 Hi, I'm Zor. Welcome to Unisor Education. Continue talking about different phenomena of light. Actually, this is the last lecture about different light phenomena. This lecture is part of the course called Physics for Teens, presented on Unisor.com. I suggest you to watch this lecture from this website. You just have to go to this course called Physics for Teens from the main home screen and choose the part which is called waves. And when you will open the waves you will have many different topics and one of them will be phenomena of light. So you go to phenomena of light Today's lecture will be one of those called Polarization of Light. I do suggest you to use the website rather than, let's say, YouTube where you found this lecture because every lecture including this one has very detailed notes. So you have a screen where you have the lecture and you have the notes right near it which basically explains in writing whatever I'm talking about in front of the board. Now the site is completely free. There are no advertisement. And also there are some exams where you can basically check yourself. You can take as many times as you want. It doesn't really matter until you get the perfect score. So back to Polarization of Light. Alright, now Polarization of Light first of all is related to wave properties of light. So let's just recall that light is transversal oscillations of electromagnetic field which means there is an electric component and there is a magnetic component. Now if you will take a look at the vectors which represent the electric and magnetic components they will always be perpendicular to themselves and perpendicular to direction of propagation. Let's say something called B, intensity of the magnetic component and this is the direction of light. We are talking about the three dimensional case, right? So these two are perpendicular to each other and the plane where they are actually happening between these two is perpendicular to direction of the light propagation. Now you can consider only electrical component and we will consider only electrical component because magnetic component is always related to it. So let's not just mention magnetic because it might actually kind of complicate the picture. So let's consider only electric component knowing that magnetic is always present and it's always perpendicular to both the electrical component and the direction of the propagation. So let's have a two dimensional case and this is the light. So what happens with electrical component? It oscillates, right? So it basically goes like this. These are amplitudes. Now obviously there is a wavelength from crest to crest or from trough to trough. There is a speed of propagation, etc. But what's important is consider this plane where oscillations occur. That's what's very important. So this is the plane of oscillations of electrical component and we are talking about one single ray of light, monochromatic, one singular phase, one singular amplitude, etc. No mixture of anything. It's actually like laser for instance can provide this type of source. So let's consider the simplest case of one particular monochromatic single phase, etc. Ray of light and this is how electrical component is oscillating. So this is the direction of light and this is a plane which coincides in this case with the white board, the plane where this occurs. Now this is an ideal situation. The real situation, let's say you can consider the light from the sun or from incadescent lamp or whatever. Now it's usually a mixture of many different rays because every tiny little piece of sun emits certain electromagnetic waves. They are not in sync, they are in completely different planes of oscillation. Let's talk about electrical component, plane of oscillations of electrical component. So if you see the ray from the sun, it's a mixture. There is an electrical component which looks like this. And there is an electrical component which is out of phase and out of plane. It will be different plane, plane is turned. So all other different amplitudes, obviously different frequencies. So it's not a monochromatic. So all these planes, this one, this one, this one, etc. They are all present. These are planes of oscillations of electrical component. And within each plane, the oscillations have, within one plane, they have a different amplitude than another and different phase, etc. So it's a mixture of all kinds of plane of oscillations, amplitudes, phases. Frequencies. Okay, fine. So that's how it is in nature. Now, there are very interesting substances which I don't know, probably have been accidentally found, but then the whole theory was developed based on that. The substances are, if you have a directed light towards that particular substance, it can be a crystal of some mineral. I remember the name Turmaline. That's kind of a, it's a natural crystal, actually, which has certain chemical composition. And what's interesting is that it has something which is called polarization plane. In this case, polarization plane is coinciding with my whiteboard. So if you have an oscillation of electric component, plane of oscillation, coinciding with the plane of polarization, it just goes exactly without any modifications. But whenever the different plane of oscillation hits this crystal or whatever the substance is, then on the output you will still have the oscillations within the same polarization plane. But maybe weaker signal. What's interesting is that if you have the plane of polarization perpendicular to plane, so let's say you have something like this, the plane of oscillation is this way and plane of polarization is this way. So they are perpendicular to each other. Then this particular ray will not go through at all. Now these are some properties, atomic properties of this particular substance, this crystal or whatever it is. And let's not go into the details of why it happens, because this is more like a physical chemical, etc. But it happens. And it's a known fact. I think now we can develop something like artificial substance or films, which really possess the same quality. So regardless of how it's actually happening or why it's happening, we will concentrate on what is happening. What is happening is on the output the light will be only in a single oscillation plane of electrical component, which basically coincides with polarization plane of this particular crystal. So let's just simplify our situation and consider not a mixture of all the different rays with different planes of oscillations, different amplitudes, etc. We will consider only one single ray, which has its own plane of oscillations. And let's consider this plane of oscillation going at certain angle to the polarization plane. So this is my vector, which describes the direction of oscillation of electrical component. So it goes up, down, up, down. The plane is not perpendicular to this particular crystal. It's not a polarization plane, but slightly at the angle. Now, what happens in this particular case? Well, as we usually do in mechanics, whenever we want to find out what's the implication of any particular force, we usually represent this force as a sum of other forces, each of which we can evaluate independently, a vector sum. Same thing here. This is basically a vector of electric field, a little intensity, and we can always break it into two components. One component I will call E in, and one is E out. Now, this component will lie in the plane which coincides with the polarization plane, and this component is perpendicular to that plane. I can do it, no problem, right? So how should I do it in practice, if you wish? Well, I can always do this. I can draw a plane perpendicular to my direction. Now, this is the plane which is not coinciding with the plane of oscillation. It's at the angle. So this, and within this plane, this vector, I can represent as sum of the vertical component, and the vertical component will correspond to my, it will be within my polarization plane, and horizontal towards me component, and that component will be perpendicular. Now, we know that these oscillations which are within plane of polarization will go through without any problems, and these oscillations going this direction, in and out of the whiteboard, would not be let through. Okay, so what is this vertical component? Well, obviously, this angle is theta. E in would be equal to E times cosine of theta. I can represent my oscillations in this plane at angle as two oscillations. One plane would be this, and one plane would be this in this plane. So one oscillation in this, I can represent the oscillation in this, and this. I don't know if my cant work was really kind of explanatory enough, but that's kind of an easy thing, and obviously we're just replacing one vector with sum of two other vectors. That's okay. Now, what I'm saying is that this component, E out, which is E times sine of theta, will not go through, and this one will be E polarized. So the polarized light would have only this component of the incoming light, and because of this coefficient, this one would be less than initial vector of electric oscillations. So basically that's the most important part. Out of, now if you have many different rays mixed together with different angles, et cetera, et cetera. Now those oscillations with electrical field oscillating within the polarization plane would go through without any change. All other at other different angles, whatever they are, will be multiplied by the cosine of this angle, angle between the plane of polarization and plane of oscillation of electrical component, which means it will be weaker. So the light here would be not as bright as light here. So most of the rays will go through, but in a weakened, with a coefficient which weakens that, and the greater deviation of the plane of oscillation from the vertical, in this particular case, from the vertical, the greater this angle, the less energy would go through, because the cosine would be smaller and smaller. Angle is bigger, cosine would be smaller. Up to a point when the cosine is equal to zero when the angle is 90 degrees. So an angle of oscillation within this plane would be 90 degrees, and obviously the cosine would be zero. So the lights which are oscillations which are within this plane will not go through, and these ones will go through without anything, and those which are in between correspondingly. Okay, so that's basically the theory of this. Now, let's talk about just a couple of words about brightness. When we perceive the light, not in terms of vector of electrical component or magnetic component, we perceive the light in terms of brightness. Now, what is brightness? The amount of energy which light actually carries with it. Now, what is the energy of the wave? Whenever you have a wave, well, the stronger the wave basically oscillates, the bigger energy it brings. So amplitude actually is a very important component of the energy. Frequency also is very important. So the more frequently it oscillates, it should really bring more energy. Now, let's talk about amplitude, because this vector has an amplitude, and obviously whatever the E is changing, it's changing by itself relative to some kind of amplitude, times usually cosine of some omega t, if you remember. E is a function of t basically, and it's amplitude times cosine of omega t, plus maybe phase shift, et cetera. So anyway, if this is multiplied by cosine, obviously amplitude is multiplied by cosine. Now, again, back to amplitude and waves on the, let's say, surface of water. The greater amplitude, the faster the water should actually be reaching the top. There is a potential energy, there is a kinetic energy, et cetera. Now, let's talk about kinetic energy. The molecules of water would probably have to travel faster to reach higher amplitude, right? And energy, kinetic energy is proportional to a square of the speed, right? d squared divided by 2. So what I want to say is, just take it for granted right now, that the energy is proportional to a square of amplitude, and amplitude is multiplied by cosine. So the energy is proportional to... Energy is proportional to square, cosine squared, et cetera. Now, I will address the energy of the light in a separate lecture. Basically, it's the next topic. But right now, just take it for granted that the intensity of the light, the brightness amount of energy which light carries on this side, depending on this angle of the plane of oscillation would be proportional to cosine squared of that angle. It's called the Malus law. Malus law. So, for instance, my plane of oscillation is at 45 degrees. So what would be the intensity of the light on that side? Well, if it's at 45 degrees, cosine is equal to square root of 2 divided by 2. Cosine square would be equal to 1 half. So the intensity, the brightness of the light of the single ray, I'm talking about single ray, monochromatic, et cetera, which has oscillations of electrical component at 45 degrees, like this approximately, 45 degrees to plane of polarization, then the brightness will be half. Now, if it's coinciding, the brightness would be 100%, because the cosine of 0 would be equal to 1. And if the brightness and if the plane of oscillations of electrical field is perpendicular, it will be 90 degree, that would be 0. So basically, as we are turning our light, or maybe the light is the same, but we are turning this crystal, which does the polarization. It's called Polaroid, by the way. So if we are turning Polaroid, we are turning plane of polarization, we are changing the brightness. If you have a screen here, it will change the brightness. And incidentally, if you will have two Polaroids like this, one is this way and another, we will turn it by 90 degree. So it will be, this plane would be polarization and this plane would be polarization. What would be on the screen behind these two? Nothing, because they will basically cut everything for any particular light. Okay, that's basically it. I do suggest you to read the notes for this lecture. There are some nice pictures. And, well, basically that's it. My next problem would be to provide exam for this topic of phenomenon of light. So as soon as I will make this exam, I will release it and correspondingly send everyone notification about this. Thanks very much and good luck.