 Hi, I'm Zor. Welcome to Unisor Education. I would like to continue talking about properties of light. In this case, I'm kind of changing the name of the topics we used to have, something which we called properties of light. Now, let's talk about phenomena of light. It's basically the same thing, just a continuation. Certain phenomena of light we have already discussed in the previous topics. Whenever we're talking about properties of light. For example, reflection, refraction, and some others. This topic is more about the details of each of these phenomena, if we can say so. So, today we'll talk about a very important principle. It's called Huygens' principle. Well, Huygens is the name of the Dutch mathematician and physicist. Sometimes it's pronounced Huygens, sometimes Huygens. It doesn't really matter. What matters is that he has introduced a very important approach to understanding what actual light is. Now, historically there were two different approaches to explain the different properties and phenomena of light. One of them is called corpuscular. That's when light consists of certain tiny corpuscles, like molecules, if you wish, which are actually flying from the source of the light to whatever light goes. Now, this was an interesting concept. One of the proponents of this was a very authoritative figure of Isaac Newton. But it did not explain some phenomena. For example, it was fine when we were talking about reflection. So, when reflection goes, light goes this and then this. Well, that's kind of like a billiard ball, basically. So, the corpuscular theory was finding that this is just a reflection, a mechanical reflection, so to speak. But whenever we were talking about something different, for example, we once talked about a reflection. Whenever the light goes at the angle here, it changes the direction between, let's say, air and glass. Now, that was not really very easy to explain using corpuscular theory. Newton was trying to explain it in some way. Let's not go into the details, but it was really, I mean, it was obviously wrong, basically. Let's put it this way. So, the new theory, new explanation actually was needed. And Christian Huygens was actually suggesting this particular explanation. And that's what I will go into the details right now. And using this explanation, I'll try to explain some phenomena which this particular approach is actually very good for. So, the first and most important aspect of Huygens' principle, as we call it right now, was that light is actually the waves. Now, what kind of waves we know? Well, at least in the 17th century, we will definitely talk about sound waves. So, what is the sound wave? Sound waves is basically mechanical change of the density of the air and its longitudinal change. So, whenever, if this is the source of sound, then it actually makes more dense the air around it. And then it was the opposite effect. This density was transferred to the next layer and next layer and then spherical wave fronts, we can talk about wave fronts, were propagating from the source of the sound. So, it's longitudinal oscillations or waves of air, of some environment in this case. Maybe it's metal or water, whatever the sound is propagating in. So, the idea of Huygens was that we have something which is penetrating everything. It's called ether or ether. It's spelled sometimes like this or letter A sometimes goes in front of it, ether. So, the idea of this substance, so to speak, is that it's everywhere, including the outer space. So, it penetrates everything. And the light is actually a longitudinal, longitudinal, what's important, longitudinal oscillations of ether. That was his idea. Now, similarly to sound, the light in the ether is supposed to be propagating in waves. So, he introduced the concept of a wave front. So, what is a wave front? Let's just be, by the way, it exists not only in light, but it exists in sound as well, and in any other waves, like waves on the surface of water. Now, what is the wave front? Well, wave front is basically the number or set of all the points around the source where the light or sound or water waves reach at the same time, at a maximum distance from the source. So, the wave front moves, it expands from the source to all the directions, and wherever it managed to reach, and all the points which basically are at the same time synchronization. So, all the points where the oscillations have reached at that time, T, that's the wave front. So, it's furthest most from the source and simultaneously achieving this oscillation. So, this is the wave front. That's a pretty nice definition, we can use it up, obviously. So, what was the principle which Huygens actually has suggested? His principle was the following. Let's say, at any time T, there is some kind of a wave front, wherever it is, doesn't really matter. Now, at time T equals to zero, if the source of the oscillation is, let's say, a point, then the wave front is basically that particular point. At time T zero, it doesn't really propagate anywhere. But let's say, at time T greater than zero, the oscillations reached certain points around this source. So, if the source is a point, then obviously it's a kind of sphere around this point, at some kind of time T. So, at that time T, each point on the wave front is considered to be a source of secondary oscillations. So, the oscillation of this particular point causes oscillation around it. So, during some extra time, let's say delta T, we have all these oscillations around it. So, there is some kind of a mini sphere which has been formed during the time delta T after certain time T. Now, what happens then? This point is a source. Now, this next point is a source. Next point is a source. All these are sources of secondary oscillations. So, where is the wave front? Well, according to Huygens, the wave front is the curve which envelopes these things. Now, the enveloping curve is basically a mathematical concept. It's very well defined, etc. Like in this particular case, it actually means it's the curve which is tangent to all these little circles. So, the mini circles represent what actually is the wave front from one particular point on the big, on the real wave front, which formed during the time delta T. So, if this is my original circle, dotted circle, was the wave front at time T, then this, the new wave front, which is tangent to all these little circles, would be a wave front at T plus delta T. So, that's the next thing. Where delta T is obviously assumed, very small one. So, that's how our oscillations propagate. So, they reach certain point and then each point is a source of propagation around it. So, there is a small circle. Okay. Now, how this idea actually came to his mind. I mean, I'm always interested in knowing how basically people came with certain very interesting ideas. Well, maybe, I don't know it from him, he lived in 17th century, but I'm just assuming, and it's actually written in many books as well. Let's just assume such a very simple experiment with the sound. So, let's say you have two rooms with a door in between. Now, one room is where you're sitting. Another room is where the source of the sound, let's say somebody is playing a violin. Now, let's just think about how the sound propagates from one room to another. So, this is a violin and this is a human being. Now, the sound doesn't go this way because there is a wall here. But sound goes this way and from here it goes this way. Why? I mean, there is no reflection here, there is no sound mirror or anything like that. It's just because every little molecule which is oscillating here and the sound definitely reaches this door, obviously, right? It becomes a source of secondary oscillation. Oscillation of this molecule causes the oscillation of molecules around it. So, that's why it's something which I believe might cause this kind of train of thought. So, it looks like there is a secondary oscillation which is caused by those molecules of air which are already oscillating because of the real sound reaching this particular thing. So, real oscillations from the source goes here and secondary oscillation goes to us. Now, this particular human being is thinking, I mean, if he will ask, where is the sound from? He will point on the door because from his perspective the sound is from the door, not from the violin. He doesn't see it, he doesn't hear direct sounds. He cannot determine this as a source of sound. This will be the source of sound. So, same thing with light basically. He assumed that reaching certain point in ether or ether, whatever you call it, the light actually is oscillating and it's causing the oscillation of other points of this ether. And that's how it propagates. So, this is the idea. So, again, reaches certain point, points actually at time t, the wave front, and each point of the wave front is the source of secondary oscillation which gives all these little spheres around it. Okay, so, that's how it is. Now, let's just think about the wave front again. What is the wave front of point if we are talking about uniform environment? Let's say vacuum. Well, obviously, since the speed of light is the same in all directions, the set of points where the light is reaching at the same time would be on a surface of the sphere. And the radius will be, obviously, c times t. That's the radius where c is the speed of light and t is the time. Now, the speed of light, as I said, is in uniform environment, is the same in all directions. So, whenever there is a certain time t greater than zero, the light will go along this distance and that would be the radius of the sphere around this point. Now, again, just out of exercise, what is the wave front if the source of light is a straight line in three-dimensional space? Well, obviously, it would be some kind of a cylinder, right? Because from this point on the same distance would be a cylindrical surface. So, a cylindrical surface would be the wave front increasing the radius of the cylinder as the time is increasing. Again, I consider that the speed is the same in all directions. It's a uniform environment. And the last source of light which I would like to consider is a plane. So, if you have a plane in space, infinite plane, obviously, I'm talking about, and it's the source of light. So, the light goes up and down, let's say, or only up doesn't really matter. And how does it go, actually? What would be the wave front? What would be the set of points where the light reaches at the same time? Well, obviously, it would be parallel plate. So, it goes further and further up or down, whatever. And the rays of light would be, obviously, perpendicular to this surface. So, these are different shapes the wave form can take. So, let's talk about, again, single point as the source of light. So, the wave front is a sphere at time t. So, what would be time t plus delta t? During the time delta t, there will be a small circle of oscillations produced by each particular point where the light has already reached. So, it will cause the oscillation of all points around it. And, obviously, all these spheres, little spheres will be of the same radius, because, again, we're talking about uniform environment. So, delta t multiplied by, see, that would be the radius of the small circles. So, this small radius is c times delta t. This one is ct plus c times delta t would be c times t plus delta t would be the radius of the sphere which is enveloping all these spheres. Well, it sounds nice, obviously. However, it's a theory. I mean, it must be somehow confirmed. And also, it must explain certain phenomena of the light. Like, for instance, refraction. Okay, so, we will do it. But before that, let me just make a very short stop. What happens if environment is not uniform? And that's why the speed would be different. So, what happens in this particular case? Well, obviously, if it's around a point, this will no longer be a sphere. It would be some kind of maybe an ellipsoid or whatever it is. It depends on how is the speed of light in this particular environment. So, maybe there is something like a border here between two different parts of space. So, here, light goes with one particular speed and when it reaches another environment like between air and glass. The speed would be less or greater, whatever it is. So, these would be smaller and this would be greater around the point. So, it's no longer a sphere. It would be something else. So, wavefront depends on properties of the environment because it depends on the speed of light. Speed of light is different. In glass, for instance, as we know, speed of light is less. Like about one and a half times less than in vacuum. So, we were talking about the uniform environment and we were talking about non-uniform environment. And the speed is different and that's what changes the wave form from original, whatever original was. A spherical or cylindrical or plane. So, whatever was original, it changes. And that's why direction will no longer be straight from this point as in a spherical case it might actually change direction. And that would be actually the source of such phenomena as reflection, for example. But we will talk about this in the next lecture. Alright, what else is necessary? Well, what's necessary is there are some problems with this theory. I mean, look at this. This light from the secondary light is emitted in all different directions. But the real rays of light we see as propagating direct lines from the source in the uniform environment. So, how can I explain that the light actually goes along the straight line in the uniform environment based on this theory? Well, quite frankly, I can come up with some explanation. It's really very shaky. But nevertheless, I'll talk about how it could have been explained without really saying that this is a real rigorous explanation. According to this theory. So, let's just consider one particular example of light source. It's very convenient actually to assume that the light source is an infinite plane in which case my light goes along straight lines. So, let's say the light has reached certain level. I'm talking about right now section of this picture, two-dimension. So, from some source of light, parallel lights reach this particular wave front. So, what happens then from this wave front? Well, we are saying that each point on the wave front is a source of secondary oscillation. So, oscillations goes to all directions. Well, these oscillations to this direction are obviously continuing this straight line. Now, what happens with other? This one, this one, this one, this one, this one. So, all these other oscillations. So, what happens? Well, I can suggest something. Let's consider this and this. These two rays of light emitted by these two points. You see, it's like two forces actually going at an angle to each other, but they are equal in the strengths. They are completely symmetrical. So, what would be the equivalent force to this one? Well, obviously, if you add this vector and this vector, you will have this vector, right? So, it looks like each pair of rays of lights will result in oscillations going this way. Because, again, you can really represent each vector as a sum of these two vectors. So, these would be added together, but these are going against each other and cancel each other. So, that's why the resulting of these two neighboring points emitting symmetrical lights would be the one which goes this way. Well, look, I'm not saying this is a real explanation, but it gives some reasonable approach, maybe, to this particular type of propagation. So, we were talking about how can we explain certain things. Now, let's talk about difficulties of explanation of certain phenomena. So, first of all, I would like to talk about corpuscular theory, where it really goes against the experiment. So, let's talk about source of light, and we will talk about small aperture, small opening, and this is some kind of a screen. Now, if this is the source of parallel lights, what would be on the screen from the corpuscular standpoint? Well, obviously, those little corpuscules which are going, and again, it's parallel rays of light perpendicular to this opening kind of thing. So, whatever goes in would be in, whatever goes out, not on the opening, will not go. So, the picture which we will see on the screen will be a light spot here, which is exactly equal to the opening, right? That from the corpuscular theory standpoint. Very reasonable. Now, what is the experiment showing? Well, experiment shows completely different picture. There will be light here, and there will be light here, and here, and here, and here, and here, and here. So, light would be actually going this way. Now, corpuscular theory will not be able to explain it. Now, the wave theory is capable of explaining this, and I'm not going into the details of how it is explained. My purpose is to criticize the corpuscular theory. So, that was one of the reasons why people like Huygens really were thinking about something else, some other theory. Now, what's interesting, the picture would not be like this is the brightest spot and then the brightest is gradually decreasing as we go out. It will be some spots, bright spots and dark spots, bright spots and dark spots as well, which is a completely different kind of phenomenon. It's called diffraction. So, from the wave standpoint, since each point here is the source of light, obviously, light goes into all directions. And you remember I was talking about cancellation of light. Now, the lights here, emitted by points which are very close to the edge, don't have as many neighbors as the points which are in the middle of this opening. So, that's why it will be less here and less here and more towards the center of it. So, this is one of the kind of a critical point about corpuscular theory. Now, does the wave theory has some kind of difficulties? Oh, absolutely. And let me just enumerate them, at least for the purpose of this lecture. First of all, if you remember, Huygens was thinking that light is oscillations of ether and longitudinal oscillations of ether. Well, by now, we know two things. Number one, there is no ether. There were many experiments that show that ether cannot really exist. It should have certain properties which it cannot really have to satisfy certain experimental facts. So, that's number one. Number two, again, by now we know that it's oscillations of electromagnetic field and it's not longitudinal, it's how is it called? I forgot the name. So, it goes across not along the direction of propagation of light. So, the propagation of light is this, but oscillations are this, not this as the sound would propagate the air. So, these are longitudinal. And this is trans-something. Okay. So, that's number one. Number two, I have tried to explain how the parallel light actually goes forward and all these rays of light somehow cancel each other and have the equivalent light goes straight forward. But to tell you the truth, it's a very shaky explanation. I mean, it needs some good math to support it and I'm not going to go into this, obviously. It's not a real rigorous explanation of this particular thing. So, the propagation of the light along the straight line is kind of questionably explained by this particular Huygens theory. Next is, now at some point people discovered the phenomenon of polarization of light. Well, right now we know that polarization is related to the following. Thank you. This is the direction of propagation of light and we have the oscillations of electromagnetic field. These oscillations are not in one particular place. It's three-dimensional, so it's every plate has it. So, the oscillation goes in all the different directions perpendicular to the propagation of light. And if I have some material, like for instance crystal of tourmaline, which lets through only in one particular plane because their internal crystal structure is such a way that it does not let the light to propagate in all the different planes, then you will have this particular polarization. What happens is, if you will take this tourmaline crystal, for instance, which goes this way, you will see the light which are less bright. And then if you will go to another tourmaline crystal which is turned by 90 degrees, so it's this particular direction which is supposed to let the light go, then it will be dark completely here because this one lets light only in one particular oscillation plate, but this one doesn't let it because it's turned around, so there is dark here. So, this is the polarization of light. Instead of oscillating in all the different directions perpendicular to the propagation, it goes only along one particular flat plane. And that cannot be explained by the Huygens principle. What else? Photoelectric effect. Light can actually heat some surface, light can actually cause certain electrons to go out from that surface, like it really hits them and kicks them out from the surface. So, if you have some kind of a metal plate and you have light here, there are certain electrons which are kicked out from the surface and if you have some kind of a source of potential energy, electric energy, these electrons can actually move from one to another, really making electric current. So, electric current would exist when the light moves on. It cannot be explained, it can be explained by a corpuscular theory because all these little corpuscules are really like hitting the atoms of the surface and can kick out the electrons, but the wave theory cannot do it. And then there is another, well, kind of strange thing. You see, if you have certain lights, let's say parallel lights, this is the wave front. So, we were talking about this picture, which causes the light to go this. But again, if each point on the wave front is actually the cause of secondary waves, so there is actually the whole sphere, the light goes into all directions, including this one, which means light should actually propagate backwards as well. So, according to this theory, light would propagate backwards as well as forward, which is not the case, light goes only one direction. So, that's just another little difficulty with this particular theory. However, it was a tremendous step forward, even if it's an ether, even if it's longitude and not the oscillations across the propagation light. Still, this particular theory was extremely important for the development of the light theories and the electromagnetic field and Maxwell's electromagnetic field explanation with his equations, etc. So, it played a very, very important role in physics of the time. And that basically was the point I would like to make. Okay. So, thanks very much. I do suggest you to read the explanation to this particular lecture on Unizor.com. Every lecture has the explanation, textual explanation. Basically, you can read it as a textbook. And obviously, it's part of the course. So, I do suggest you to take the whole course of physics as well as the course of mathematics, which is also on the same website. It's called Math for Teens. So, good luck. Thank you.