59.130 --> 00:36:00.900 Originally, I have two slits. 00:36:00.900 --> 00:36:05.440 And now, I drew it in three holes on the wall. 00:36:05.440 --> 00:36:11.140 And, again, I have the distance between the slits to be d. 00:36:11.140 --> 00:36:16.060 And I call this slit number 1, 2, and 3. 00:36:16.060 --> 00:36:19.150 And we were wondering what would be the interference 00:36:19.150 --> 00:36:23.380 pattern on the screen, which is actually 00:36:23.380 --> 00:36:28.540 far away from the wall, as a distance of L. 00:36:28.540 --> 00:36:32.020 And I'm interested in their intensity 00:36:32.020 --> 00:36:34.130 at the point P on this screen. 00:36:34.130 --> 00:36:35.500 OK? 00:36:35.500 --> 00:36:39.310 So what I am going to do is to basically repeat 00:36:39.310 --> 00:36:43.080 what we have done in the previous example. 00:36:43.080 --> 00:36:46.540 I'm trying to connect 1 to the P, 2 P, 00:36:46.540 --> 00:36:50.150 and the 3 P, basically, connect the slit 00:36:50.150 --> 00:36:54.400 to the point of interest on the screen. 00:36:54.400 --> 00:36:58.390 And I can actually also-- 00:36:58.390 --> 00:37:03.520 you know this angle, this 1 P to the horizontal direction, 00:37:03.520 --> 00:37:09.280 this angle is called theta in my notation. 00:37:09.280 --> 00:37:11.850 Then clearly, I can go ahead and calculate 00:37:11.850 --> 00:37:15.280 what will be the optical path length 00:37:15.280 --> 00:37:17.710 difference between of the light coming 00:37:17.710 --> 00:37:21.650 from slit number 1, slit number 2 and the slit number 3. 00:37:21.650 --> 00:37:22.205 OK? 00:37:22.205 --> 00:37:27.020 And in this case, what I'm interested 00:37:27.020 --> 00:37:33.530 is delta 1, 2 and delta 1, 3. 00:37:33.530 --> 00:37:34.850 Right? 00:37:34.850 --> 00:37:39.770 Since the screen is really far away from the wall, 00:37:39.770 --> 00:37:42.860 therefore, I can actually savor the assurance 00:37:42.860 --> 00:37:49.640 that these two angle is actually theta because the three lines, 00:37:49.640 --> 00:37:52.210 due to the large distance, this L 00:37:52.210 --> 00:37:54.030 is actually really, really large. 00:37:54.030 --> 00:37:56.870 Therefore, they are actually almost parallel to each other. 00:37:56.870 --> 00:37:57.800 OK? 00:37:57.800 --> 00:38:02.270 So what is going to happen is that delta 1, 2, which 00:38:02.270 --> 00:38:05.170 is the phase difference between light 00:38:05.170 --> 00:38:08.590 from the first slit and second slit, 00:38:08.590 --> 00:38:17.330 is actually going to be equal to delta 2, 3. 00:38:17.330 --> 00:38:19.100 It's going to be equal to the phase 00:38:19.100 --> 00:38:22.250 difference between the second slit, the light 00:38:22.250 --> 00:38:24.450 from second slit and third slit. 00:38:24.450 --> 00:38:26.330 And what is actually that number? 00:38:26.330 --> 00:38:31.275 This number is going to be equal to d sine theta 00:38:31.275 --> 00:38:34.432 divided by lambda times 2 pi. 00:38:34.432 --> 00:38:38.150 It's exactly the same as what we actually 00:38:38.150 --> 00:38:39.840 get from the first example. 00:38:39.840 --> 00:38:40.340 OK? 00:38:43.310 --> 00:38:45.790 Therefore, what is going to happen 00:38:45.790 --> 00:38:51.190 is that no matter what theta I choose, 00:38:51.190 --> 00:38:54.700 the phase difference between nearby slit 00:38:54.700 --> 00:38:58.000 is actually a constant, which is actually this one. 00:38:58.000 --> 00:39:01.710 And I will call this phase difference to be delta. 00:39:04.650 --> 00:39:08.670 I would like to ask you a question now. 00:39:08.670 --> 00:39:13.530 The question is, how do we choose the delta 00:39:13.530 --> 00:39:22.030 here such that I have completely destructive interference? 00:39:22.030 --> 00:39:29.802 Now, I have three vectors, vector E1, vector E2, 00:39:29.802 --> 00:39:31.295 and the vector E3. 00:39:37.600 --> 00:39:41.500 The phase difference between E1, E2, and E3, 00:39:41.500 --> 00:39:47.330 the nearby phase difference is actually delta. 00:39:47.330 --> 00:39:51.190 So the question is, how do I actually completely cancel 00:39:51.190 --> 00:39:54.070 the electric field so that I have completely 00:39:54.070 --> 00:39:55.600 destructive interference? 00:39:55.600 --> 00:39:59.520 Can somebody help me here? 00:39:59.520 --> 00:40:04.890 The hint is that you can actually use this vector sum 00:40:04.890 --> 00:40:08.244 idea in the complex frame. 00:40:08.244 --> 00:40:09.240 STUDENT: [INAUDIBLE] 00:40:09.240 --> 00:40:10.610 PROFESSOR: Yes, very good. 00:40:10.610 --> 00:40:14.460 To form a triangle in the complex frame, right? 00:40:14.460 --> 00:40:21.150 So what we can do is now choose the phase difference 00:40:21.150 --> 00:40:29.630 delta to be such that E1, E2, and E3 actually 00:40:29.630 --> 00:40:32.410 form a triangle. 00:40:32.410 --> 00:40:34.930 You see what I mean? 00:40:34.930 --> 00:40:37.570 Therefore, you can actually already get 00:40:37.570 --> 00:40:41.650 what would be the required delta value. 00:40:41.650 --> 00:40:49.110 The required delta value is going to be 2 pi divided by 3. 00:40:49.110 --> 00:40:50.520 Right? 00:40:50.520 --> 00:40:52.350 OK? 00:40:52.350 --> 00:40:53.030 So very good. 00:40:53.030 --> 00:40:55.320 So now, we are not afraid anymore. 00:40:55.320 --> 00:40:57.720 So how about four slit experiment? 00:40:57.720 --> 00:41:01.890 I just add another slit, d essentially the distance 00:41:01.890 --> 00:41:04.670 between the fourth slit and the third slit. 00:41:04.670 --> 00:41:13.430 What will be the delta required to have 00:41:13.430 --> 00:41:15.114 destructive interference? 00:41:19.090 --> 00:41:21.386 Anybody can help me? 00:41:21.386 --> 00:41:23.240 STUDENT: [INAUDIBLE] 00:41:23.240 --> 00:41:24.820 YEN-JIE LEE: Very good. 00:41:24.820 --> 00:41:31.150 So if you have four slit, based on this intuition, 00:41:31.150 --> 00:41:37.460 which we developed from the complex notation vector 00:41:37.460 --> 00:41:42.010 sum, what is going to happen is that if you have four slit, 00:41:42.010 --> 00:41:49.251 the delta will be equal to 2 pi divided by 4. 00:41:49.251 --> 00:41:49.750 OK? 00:41:49.750 --> 00:41:52.450 So what does this tell us? 00:41:52.450 --> 00:41:55.950 So remember, the sine theta, sine 00:41:55.950 --> 00:41:58.360 theta is telling you the location where 00:41:58.360 --> 00:41:59.710 you get the minima. 00:41:59.710 --> 00:42:00.640 OK? 00:42:00.640 --> 00:42:04.630 So this is actually the power profile, or, say, 00:42:04.630 --> 00:42:07.101 the intensity profile. 00:42:07.101 --> 00:42:07.600 OK? 00:42:07.600 --> 00:42:10.330 And this is actually equal to 0. 00:42:10.330 --> 00:42:11.940 And this is actually delta. 00:42:11.940 --> 00:42:13.030 OK? 00:42:13.030 --> 00:42:19.410 The place which you get zero intensity 00:42:19.410 --> 00:42:25.790 is actually becoming closer and closer to zero. 00:42:25.790 --> 00:42:26.290 Right? 00:42:26.290 --> 00:42:29.290 Because sine theta, which is the angle 00:42:29.290 --> 00:42:33.850 between horizontal direction and this observer P, 00:42:33.850 --> 00:42:36.340 is proportional to delta. 00:42:36.340 --> 00:42:40.510 When you have destructive interference at angle 00:42:40.510 --> 00:42:45.400 which is smaller, smaller, and smaller, that means what? 00:42:45.400 --> 00:42:51.310 That means the central Gaussian-like structure 00:42:51.310 --> 00:42:55.315 is going to be becoming narrower and narrower. 00:42:58.730 --> 00:43:00.125 Does that make sense? 00:43:02.980 --> 00:43:03.650 Very good. 00:43:03.650 --> 00:43:07.270 So at least we found something interesting now. 00:43:07.270 --> 00:43:13.330 That means, ha, one idea to get very narrow 00:43:13.330 --> 00:43:16.870 electromagnetic wave pointing to some direction 00:43:16.870 --> 00:43:22.180 is to have a huge number of point light source 00:43:22.180 --> 00:43:26.830 and slit experiment such that I can actually 00:43:26.830 --> 00:43:32.200 construct something which is actually very narrow in angle. 00:43:32.200 --> 00:43:36.070 And I can use that to shoot the object which 00:43:36.070 --> 00:43:38.282 I would like to detect. 00:43:38.282 --> 00:43:40.690 You see what I mean? 00:43:40.690 --> 00:43:43.800 Does that make sense? 00:43:43.800 --> 00:43:46.551 OK? 00:43:46.551 --> 00:43:47.050 All right. 00:43:47.050 --> 00:43:47.920 So that's very good. 00:43:47.920 --> 00:43:53.901 So now, let's actually consider an N slit interference pattern 00:43:53.901 --> 00:43:54.400 OK? 00:43:54.400 --> 00:43:58.720 So suppose, now, I have not only 1, 2, 3, and then many 00:43:58.720 --> 00:44:01.610 more until N slit. 00:44:01.610 --> 00:44:03.010 All right? 00:44:03.010 --> 00:44:07.600 I can now go ahead and calculate the E total, which 00:44:07.600 --> 00:44:15.130 is the total electric field coming from all of the slit 00:44:15.130 --> 00:44:17.260 we have. 00:44:17.260 --> 00:44:24.430 Basically, this will be equal to E0 exponential i omega t 00:44:24.430 --> 00:44:36.110 minus kR where I define r1 is roughly capital R. OK? 00:44:36.110 --> 00:44:37.920 That's essentially the contribution 00:44:37.920 --> 00:44:41.980 from slit number 1 OK? 00:44:41.980 --> 00:44:44.170 And this contribution from slit number 1 00:44:44.170 --> 00:44:51.790 is going to be looking like exponential i omega t minus kR 00:44:51.790 --> 00:44:54.670 minus delta, right, because there is a phase 00:44:54.670 --> 00:44:57.640 difference between the light coming 00:44:57.640 --> 00:45:02.440 from first slit and the second slit, which is actually delta. 00:45:02.440 --> 00:45:03.640 All right? 00:45:03.640 --> 00:45:05.150 So what would be the third term? 00:45:05.150 --> 00:45:07.652 So these actually coming from slit number 2. 00:45:07.652 --> 00:45:08.860 What would be the third term? 00:45:08.860 --> 00:45:15.310 Exponential i omega t minus kR minus what? 00:45:15.310 --> 00:45:16.130 STUDENT: 2 delta. 00:45:16.130 --> 00:45:18.370 YEN-JIE LEE: 2 delta, yeah, because you 00:45:18.370 --> 00:45:21.730 can see that coming from here, seems 00:45:21.730 --> 00:45:25.190 the distance between theta as constant, which is d. 00:45:25.190 --> 00:45:30.510 Therefore, the phase difference between nearby slits 00:45:30.510 --> 00:45:32.440 is actually a constant. 00:45:32.440 --> 00:45:36.910 Therefore, I accumulating the phase difference now. 00:45:36.910 --> 00:45:39.682 I get 2 delta here. 00:45:39.682 --> 00:45:41.140 And this is actually a contribution 00:45:41.140 --> 00:45:42.040 from the first slit. 00:45:42.040 --> 00:45:48.140 And the et cetera, et cetera, until the Nth slit, 00:45:48.140 --> 00:45:50.350 which is actually going to be exponential 00:45:50.350 --> 00:45:58.810 i omega t minus kR minus N minus 1 delta. 00:45:58.810 --> 00:46:01.830 And summing all those things together, and all of them 00:46:01.830 --> 00:46:05.700 are in the Z direction. 00:46:05.700 --> 00:46:08.030 OK? 00:46:08.030 --> 00:46:10.520 So I'm now going to calculate this dimension. 00:46:10.520 --> 00:46:17.280 So basically, you are getting E0 exponential i omega t minus kR. 00:46:17.280 --> 00:46:21.820 I can actually factorize these factor out. 00:46:21.820 --> 00:46:28.910 And what am I going to get is 1 plus exponential minus i delta 00:46:28.910 --> 00:46:32.220 plus exponential minus exponential minus i 00:46:32.220 --> 00:46:35.430 2 delta plus blah, blah, blah. 00:46:35.430 --> 00:46:39.160 And basically, you will get exponential minus i 00:46:39.160 --> 00:46:42.730 minus 1 delta in the first term. 00:46:42.730 --> 00:46:48.050 And all those things are pointing to the Z direction. 00:46:48.050 --> 00:46:50.830 And this, I know how to actually calculate. 00:46:50.830 --> 00:46:52.040 Right? 00:46:52.040 --> 00:46:56.120 Just a reminder, basically, if you calculate summation 00:46:56.120 --> 00:47:01.130 N equal to 0 to N minus 1 r to the Nth. 00:47:01.130 --> 00:47:03.530 And these will give you 1 minus r 00:47:03.530 --> 00:47:08.510 to the N divided by phi minus r. 00:47:08.510 --> 00:47:09.440 OK? 00:47:09.440 --> 00:47:13.010 So basically, I can now go ahead and calculate this. 00:47:13.010 --> 00:47:22.640 And this will basically give you 1 minus-- 00:47:22.640 --> 00:47:26.220 OK, so the small r here has been replaced by exponential 00:47:26.220 --> 00:47:28.550 minus i delta, right? 00:47:28.550 --> 00:47:30.770 So therefore, what I'm going to get 00:47:30.770 --> 00:47:40.070 is 1 minus exponential minus i delta N for the upper part. 00:47:40.070 --> 00:47:44.320 And then I have 1 minus exponential 00:47:44.320 --> 00:47:47.530 minus i delta in the lower part. 00:47:47.530 --> 00:47:48.950 OK? 00:47:48.950 --> 00:47:53.710 So that actually make use of this formula, which are here. 00:47:53.710 --> 00:47:57.321 And, again, it should be simplify these series. 00:47:57.321 --> 00:47:57.820 All right? 00:48:00.330 --> 00:48:02.550 As usual, what I'm going to do is 00:48:02.550 --> 00:48:08.050 to use the trick similar to what I have done there 00:48:08.050 --> 00:48:11.040 to actually get cosine function out 00:48:11.040 --> 00:48:13.500 of the exponential functions. 00:48:13.500 --> 00:48:14.250 All right? 00:48:14.250 --> 00:48:17.460 So what I'm going to do is to factorize out 00:48:17.460 --> 00:48:23.470 exponential minus i delta N over 2 for the upper part. 00:48:23.470 --> 00:48:26.870 So basically, I get exponential minus i delta 00:48:26.870 --> 00:48:34.320 N divided by 2, exponential i delta N divided by 2 00:48:34.320 --> 00:48:39.683 minus exponential minus i delta N divided by 2. 00:48:39.683 --> 00:48:40.182 OK? 00:48:43.360 --> 00:48:46.980 This is actually divided by exponential 00:48:46.980 --> 00:48:52.620 minus i delta over 2 exponential i delta 00:48:52.620 --> 00:48:58.908 over 2 minus exponential minus i delta over 2. 00:48:58.908 --> 00:49:00.270 All right? 00:49:00.270 --> 00:49:02.460 The reason I'm doing this is because I 00:49:02.460 --> 00:49:06.600 would like to actually make this a cosine function. 00:49:06.600 --> 00:49:08.550 OK? 00:49:08.550 --> 00:49:10.020 Any questions so far? 00:49:14.830 --> 00:49:16.150 OK. 00:49:16.150 --> 00:49:18.340 So if no question, then basically, 00:49:18.340 --> 00:49:22.010 this expression can be, again, rewritten 00:49:22.010 --> 00:49:28.030 as exponential minus i delta N minus 1 divided 00:49:28.030 --> 00:49:33.340 by 2, because I have this denominator nominator 00:49:33.340 --> 00:49:38.020 exponential i delta N over 2 and that exponential minus i delta 00:49:38.020 --> 00:49:39.321 divided by 2. 00:49:39.321 --> 00:49:39.820 OK? 00:49:39.820 --> 00:49:42.460 Therefore, I can combine them all together 00:49:42.460 --> 00:49:45.950 and then get this expression here. 00:49:45.950 --> 00:49:49.180 And this is actually exponential minus exponential. 00:49:49.180 --> 00:49:52.640 Therefore, I am going to get sine out of it. 00:49:52.640 --> 00:49:56.520 And basically, I get sine and delta 00:49:56.520 --> 00:50:02.265 divided by 2 divided by sine delta over 2. 00:50:06.510 --> 00:50:07.030 OK. 00:50:07.030 --> 00:50:09.670 So now, I can actually go ahead and calculate 00:50:09.670 --> 00:50:13.270 what will be the resulting intensity. 00:50:13.270 --> 00:50:14.200 Right? 00:50:14.200 --> 00:50:19.290 The resulting intensity is going to be 00:50:19.290 --> 00:50:24.710 proportional to the square of the electric field. 00:50:24.710 --> 00:50:25.210 Right? 00:50:25.210 --> 00:50:30.510 So basically, the intensity will be proportional to E square. 00:50:30.510 --> 00:50:36.166 And that is actually equal to E times E star. 00:50:36.166 --> 00:50:39.300 E and the E is a complex conjugate. 00:50:39.300 --> 00:50:41.070 And basically, you will see that this 00:50:41.070 --> 00:50:49.810 will be proportional to sine and delta divided by 2 divided 00:50:49.810 --> 00:50:56.160 by sine delta over 2 square. 00:50:56.160 --> 00:51:01.950 Therefore, the intensity will be equal to i 00:51:01.950 --> 00:51:08.880 0 times sine and delta divided by 2 00:51:08.880 --> 00:51:12.860 divided by sine delta over 2. 00:51:12.860 --> 00:51:16.256 And then square that. 00:51:16.256 --> 00:51:17.684 Any questions? 00:51:21.020 --> 00:51:26.090 So after all this work, we have arrived at expression which 00:51:26.090 --> 00:51:28.592 is very hard to understand. 00:51:28.592 --> 00:51:29.092 Right? 00:51:29.092 --> 00:51:33.080 [LAUGHS] So what I'm going to do to help you 00:51:33.080 --> 00:51:38.830 is to really plot the result as a function of delta 00:51:38.830 --> 00:51:40.440 on the screen. 00:51:40.440 --> 00:51:44.050 You can see there are four plots here. 00:51:44.050 --> 00:51:46.380 The first one is N equal to 3. 00:51:46.380 --> 00:51:48.860 The upper left one is N equal to 3. 00:51:48.860 --> 00:51:52.270 So you can see that the pattern looks like this. 00:51:52.270 --> 00:51:56.140 So at delta equal to 0, surprise nobody, 00:51:56.140 --> 00:51:57.700 you are going to get maxima. 00:51:57.700 --> 00:51:58.200 Right? 00:51:58.200 --> 00:52:02.850 Because delta is equal to 0, you are adding N vectors 00:52:02.850 --> 00:52:04.700 the most efficient way. 00:52:04.700 --> 00:52:07.020 Therefore, you are going to get the maxima, which 00:52:07.020 --> 00:52:09.440 is i equal to i 0. 00:52:09.440 --> 00:52:10.980 OK? 00:52:10.980 --> 00:52:16.290 And if you move away from the center, delta equal to 0, 00:52:16.290 --> 00:52:20.970 and you see that is a small bump in between. 00:52:20.970 --> 00:52:22.800 Then you can continue and continue. 00:52:22.800 --> 00:52:26.820 And you see that there's another big peak again. 00:52:26.820 --> 00:52:27.540 You see? 00:52:27.540 --> 00:52:29.010 So that's essentially the structure 00:52:29.010 --> 00:52:33.660 if you plot this result, i equal to something proportional 00:52:33.660 --> 00:52:37.890 to sine square this expression there. 00:52:37.890 --> 00:52:43.850 And that's essentially what you will get when N is equal to 3. 00:52:43.850 --> 00:52:45.510 OK? 00:52:45.510 --> 00:52:49.380 And this is essentially how I remember this pattern. 00:52:49.380 --> 00:52:50.760 OK? 00:52:50.760 --> 00:52:55.710 So when N is equal to 3, you have a family 00:52:55.710 --> 00:52:58.935 of two adult and one child. 00:52:58.935 --> 00:52:59.920 [LAUGHTER] 00:52:59.920 --> 00:53:00.420 Right? 00:53:00.420 --> 00:53:03.170 So basically, you have two big peak. 00:53:03.170 --> 00:53:06.920 And between them, there's a small peak. 00:53:06.920 --> 00:53:07.420 OK? 00:53:07.420 --> 00:53:09.850 That's actually how I remember this pattern. 00:53:09.850 --> 00:53:12.880 And I think it's pretty nice, right? 00:53:12.880 --> 00:53:15.555 So you can have N equal to 4. 00:53:15.555 --> 00:53:17.560 It's a bigger family. 00:53:17.560 --> 00:53:19.570 You have two adults. 00:53:19.570 --> 00:53:22.680 The adults are slimmer, OK? 00:53:22.680 --> 00:53:23.626 All right? 00:53:23.626 --> 00:53:25.810 [LAUGHTER] 00:53:25.810 --> 00:53:28.780 Because they have a lot of work to do. 00:53:28.780 --> 00:53:30.600 Then they have two child. 00:53:30.600 --> 00:53:32.286 All right? 00:53:32.286 --> 00:53:37.002 N equal to 5, how many children do we have? 00:53:37.002 --> 00:53:37.960 STUDENT: We have three. 00:53:37.960 --> 00:53:39.260 YEN-JIE LEE: Three. 00:53:39.260 --> 00:53:43.910 Therefore, the adults are really frustrated. 00:53:43.910 --> 00:53:49.560 So they are even slimmer in a happy way, making it positive. 00:53:49.560 --> 00:53:52.020 And N equal to 6, woo. 00:53:52.020 --> 00:53:55.830 Oh my god, I have four children in the family. 00:53:55.830 --> 00:53:56.670 All right? 00:53:56.670 --> 00:54:00.610 So there are two things which we learned from here. 00:54:00.610 --> 00:54:06.540 The first one is that the number of big peak, which 00:54:06.540 --> 00:54:13.770 I would call it principal maxima, the number 00:54:13.770 --> 00:54:16.580 of principal maxima is actually pretty 00:54:16.580 --> 00:54:22.116 similar as a function of delta. 00:54:22.116 --> 00:54:26.630 But the number of secondary maxima 00:54:26.630 --> 00:54:30.710 increase as a function of N value. 00:54:30.710 --> 00:54:35.150 N value is actually telling you how many slits 00:54:35.150 --> 00:54:38.020 you have in the experiment. 00:54:38.020 --> 00:54:44.060 And also, you can see that the delta is actually becoming-- 00:54:44.060 --> 00:54:48.130 the first minima, the delta value 00:54:48.130 --> 00:54:51.580 is actually decreasing as a function of N value. 00:54:51.580 --> 00:54:52.580 Right? 00:54:52.580 --> 00:54:55.660 So the parents are getting slimmer. 00:54:55.660 --> 00:54:56.390 All right? 00:54:56.390 --> 00:54:59.120 So therefore, you can see that if I 00:54:59.120 --> 00:55:04.130 would like to have a radar which is actually pointing 00:55:04.130 --> 00:55:06.920 to a very specific direction, what 00:55:06.920 --> 00:55:12.870 essentially the choice of N value which we will need? 00:55:12.870 --> 00:55:14.870 Infinity or a very large number. 00:55:14.870 --> 00:55:15.420 OK? 00:55:15.420 --> 00:55:18.300 For sure in your life, we cannot do infinity. 00:55:18.300 --> 00:55:22.410 But now, we have found a way to actually design 00:55:22.410 --> 00:55:28.890 our radar since sine theta is actually proportional to delta. 00:55:28.890 --> 00:55:30.990 Therefore, what we actually really need 00:55:30.990 --> 00:55:36.390 to do is to really maximize the number of slits 00:55:36.390 --> 00:55:39.650 we have so that actually we can create a radar which 00:55:39.650 --> 00:55:45.390 would really point toward the direction of the enemy, which 00:55:45.390 --> 00:55:48.700 is shown there, invading the earth. 00:55:48.700 --> 00:55:49.200 OK. 00:55:49.200 --> 00:55:50.670 [LAUGHTER] 00:55:50.670 --> 00:55:52.630 And we can actually detect it. 00:55:52.630 --> 00:55:53.130 OK. 00:55:53.130 --> 00:55:56.880 So we will take a five minute break before we actually 00:55:56.880 --> 00:56:01.530 go to the last part of the course, which is the connection 00:56:01.530 --> 00:56:04.360 to quantum mechanics. 00:56:04.360 --> 00:56:05.880 So we come back at 35. 00:56:05.880 --> 00:56:09.880 [SIDE CONVERSATIONS] 00:56:12.380 --> 00:56:13.880 [SIDE CONVERSATIONS] 00:56:13.880 --> 00:56:17.080 YEN-JIE LEE: OK so welcome come back from the break. 00:56:17.080 --> 00:56:21.370 So before we move to the connection 00:56:21.370 --> 00:56:24.250 to quantum mechanics, I would like 00:56:24.250 --> 00:56:27.085 to talk some more about what we have learned 00:56:27.085 --> 00:56:29.110 from the design of the radar. 00:56:29.110 --> 00:56:30.040 OK? 00:56:30.040 --> 00:56:33.940 So this essentially what we actually get. 00:56:33.940 --> 00:56:40.410 The position of the minima that required the phase difference 00:56:40.410 --> 00:56:45.100 delta is actually equal to 2 pi divided by N value, 00:56:45.100 --> 00:56:48.820 because it was this delta value. 00:56:48.820 --> 00:56:53.080 The N vectors is going to cancel each other. 00:56:53.080 --> 00:56:56.600 And you are going to form something like a circle 00:56:56.600 --> 00:57:02.920 if you choose delta equal to 2 pi divided by capital N. OK? 00:57:02.920 --> 00:57:05.090 And don't forget why this is actually delta. 00:57:05.090 --> 00:57:12.600 The delta is actually d sine theta divided by lambda. 00:57:12.600 --> 00:57:13.650 Right? 00:57:13.650 --> 00:57:14.470 OK? 00:57:14.470 --> 00:57:17.900 And times 2 pi. 00:57:17.900 --> 00:57:19.221 OK? 00:57:19.221 --> 00:57:19.720 Right? 00:57:19.720 --> 00:57:24.100 So therefore, you can see that the sine theta is actually 00:57:24.100 --> 00:57:28.580 proportional to lambda divided by N times d. 00:57:28.580 --> 00:57:31.030 OK? 00:57:31.030 --> 00:57:34.960 And in this case, you can see that if you increase 00:57:34.960 --> 00:57:38.900 N value, the resolution or the width 00:57:38.900 --> 00:57:43.270 of the central principal maxima is 00:57:43.270 --> 00:57:46.180 going to be decreasing as a function, though, 00:57:46.180 --> 00:57:47.860 N value you're putting. 00:57:47.860 --> 00:57:53.530 So in short, how do I actually design a high-resolution radar? 00:57:53.530 --> 00:57:59.720 What I really need is to have lambda to be small. 00:57:59.720 --> 00:58:00.310 OK? 00:58:00.310 --> 00:58:04.930 So that means I need to use high-frequency electromagnetic 00:58:04.930 --> 00:58:05.920 wave. 00:58:05.920 --> 00:58:09.310 I can maximize the N value. 00:58:09.310 --> 00:58:11.960 I can actually make d very large. 00:58:11.960 --> 00:58:15.980 That means I'm going to have a very large radar design. 00:58:15.980 --> 00:58:16.840 Right? 00:58:16.840 --> 00:58:20.480 Then I can have a very good resolution. 00:58:20.480 --> 00:58:21.110 OK. 00:58:21.110 --> 00:58:23.070 So we are almost done with radar. 00:58:23.070 --> 00:58:25.900 But there's a problem. 00:58:25.900 --> 00:58:30.680 The problem is that if you look at this, if this is actually 00:58:30.680 --> 00:58:34.760 the position of the principal minima, 00:58:34.760 --> 00:58:36.950 you can see that is always pointing 00:58:36.950 --> 00:58:43.520 to the center of the radar where the delta is equal to 0. 00:58:43.520 --> 00:58:44.240 OK? 00:58:44.240 --> 00:58:49.360 And then that means I can only scan in one direction. 00:58:49.360 --> 00:58:54.970 There is a reason why those radar are called phased radar. 00:58:54.970 --> 00:58:57.160 That is because now I can actually 00:58:57.160 --> 00:59:02.020 change the relative phase of all those point source emitted 00:59:02.020 --> 00:59:05.680 from the radar so that I can shift 00:59:05.680 --> 00:59:09.711 the direction of the central principal maxima. 00:59:09.711 --> 00:59:10.210 OK? 00:59:10.210 --> 00:59:13.630 So what is actually done here is like this. 00:59:13.630 --> 00:59:17.500 So basically, I can have introduced 00:59:17.500 --> 00:59:21.760 before emitting the electromagnetic wave, 00:59:21.760 --> 00:59:26.550 I can introduce a zero additional phase difference. 00:59:26.550 --> 00:59:29.830 And for the second one, I introduce additional phase 00:59:29.830 --> 00:59:31.690 difference of phi. 00:59:31.690 --> 00:59:32.360 OK? 00:59:32.360 --> 00:59:35.290 And for the third one, I introduce 00:59:35.290 --> 00:59:40.630 additional phase difference between the third slit-- 00:59:40.630 --> 00:59:44.430 or say the third emitter and the first emitter by 2 delta. 00:59:44.430 --> 00:59:48.730 And for N's emitter, I introduce a phase difference 00:59:48.730 --> 00:59:51.720 of N minus 1 phi. 00:59:51.720 --> 00:59:53.560 OK? 00:59:53.560 --> 01:00:01.040 If I add this phase difference into the setup, what 01:00:01.040 --> 01:00:03.440 I'm going to get is like this. 01:00:03.440 --> 01:00:11.280 So basically, delta will become 2 pi divided by lambda d sine 01:00:11.280 --> 01:00:15.892 theta minus phi angle. 01:00:15.892 --> 01:00:17.720 All right? 01:00:17.720 --> 01:00:23.180 And this phi is actually the artificial eddy phase 01:00:23.180 --> 01:00:25.490 difference between those source. 01:00:25.490 --> 01:00:26.330 OK? 01:00:26.330 --> 01:00:29.270 And that means I will require-- 01:00:29.270 --> 01:00:40.030 and this will be equal to 2 pi divided by N value, such 01:00:40.030 --> 01:00:42.790 as you have completely destructive interference. 01:00:42.790 --> 01:00:43.930 OK? 01:00:43.930 --> 01:00:47.620 I can now make this phi to be time-dependent. 01:00:47.620 --> 01:00:49.390 For example, it's increasing as a function 01:00:49.390 --> 01:00:53.530 of time, phi times t, right? 01:00:53.530 --> 01:01:00.180 Then what is going to happen is that as a function of time, 01:01:00.180 --> 01:01:03.400 I'm going to change the sine theta value 01:01:03.400 --> 01:01:07.690 so that I can get a complete cancellation, 2 pi over N. 01:01:07.690 --> 01:01:08.620 Right? 01:01:08.620 --> 01:01:12.220 So effectively, I'm changing the angle 01:01:12.220 --> 01:01:19.840 of the central principal maxima by introducing 01:01:19.840 --> 01:01:23.860 additional artificial phase difference between all 01:01:23.860 --> 01:01:25.590 those point source. 01:01:25.590 --> 01:01:26.290 OK? 01:01:26.290 --> 01:01:28.630 And this is actually the way we can actually 01:01:28.630 --> 01:01:34.180 rotate the place we are scanning up and down 01:01:34.180 --> 01:01:39.320 and get a very nice result to detect the enemy. 01:01:39.320 --> 01:01:40.620 OK? 01:01:40.620 --> 01:01:41.513 Any questions? 01:01:44.411 --> 01:01:45.821 No? 01:01:45.821 --> 01:01:46.320 OK. 01:01:46.320 --> 01:01:50.230 So now, I'm going to move on and discuss 01:01:50.230 --> 01:01:54.280 a very interesting experiment. 01:01:54.280 --> 01:01:59.250 So this is very exciting experiment content, 01:01:59.250 --> 01:02:02.640 billiard balls and the two slits. 01:02:02.640 --> 01:02:03.996 OK? 01:02:03.996 --> 01:02:05.370 And we will wonder, then, what is 01:02:05.370 --> 01:02:08.040 going to happen when those balls especially 01:02:08.040 --> 01:02:09.300 pass through the slit. 01:02:09.300 --> 01:02:12.220 Can anybody actually tell me what she is going to happen? 01:02:12.220 --> 01:02:15.060 And what will be the statistics, or say, 01:02:15.060 --> 01:02:19.740 the count, which I am going to go on to get in the receiver 01:02:19.740 --> 01:02:20.710 later? 01:02:20.710 --> 01:02:23.930 Anybody can actually tell me? 01:02:23.930 --> 01:02:27.950 If I actually shoot a lot of balls through this slit-- 01:02:27.950 --> 01:02:30.410 don't be shy, right? 01:02:30.410 --> 01:02:31.730 It's easy. 01:02:31.730 --> 01:02:34.210 No? 01:02:34.210 --> 01:02:35.664 Nobody wants-- 01:02:35.664 --> 01:02:37.452 STUDENT: They make [INAUDIBLE] 01:02:37.452 --> 01:02:39.180 YEN-JIE LEE: Yeah, that's right. 01:02:39.180 --> 01:02:40.630 Right? 01:02:40.630 --> 01:02:42.628 Doesn't surprise nobody, right? 01:02:42.628 --> 01:02:46.500 [LAUGHS] Yeah, too afraid of answering questions. 01:02:46.500 --> 01:02:51.980 OK, you can see that they make two path, right? 01:02:51.980 --> 01:02:52.820 No? 01:02:52.820 --> 01:02:53.450 Right? 01:02:53.450 --> 01:02:54.050 OK. 01:02:54.050 --> 01:02:55.190 Very good. 01:02:55.190 --> 01:02:59.630 So now, this is the exciting part. 01:02:59.630 --> 01:03:06.110 Now, instead of shooting billiard balls, what I'm going 01:03:06.110 --> 01:03:09.500 to do is to shoot electrons. 01:03:09.500 --> 01:03:12.680 So I can actually prepare an electron source 01:03:12.680 --> 01:03:16.160 and heat it up, such that it start to emit electrons. 01:03:16.160 --> 01:03:20.510 And I have two slits and have them pass through this slits. 01:03:20.510 --> 01:03:22.670 And I have a screen, which actually 01:03:22.670 --> 01:03:25.670 have an electron detector to count 01:03:25.670 --> 01:03:30.630 the number of electron which I am going to get on the screen. 01:03:30.630 --> 01:03:34.200 The reason why I call it single electron source 01:03:34.200 --> 01:03:41.040 is because each time I control my experiment such that it only 01:03:41.040 --> 01:03:45.524 emit one electron every time. 01:03:45.524 --> 01:03:46.940 OK? 01:03:46.940 --> 01:03:52.750 The question I'm trying to ask is, will I 01:03:52.750 --> 01:03:55.330 see some pattern, which is actually 01:03:55.330 --> 01:04:04.460 light like billiard balls, and they form two piles in a pack? 01:04:04.460 --> 01:04:07.420 That's actually option number one. 01:04:07.420 --> 01:04:12.410 Or I'm going to see really something crazy? 01:04:12.410 --> 01:04:16.480 It's the electron is going to be interfere-- 01:04:16.480 --> 01:04:21.150 it's going through the interference with itself. 01:04:21.150 --> 01:04:23.950 And that essentially option number two. 01:04:23.950 --> 01:04:24.450 OK? 01:04:24.450 --> 01:04:27.900 The lure of 8.03 is that everybody had to choose one. 01:04:27.900 --> 01:04:28.830 OK? 01:04:28.830 --> 01:04:36.640 So how many of you think what is going to happen is number one? 01:04:36.640 --> 01:04:38.410 Come on. 01:04:38.410 --> 01:04:41.680 I have only one electron each time. 01:04:41.680 --> 01:04:43.445 Nobody think so? 01:04:43.445 --> 01:04:43.945 Wow. 01:04:47.620 --> 01:04:49.283 Maybe all of you are wrong. 01:04:49.283 --> 01:04:55.110 [LAUGHS] How about the second option? 01:04:55.110 --> 01:04:55.867 STUDENT: [LAUGHS] 01:04:55.867 --> 01:04:57.450 YEN-JIE LEE: Hey, some of you actually 01:04:57.450 --> 01:04:58.580 didn't raise your hand. 01:04:58.580 --> 01:04:59.080 Come on. 01:04:59.080 --> 01:04:59.580 Come on. 01:04:59.580 --> 01:05:00.130 [LAUGHTER] 01:05:00.130 --> 01:05:02.260 OK, everybody. 01:05:02.260 --> 01:05:03.630 Wow. 01:05:03.630 --> 01:05:06.080 What is actually happening to you brain? 01:05:06.080 --> 01:05:08.310 [LAUGHTER] 01:05:08.310 --> 01:05:10.410 My brain is not functional like this. 01:05:10.410 --> 01:05:11.140 OK. 01:05:11.140 --> 01:05:16.200 So I really hope that I can bring the experiment to here. 01:05:16.200 --> 01:05:17.630 But unfortunately, that's actually 01:05:17.630 --> 01:05:19.910 going to be difficult. OK? 01:05:19.910 --> 01:05:21.440 So what I'm going to do is that I'm 01:05:21.440 --> 01:05:25.500 going to show you the experimental result, 01:05:25.500 --> 01:05:26.870 this video. 01:05:26.870 --> 01:05:30.680 And we are going to see what is going to happen. 01:05:30.680 --> 01:05:33.660 You see that there are dots popping out. 01:05:33.660 --> 01:05:34.830 What are those? 01:05:34.830 --> 01:05:40.340 Those are the detected electron one-by-one on screen. 01:05:40.340 --> 01:05:41.090 OK? 01:05:41.090 --> 01:05:45.630 So basically, you can see that the number of dots 01:05:45.630 --> 01:05:47.810 are increasing as a function of time. 01:05:47.810 --> 01:05:52.010 And I actually-- I mean, speeding up things a bit 01:05:52.010 --> 01:05:54.480 so that actually you can see the pattern quicker. 01:05:54.480 --> 01:05:54.980 OK. 01:05:54.980 --> 01:05:57.021 So you can see that there are more and more dots. 01:05:57.021 --> 01:05:59.000 And each time, you can see that I only get 01:05:59.000 --> 01:06:04.373 one electron per image here. 01:06:04.373 --> 01:06:05.260 Right? 01:06:05.260 --> 01:06:07.010 So you can see now there are more and more 01:06:07.010 --> 01:06:09.880 and more and more, and accumulating more data, 01:06:09.880 --> 01:06:12.800 like what we actually done in The Large Hadron Collider. 01:06:12.800 --> 01:06:15.590 We wait there, collect more data. 01:06:15.590 --> 01:06:18.410 And we are speeding things up. 01:06:18.410 --> 01:06:21.320 And you can see that, wow, something's 01:06:21.320 --> 01:06:24.250 actually developing. 01:06:24.250 --> 01:06:24.960 What is that? 01:06:28.410 --> 01:06:30.120 Can you see it? 01:06:30.120 --> 01:06:34.270 Now, you are speeding up like 1,000 times faster. 01:06:34.270 --> 01:06:37.026 You can see what pattern? 01:06:37.026 --> 01:06:38.874 STUDENT: Interference pattern. 01:06:38.874 --> 01:06:40.290 YEN-JIE LEE: Interference pattern. 01:06:40.290 --> 01:06:43.510 What is going on? 01:06:43.510 --> 01:06:44.660 You are not surprised? 01:06:44.660 --> 01:06:45.620 STUDENT: No. 01:06:45.620 --> 01:06:46.600 YEN-JIE LEE: Oh my god. 01:06:46.600 --> 01:06:47.320 What is going on? 01:06:47.320 --> 01:06:50.250 [LAUGHTER] 01:06:50.250 --> 01:06:53.490 I'm so surprised. 01:06:53.490 --> 01:06:54.750 Look at this. 01:06:54.750 --> 01:07:00.300 So I have emission of one electron each time. 01:07:00.300 --> 01:07:04.815 And that is actually the four snapshot which I took-- 01:07:04.815 --> 01:07:07.480 which actually this experiment, Hitachi Group 01:07:07.480 --> 01:07:08.940 actually did this experiment. 01:07:08.940 --> 01:07:13.880 You can actually click on this link to the more detail. 01:07:13.880 --> 01:07:17.600 And they took four snapshots of the experiment. 01:07:17.600 --> 01:07:20.240 And you can see that in the beginning, 01:07:20.240 --> 01:07:23.570 you can see clearly each time you only get 01:07:23.570 --> 01:07:27.230 one electron out of the source. 01:07:27.230 --> 01:07:28.760 OK? 01:07:28.760 --> 01:07:31.140 But as a function of time, you're 01:07:31.140 --> 01:07:33.420 accumulating more and more. 01:07:33.420 --> 01:07:35.580 And you see that clearly, there's 01:07:35.580 --> 01:07:43.410 a pattern forming, which, is actually consistent with what 01:07:43.410 --> 01:07:47.540 we see in this calculation. 01:07:47.540 --> 01:07:48.040 OK? 01:07:48.040 --> 01:07:52.470 So I think that's actually truly amazing. 01:07:52.470 --> 01:07:55.050 And what does that mean? 01:07:55.050 --> 01:08:02.011 That means the electron is playing with itself. 01:08:02.011 --> 01:08:04.115 It's interfering with itself. 01:08:06.620 --> 01:08:07.220 Right? 01:08:07.220 --> 01:08:08.960 That's really strange. 01:08:08.960 --> 01:08:09.980 What is going to happen? 01:08:09.980 --> 01:08:11.130 What is going on? 01:08:11.130 --> 01:08:17.630 So one single electron pass through both slit, which is 01:08:17.630 --> 01:08:19.050 actually the option you choose. 01:08:19.050 --> 01:08:21.220 Surprise me. 01:08:21.220 --> 01:08:25.630 And then they interfere like waves. 01:08:25.630 --> 01:08:31.020 And they produce the pattern which we see on the screen. 01:08:31.020 --> 01:08:35.850 That is actually really crazy to me. 01:08:35.850 --> 01:08:40.359 What is actually even more crazy is this situation. 01:08:40.359 --> 01:08:47.160 So now, if I make measurement in front of the slit, OK, so now, 01:08:47.160 --> 01:08:50.970 I puts on a little device. 01:08:50.970 --> 01:08:54.750 When the electron pass through one of the slit, 01:08:54.750 --> 01:08:57.701 I say, send me a signal. 01:08:57.701 --> 01:08:58.200 OK? 01:08:58.200 --> 01:09:01.950 So now, I can clearly know that which 01:09:01.950 --> 01:09:05.939 slit the electron is actually going through 01:09:05.939 --> 01:09:07.200 in the experiment. 01:09:07.200 --> 01:09:08.220 OK? 01:09:08.220 --> 01:09:13.170 And the crazy thing is that if I do that, then it 01:09:13.170 --> 01:09:16.359 becomes two piles. 01:09:16.359 --> 01:09:17.054 OK? 01:09:17.054 --> 01:09:19.220 Of course, maybe there are some diffraction pattern. 01:09:19.220 --> 01:09:22.370 But it really changes the pattern 01:09:22.370 --> 01:09:25.279 of the experimental result. And that is actually 01:09:25.279 --> 01:09:27.319 really very strange. 01:09:27.319 --> 01:09:30.500 And we are going to talk about that briefly 01:09:30.500 --> 01:09:33.960 in the next lecture. 01:09:33.960 --> 01:09:37.365 So before the end, I'm going to show you 01:09:37.365 --> 01:09:39.920 an additional demonstration which 01:09:39.920 --> 01:09:43.189 motivate the discussion what we are going 01:09:43.189 --> 01:09:47.109 to have in the next lecture. 01:09:47.109 --> 01:09:55.920 So now, I can actually turn off the light again and also hide 01:09:55.920 --> 01:09:57.950 the image. 01:09:57.950 --> 01:09:58.460 OK. 01:09:58.460 --> 01:10:00.978 I hope I can find the pattern. 01:10:00.978 --> 01:10:04.620 [LAUGHS] All right. 01:10:04.620 --> 01:10:08.290 So here, I have two laser. 01:10:08.290 --> 01:10:11.940 So I'm going to turn up the first laser. 01:10:11.940 --> 01:10:17.970 And this laser is going to pass through a two slit-- 01:10:17.970 --> 01:10:24.480 a two really nearby slit and form an interference pattern. 01:10:24.480 --> 01:10:26.490 As you can see on the wall-- 01:10:26.490 --> 01:10:29.850 I hope you can see, I don't know if you can see clearly-- 01:10:29.850 --> 01:10:35.760 that you can see there are many, many dots, nearby dots, 01:10:35.760 --> 01:10:38.670 which actually shows you the position 01:10:38.670 --> 01:10:43.270 of the principal maximas, right, because are actually 01:10:43.270 --> 01:10:45.120 two slit experiment. 01:10:45.120 --> 01:10:49.880 Therefore, how many children do we have in the family? 01:10:49.880 --> 01:10:50.890 Zero, right? 01:10:50.890 --> 01:10:52.720 Because they are-- 01:10:52.720 --> 01:10:54.580 OK, they just got married, maybe. 01:10:54.580 --> 01:10:56.460 [LAUGHS] All right. 01:10:56.460 --> 01:10:59.470 So therefore, you will see only adults. 01:10:59.470 --> 01:11:04.210 And that is actually the principal maximas. 01:11:04.210 --> 01:11:07.420 You can see many, many nearby dots. 01:11:07.420 --> 01:11:10.000 They are almost equally bright. 01:11:10.000 --> 01:11:10.900 OK? 01:11:10.900 --> 01:11:15.050 But there's something happening to this pattern as well. 01:11:15.050 --> 01:11:17.620 And you can see that-- wait, wait, wait a second. 01:11:17.620 --> 01:11:21.760 In the calculation we get the principle maxima 01:11:21.760 --> 01:11:24.040 to have the same height, right? 01:11:24.040 --> 01:11:28.250 That means you are going to get exactly those same intensity 01:11:28.250 --> 01:11:30.790 for all the maximas. 01:11:30.790 --> 01:11:33.440 But you don't see that here. 01:11:33.440 --> 01:11:38.940 You can see that if you move away from the center too much, 01:11:38.940 --> 01:11:42.210 the intensity is decreasing. 01:11:42.210 --> 01:11:43.470 You see at the edge? 01:11:43.470 --> 01:11:49.440 It actually even goes to zero. 01:11:49.440 --> 01:11:50.750 Right? 01:11:50.750 --> 01:11:52.350 What is actually happening? 01:11:52.350 --> 01:11:57.490 Something clearly is actually missing in our calculation. 01:11:57.490 --> 01:12:01.780 And that missing part is actually 01:12:01.780 --> 01:12:06.270 diffraction, which we will talk about that in the next lecture. 01:12:06.270 --> 01:12:14.800 So if you compare this pattern to the second demo, 01:12:14.800 --> 01:12:17.410 you can see in the right hand side 01:12:17.410 --> 01:12:20.560 setup, which I have here, which I should give you 01:12:20.560 --> 01:12:22.540 a projection on the wall, which is actually 01:12:22.540 --> 01:12:30.190 lower part of the demo, you can see that this laser actually 01:12:30.190 --> 01:12:32.800 pass through a single slit. 01:12:32.800 --> 01:12:36.340 But this slit is actually pretty wide. 01:12:36.340 --> 01:12:37.120 OK? 01:12:37.120 --> 01:12:42.400 And you can see that indeed, you see the laser coming out, 01:12:42.400 --> 01:12:46.730 but essentially, not a single spot. 01:12:46.730 --> 01:12:49.160 And it has some kind of pattern, which 01:12:49.160 --> 01:12:52.130 is actually popping out there. 01:12:52.130 --> 01:12:56.000 And this is also related to interference 01:12:56.000 --> 01:12:58.740 between infinite number of source. 01:12:58.740 --> 01:12:59.240 OK? 01:12:59.240 --> 01:13:04.700 And you can see that the pattern seems to really pretty 01:13:04.700 --> 01:13:11.060 similar to the pattern we see in the upper demo, 01:13:11.060 --> 01:13:15.380 except that upper demo have individual similar structure, 01:13:15.380 --> 01:13:19.820 which is the principal maxima from the two slit interference. 01:13:19.820 --> 01:13:25.400 And we are going to solve the mystery in the lecture 01:13:25.400 --> 01:13:26.830 next time. 01:13:26.830 --> 01:13:27.330 OK. 01:13:27.330 --> 01:13:29.170 So thank you very much. 01:13:29.170 --> 01:13:33.300 And if you have any questions related to the lecture today, 01:13:33.300 --> 01:13:35.206 I will be here to answer your questions. 01:13:43.850 --> 01:13:46.920 So this is a demo which we would like 01:13:46.920 --> 01:13:52.080 to show you, Single Slit and the Double Slit Interference 01:13:52.080 --> 01:13:52.991 Pattern. 01:13:52.991 --> 01:13:53.490 OK? 01:13:53.490 --> 01:13:56.730 So the first scene is the setup. 01:13:56.730 --> 01:14:00.210 So we have a laser beam, which is actually 01:14:00.210 --> 01:14:10.730 passing through this either single slit or double slit 01:14:10.730 --> 01:14:11.790 experiment. 01:14:11.790 --> 01:14:17.030 And then the laser beam will be going through this 01:14:17.030 --> 01:14:20.550 and interfere and show interesting pattern 01:14:20.550 --> 01:14:22.410 on the screen. 01:14:22.410 --> 01:14:25.050 And there are two setup. 01:14:25.050 --> 01:14:30.130 The left-hand side one is two slit interference experiment. 01:14:30.130 --> 01:14:36.940 And right-hand side is a single slit diffraction experiment. 01:14:36.940 --> 01:14:40.860 So you can see left-hand side one, I already turned it on. 01:14:40.860 --> 01:14:43.290 Laser beam passed through two slits. 01:14:43.290 --> 01:14:47.990 And they form complicated pattern on the screen. 01:14:47.990 --> 01:14:51.400 And you can see there are two kinds of structure here. 01:14:51.400 --> 01:14:54.000 The first one is the very fine structure, 01:14:54.000 --> 01:14:58.070 which you can see that it's like some row of dots 01:14:58.070 --> 01:15:00.120 in the center of the pattern. 01:15:00.120 --> 01:15:05.740 And there are larger scale pattern as well, 01:15:05.740 --> 01:15:10.100 which you can see that the overall intensity of all 01:15:10.100 --> 01:15:13.160 those little dots are also variating 01:15:13.160 --> 01:15:17.880 as a function of distance with respect to the center. 01:15:17.880 --> 01:15:21.190 So during the lecture, we were wondering what actually 01:15:21.190 --> 01:15:23.500 cause this kind of pattern. 01:15:23.500 --> 01:15:25.230 And the answer is that this is actually 01:15:25.230 --> 01:15:30.390 coming from the effect of single slit interference. 01:15:30.390 --> 01:15:33.400 The reason why we have this pattern 01:15:33.400 --> 01:15:37.000 is because the two slit is actually not 01:15:37.000 --> 01:15:41.060 infinitely narrow in my setup. 01:15:41.060 --> 01:15:45.360 Therefore, within a single slit, there 01:15:45.360 --> 01:15:49.800 is already a interference pattern coming out of it. 01:15:49.800 --> 01:15:55.710 Therefore, the compound effect, results in a very complicated 01:15:55.710 --> 01:15:57.570 structure we see on the screen. 01:15:57.570 --> 01:16:00.600 So to demonstrate this effect, now, I'm 01:16:00.600 --> 01:16:05.160 going to turn on the right-hand side setup. 01:16:05.160 --> 01:16:06.870 In the right-hand side setup, I am 01:16:06.870 --> 01:16:10.140 going to have the laser beam, which 01:16:10.140 --> 01:16:15.840 you see emitting from here, pass through a single slit. 01:16:15.840 --> 01:16:19.500 I actually set it up so that they 01:16:19.500 --> 01:16:24.300 have the same width between the single slit experiment 01:16:24.300 --> 01:16:26.730 and double slit experiment. 01:16:26.730 --> 01:16:35.960 And then you can see after I turn it on, 01:16:35.960 --> 01:16:41.450 you can see that now, we have two sets of pattern. 01:16:41.450 --> 01:16:46.580 The lower set is actually coming from a single slit interference 01:16:46.580 --> 01:16:47.540 experiment. 01:16:47.540 --> 01:16:52.760 And you can see very nicely that first of all, it 01:16:52.760 --> 01:16:56.690 has a similar pattern, like what we see in the double slit 01:16:56.690 --> 01:16:58.080 experiment. 01:16:58.080 --> 01:17:02.460 Secondly, you can see that basically, we carefully tune 01:17:02.460 --> 01:17:05.060 these two experiments so that the distance 01:17:05.060 --> 01:17:09.750 between the slit and the screen is roughly the same. 01:17:09.750 --> 01:17:12.920 Finally, we also set it up, as I've mentioned before, 01:17:12.920 --> 01:17:16.120 such that the width of the individual slit 01:17:16.120 --> 01:17:19.490 in the double and the single slit experiment are the same. 01:17:19.490 --> 01:17:22.850 And you can see that with single slit experiment, 01:17:22.850 --> 01:17:27.140 we also see a very similar pattern 01:17:27.140 --> 01:17:29.900 that you have a central maxima. 01:17:29.900 --> 01:17:40.850 You have a high-intensity light going toward the center 01:17:40.850 --> 01:17:42.590 of the pattern. 01:17:42.590 --> 01:17:49.320 And the intensity actually decrease dramatically really 01:17:49.320 --> 01:17:52.250 quickly as a function of distance. 01:17:52.250 --> 01:17:55.460 And also, you can see that the pattern actually 01:17:55.460 --> 01:17:59.780 matches with what you see in the double slit experiment 01:17:59.780 --> 01:18:00.680 very well. 01:18:00.680 --> 01:18:03.710 And that is actually pretty remarkable. 01:18:03.710 --> 01:18:08.240 And from these two experiment, we 01:18:08.240 --> 01:18:12.510 understand why we have also a complicated structure 01:18:12.510 --> 01:18:15.620 in the double slit experiment, not 01:18:15.620 --> 01:18:18.700 just like many, many little maximas, 01:18:18.700 --> 01:18:20.510 many, many little dots. 01:18:20.510 --> 01:18:23.620 But also, you have this overall modulation 01:18:23.620 --> 01:18:25.370 in the light intensity. 01:18:25.370 --> 01:18:29.060 And that is actually mainly coming from the single slit 01:18:29.060 --> 01:18:30.910 diffraction pattern.