1 00:00:00,060 --> 00:00:06,570 The aim of the section is to learn about the very early concepts of electrodynamics, so we will discuss 2 00:00:06,750 --> 00:00:11,000 charges, electric fields, magnetic fields, but also light. 3 00:00:11,730 --> 00:00:15,750 So this very first lecture is about the early theories of light. 4 00:00:17,310 --> 00:00:24,270 So the more modern theory started in 16 and 37 and then also several years later, this car. 5 00:00:24,270 --> 00:00:29,360 And Newton said that light behaves like it consists out of particles. 6 00:00:30,150 --> 00:00:36,060 So he said that every source of light emits a large number of particles which are perfectly elastic, 7 00:00:36,390 --> 00:00:37,730 rigid and weightless. 8 00:00:38,730 --> 00:00:45,450 And as it turns out, this theory can describe several phenomena of light quite well, for example, 9 00:00:45,450 --> 00:00:45,870 a mirror. 10 00:00:46,620 --> 00:00:52,800 So imagine you are this child here holding a balloon and you look in the mirror, then you can consider 11 00:00:53,100 --> 00:01:00,420 these beams of light here that go in a straight line and which are deflected or reflected at the mirror 12 00:01:00,720 --> 00:01:04,170 so that they will hit, for example, the balloon or your feet. 13 00:01:04,680 --> 00:01:12,180 So this means you will see these two objects of the feet and the balloon on the other side of the mirror 14 00:01:12,180 --> 00:01:14,970 when you continue these beams along the other side. 15 00:01:15,540 --> 00:01:19,940 Well, actually, what you are seeing is the reflected light which goes along this direction. 16 00:01:20,670 --> 00:01:23,730 So that's something we can explain with a particle theory. 17 00:01:24,480 --> 00:01:30,530 But there are other phenomena like refraction, diffraction or interference that we cannot explain with 18 00:01:30,540 --> 00:01:33,120 by this theory, which means it's not correct. 19 00:01:33,460 --> 00:01:38,010 Another important field of early electrodynamics is geometrical optics. 20 00:01:38,910 --> 00:01:44,880 And in a sense, this can also be explained by a particle theory of light where we consider these beams 21 00:01:44,880 --> 00:01:48,120 of light particles going along a straight direction. 22 00:01:48,930 --> 00:01:53,880 So, for example, imagine you are this flower here and you look in a spherical mirror. 23 00:01:54,240 --> 00:02:00,570 Then you can consider all of these different beams of light that hit this focus point of the mirror. 24 00:02:00,870 --> 00:02:04,220 And you can construct then the image that you will see. 25 00:02:04,710 --> 00:02:10,710 And as it turns out, you will see yourself upside down and with a much smaller size. 26 00:02:11,700 --> 00:02:17,370 So that's probably something you have learned quite early in school, how to construct these images 27 00:02:17,670 --> 00:02:19,380 based on these spherical mirrors. 28 00:02:19,830 --> 00:02:25,620 And quite similarly, you can construct the images of objects when you look through a lens. 29 00:02:26,670 --> 00:02:33,120 For example, if you take flour and put it quite far away from the lens, you can construct the image 30 00:02:33,120 --> 00:02:38,340 using, again, these beams of light going through this focus point here, for example. 31 00:02:38,970 --> 00:02:44,570 And you will see in this case, the flour will be upside down and also will have a much smaller size. 32 00:02:45,270 --> 00:02:52,050 So it seems like this is also possible to be described by a particle theory of light. 33 00:02:52,890 --> 00:02:59,700 But in reality, this is not true because we cannot really say what is happening inside of the lens. 34 00:03:00,360 --> 00:03:05,100 And in order to understand what is happening here, we need to use a different theory. 35 00:03:05,220 --> 00:03:07,050 And this is a wave theory of light. 36 00:03:07,950 --> 00:03:16,170 So this was first really explained in 16 seventy eight by Huygens, who predicted this wave theory of 37 00:03:16,170 --> 00:03:19,680 light, where he said that light consists out of waves. 38 00:03:19,710 --> 00:03:24,630 You can see them here and these individual blue sinusoidal functions. 39 00:03:25,290 --> 00:03:34,200 And in red, you see here these wave fronds, which are basically positions or planes where the wave 40 00:03:34,200 --> 00:03:35,400 is in the same state. 41 00:03:35,940 --> 00:03:43,010 So these wave runs are always perpendicular to the direction in which the wave is propagating. 42 00:03:44,550 --> 00:03:53,160 And when you consider such a wave theory for light, you can finally explain phenomena like refraction 43 00:03:53,160 --> 00:03:56,970 diffraction and also you can explain the different colors of light. 44 00:03:57,960 --> 00:04:05,480 For example, here, what you can see is when you go, for example, from air to glass, so you take 45 00:04:05,610 --> 00:04:10,020 light and shine it onto this interface of air and glass. 46 00:04:10,530 --> 00:04:17,100 You will see that the light is much faster in air and it's a bit slower in the glass. 47 00:04:18,000 --> 00:04:25,440 So what happens is that the wavelength and therefore the distance between these two wave fronts will 48 00:04:25,440 --> 00:04:27,420 be much smaller in the glass. 49 00:04:28,200 --> 00:04:35,760 And as a consequence, because this distance must be smaller, the direction of the light propagation 50 00:04:35,760 --> 00:04:36,540 will change. 51 00:04:37,380 --> 00:04:44,130 And it turns out that when you go into an optically dense medium like like, yeah. 52 00:04:44,130 --> 00:04:53,490 Like glass or also in water, the direction of propagation will be changed towards this Dasht black 53 00:04:53,490 --> 00:04:56,040 line, which is perpendicular to this interface. 54 00:04:57,220 --> 00:04:59,280 So this is, for example, why when you look. 55 00:05:00,000 --> 00:05:07,620 And water, everything looks a bit at a different angle now, another phenomenon that you can observe 56 00:05:07,620 --> 00:05:09,310 is the direction. 57 00:05:09,400 --> 00:05:15,690 So when you take a beam of light and consider it as a wave and you shine onto it, such a small slit 58 00:05:15,690 --> 00:05:23,280 here, what you will see is that after the slit, you will see such spherical waves because starting 59 00:05:23,280 --> 00:05:29,150 from this slit here, the the wave starts to propagate into all different directions because these wave 60 00:05:29,150 --> 00:05:30,390 fronts are deformed. 61 00:05:32,100 --> 00:05:40,170 And also what you can see is that when you assume that light of different color has different wavelengths, 62 00:05:40,590 --> 00:05:45,570 that you can split up light into the different components. 63 00:05:46,410 --> 00:05:54,210 So let's say you start from sunlight, which is essentially white, or you could also see a very bright 64 00:05:54,210 --> 00:05:54,620 yellow. 65 00:05:55,230 --> 00:06:02,100 And what we know is that this light consists of a superposition of all different colors, so all different 66 00:06:02,100 --> 00:06:02,820 wavelengths. 67 00:06:03,960 --> 00:06:11,850 So now when you consider this interface here of air and glass in such a prism, what you will see is 68 00:06:11,850 --> 00:06:17,910 you will find different refraction patterns corresponding to the different colors of light. 69 00:06:18,090 --> 00:06:24,030 So depending on the wavelength of the light wave that you want to consider, the angle here is a bit 70 00:06:24,030 --> 00:06:24,590 different. 71 00:06:24,960 --> 00:06:30,840 For example, for purple, the angle will be the smallest and ferraz, the angle will be the largest 72 00:06:30,960 --> 00:06:32,900 sort of light starts to split up. 73 00:06:33,730 --> 00:06:41,280 And you have here the second interface where you will again see some additionals splitting of the light. 74 00:06:41,550 --> 00:06:48,390 So you can really then hold here a piece of paper, for example, and see how the light split up into 75 00:06:48,390 --> 00:06:49,320 the different colors. 76 00:06:49,800 --> 00:06:55,080 So that is obviously something that cannot be explained by a particle theory of light. 77 00:06:56,370 --> 00:07:04,020 So it turns out that the wave theory of light was believed to be the correct theory for quite a long 78 00:07:04,020 --> 00:07:04,400 time. 79 00:07:04,980 --> 00:07:10,260 And the main reason or the main experiment why this was believed is the double slit experiment. 80 00:07:11,310 --> 00:07:18,120 So what we do here is we have two slits there for the double slit experiment and we take a source of 81 00:07:18,120 --> 00:07:20,790 light with the beams of light. 82 00:07:21,030 --> 00:07:24,930 And then here we have a screen to detect the intensity pattern. 83 00:07:25,920 --> 00:07:29,760 So first tell us discuss what happens when light is the particle. 84 00:07:30,780 --> 00:07:38,340 So when light is a particle, we can take the light bulb here and construct these individual beams of 85 00:07:38,340 --> 00:07:38,670 light. 86 00:07:39,000 --> 00:07:43,170 And what we expect then here is an intensity pattern that looks like this. 87 00:07:44,910 --> 00:07:51,510 So mainly the light goes to through these two slits, hits the screen and gives maximum in the intensity. 88 00:07:52,500 --> 00:08:00,750 However, when this experiment was conducted, it was seen that the detected intensity looks like this. 89 00:08:01,620 --> 00:08:07,680 So this is in total disagreement with the expectation from light being a particle. 90 00:08:07,800 --> 00:08:11,670 So what we have to consider here is that light is a wave. 91 00:08:12,870 --> 00:08:15,630 So, again, we have these wave fronts here. 92 00:08:15,810 --> 00:08:19,050 Our light bulb is very symmetric, basically. 93 00:08:19,320 --> 00:08:22,610 So we see these radial wave fronts here. 94 00:08:22,890 --> 00:08:28,020 And if we are far away from the light source, there will be these parallel lines here. 95 00:08:28,050 --> 00:08:30,030 So it is a bit of an approximation. 96 00:08:30,030 --> 00:08:36,240 But you can see here when we just go along this direction, these look a bit like parallel lines and 97 00:08:36,240 --> 00:08:41,550 this approximation becomes better and better the far away we are from the light bulb. 98 00:08:42,960 --> 00:08:48,990 So when these wave fronts hits these two slits, we will again see the phenomenon that we have discussed 99 00:08:48,990 --> 00:08:49,560 earlier. 100 00:08:49,590 --> 00:08:52,640 So we get here these radio wave fronts. 101 00:08:53,250 --> 00:09:00,000 And again, if we are quite far away from these two slits, we will get such straight lines for the 102 00:09:00,000 --> 00:09:06,840 way fronts again and we will have these wave fronts starting from these two slits. 103 00:09:06,840 --> 00:09:14,070 So they will interfere here at these positions and especially they will interfere close to the screen. 104 00:09:15,510 --> 00:09:22,260 So now if we take these two beams with these straight line fronds on top of them, we can look at the 105 00:09:22,260 --> 00:09:25,140 length of these two different beams and compare them. 106 00:09:25,890 --> 00:09:31,350 And it turns out that if or when you look here, this black line and this black line, they are of equal 107 00:09:31,350 --> 00:09:31,920 length. 108 00:09:31,920 --> 00:09:40,080 And the only difference in the length is here, this area and this length of this red triangle, which 109 00:09:40,080 --> 00:09:41,460 I called Delta in here. 110 00:09:43,170 --> 00:09:52,410 And now the condition so that we get a maximum here in this intensity spectrum is that when here we 111 00:09:52,410 --> 00:09:57,300 have an interference of two máxima in the waves. 112 00:09:57,950 --> 00:10:00,980 So this means we have a positive interference. 113 00:10:01,230 --> 00:10:04,380 So the phases of the waves must be equal. 114 00:10:05,460 --> 00:10:11,490 And this can only be true if this delta here is a multiple of the wavelength itself. 115 00:10:12,780 --> 00:10:18,840 So we have a condition for this length here, Delta and as end times lambda, which is the wavelength. 116 00:10:19,320 --> 00:10:23,390 And we also know that this side of the triangle can be measured. 117 00:10:23,430 --> 00:10:27,720 So let's call it a this is something that is determined by the double slit itself. 118 00:10:27,720 --> 00:10:29,760 It's the distance between the two slits. 119 00:10:31,530 --> 00:10:33,920 Now, we can also draw here a second triangle. 120 00:10:34,140 --> 00:10:40,110 So this is on one side, the distance from the double slit to the screen, let's call it D. 121 00:10:40,740 --> 00:10:48,090 And then we have here the distance from this middle point to the position where we expect this intensity 122 00:10:48,090 --> 00:10:48,630 maximum. 123 00:10:49,320 --> 00:10:54,810 So that is X and that's also give it an index, because you can see here we have several maximum. 124 00:10:55,140 --> 00:10:59,130 So this could be a zero x one, two, three. 125 00:11:00,810 --> 00:11:05,050 And now if we consider the distance here quite far. 126 00:11:05,310 --> 00:11:10,380 So basically this angle here is very small and this angle here is very small. 127 00:11:11,270 --> 00:11:17,310 We can say that Delta and over a so this ratio here is equal to this ratio. 128 00:11:17,560 --> 00:11:18,730 Extend over the. 129 00:11:19,350 --> 00:11:21,560 So this is not totally correct. 130 00:11:21,570 --> 00:11:29,610 It would be correct to say that the ratio of Delta and over this side here is equal to and over this 131 00:11:29,820 --> 00:11:34,610 D but since this angle is very small, these two sides are almost of equal length. 132 00:11:34,620 --> 00:11:36,750 So we can say that this is true here. 133 00:11:37,290 --> 00:11:43,790 So we get a condition for the position of the intensity, maximum distribution and the experiment. 134 00:11:44,550 --> 00:11:53,040 So we know that X and is now D over A, which are both determined by our experiment times, the wavelength 135 00:11:53,220 --> 00:11:56,720 times and number zero one to the three. 136 00:11:56,730 --> 00:11:59,020 And we can also go along the negative direction. 137 00:12:00,930 --> 00:12:05,850 So this experiment could not be explained with light being a particle. 138 00:12:06,600 --> 00:12:11,040 So it was really necessary to consider light as being a wave. 139 00:12:12,270 --> 00:12:20,850 So this double slit experiment was really the reason why in 1864 actual formulated his Maxwell's equations 140 00:12:21,270 --> 00:12:25,750 and these equations will be the main focus point of this whole course. 141 00:12:26,130 --> 00:12:32,640 So they are the fundamental equations that allow to describe the classical electrodynamics. 142 00:12:33,840 --> 00:12:40,040 And also it turns out that it was quite absurd at that time to think of light as being consistent out 143 00:12:40,050 --> 00:12:43,740 of particles because light does not have a mass and light. 144 00:12:43,970 --> 00:12:49,310 Does not have a charge, so this makes light quite different to Electron's, for example. 145 00:12:50,570 --> 00:12:57,530 So this is really the status quo in 1864 and I would say even until 1900. 146 00:12:58,280 --> 00:13:04,060 And this is also the state of physics that we want to focus here in this course. 147 00:13:05,310 --> 00:13:10,050 Still, I want to tell you also in this lecture that this is not the whole truth. 148 00:13:10,790 --> 00:13:16,550 So in the year around 1900, there were two famous experiments. 149 00:13:16,580 --> 00:13:24,230 This was the photoelectric effect and the black body radiation and the interpretation or the understanding 150 00:13:24,230 --> 00:13:25,880 of these two effects required. 151 00:13:26,090 --> 00:13:29,240 That light must also have particle like properties. 152 00:13:30,260 --> 00:13:36,800 So it was Einstein who delivered the explanation to the photoelectric effect and which in the end also 153 00:13:37,040 --> 00:13:41,990 gave rise to this wave particle dualism of light and also of matter. 154 00:13:42,890 --> 00:13:50,940 So it turns out that today the common conception of light and also of matter is that it consists out 155 00:13:50,970 --> 00:13:54,920 of particle like properties and wavelike properties. 156 00:13:55,640 --> 00:13:58,490 And in some phenomena, the wavelike properties dominate. 157 00:13:58,500 --> 00:14:04,130 For example, in our double slit experiment and in other experiments, the particle like properties 158 00:14:04,130 --> 00:14:05,800 become much more important. 159 00:14:06,920 --> 00:14:14,090 And this whole dualism of waves and particles was a starting point of the theory called quantum mechanics. 160 00:14:14,900 --> 00:14:18,260 So this is nothing that we want to consider here in discourse. 161 00:14:18,260 --> 00:14:25,010 But if you're really interesting, interested in this field of physics, please have a look at my course 162 00:14:25,010 --> 00:14:26,120 here on this website. 163 00:14:27,440 --> 00:14:34,880 But also, I must tell you that it's still quite difficult to understand everything that is involved 164 00:14:34,880 --> 00:14:40,280 in this wave particle dualism and in quantum mechanics, because even Einstein, after working for more 165 00:14:40,280 --> 00:14:45,590 than 50 years in this field, was still not so sure what light actually is. 166 00:14:46,550 --> 00:14:51,920 However, it turns out that for the majority of experiments, we are good to go when we say that light 167 00:14:51,920 --> 00:14:52,510 is a wave. 168 00:14:52,670 --> 00:14:55,940 So this is what this whole electrodynamics is about. 169 00:14:56,750 --> 00:15:01,400 So that was a lecture about the early theory of light and the following lecture. 170 00:15:01,410 --> 00:15:07,790 We want to consider the early theories of charge, electric field, and also we want to formulate the 171 00:15:07,790 --> 00:15:08,510 Coulomb law.