Hello, everyone, and welcome back. So in this video, we're going to talk about a new concept called polarization, which has to do with the orientation of light and also its intensity. So we're going to talk about a couple of conceptual things you'll need to solve problems, and we'll also go through a pretty straightforward equation. So let's just jump right in.

So what's polarization all about? Well, back when we first studied the electromagnetic waves, we said the electric field oscillates in one axis and the magnetic field oscillates in a different axis, and that's basically what polarization has to deal with. The polarization of an electromagnetic wave is always just going to be the direction or the axis that the electric field is oscillating along. So, for example, for this wave over here on the left, the electric field oscillates purely on the z-axis. It doesn't go forwards and backwards or off at some angle. So, basically, what we say is that's the polarization. The polarization of this light here, this electromagnetic wave, is going to be along the z-axis.

Now, obviously, drawing these diagrams and these waves would be super complicated over and over again, so we have very compact ways of representing this by using what's called a polarization diagram. Basically, what this looks like is it just looks like a double-headed arrow that points along the appropriate direction. That's all polarization is.

Now let's take a look at a different example because there are many different possibilities for the polarization angle or direction. Let's take a look at this wave over here. This wave points along the same exact direction. The only difference is it kind of looks like the first diagram if you were to sort of tilt it a little bit. So if you were to sort of tilt it by 30 degrees, now what happens is the electric field oscillates not purely along the z-axis, but it kind of oscillates at some angle here. So what we'd say is that this angle, this polarization, is 30 degrees with respect to the z-axis. All right? So basically, it would just look like this. We're going to draw this double-headed arrow, and we would just indicate with little dotted line that this angle here is 30 degrees. That's really all the polarization has to deal with.

Now there's also such a thing as unpolarized lights, which basically just means that the electric fields don't point in a specific direction but actually just many random directions. Now in a lot of problems, we're going to see unpolarized lights. Usual examples are going to be sunlight or light that's coming from light bulbs or something like that. Most of the time, it'll actually just tell you if it's unpolarized. But, basically, the way that we represent unpolarized light is by using a double-headed arrow, except in all directions. So usually, what I do is you're just going to see a couple of lines, maybe like 3 or 4 of them, with all of the arrows like this, and this just represents unpolarized light.

Now let's talk about a polarizer very quickly. A polarizer looks like a little circle with a little grating, and it's basically just a filter. A polarizer is a filter that only allows components that are parallel to the transmission axis to pass through. So when you have this unpolarized light that's moving this way and it passes through the polarizer, the only thing allowed to pass through is this component of the light here, the component that is parallel to this transmission axis. What happens to the other components? Well, they basically just get absorbed or they get blocked, so these components now are no longer allowed to pass through. So what happens here is that when unpolarized lights get passed through a polarization filter or a polarizer, then it becomes polarized. And, basically, what it looks like here is the only component that's allowed to survive is the vertical component.

Now the other thing that happens is that the intensity also decreases by a factor of one-two, because you're now removing a lot of the light components. So basically, there's actually a very simple equation for this. It's that:

I = 1 2 I 0and we just call this the one-half rule. So whenever you have unpolarized light that becomes polarized, its intensity decreases by a half, and it becomes polarized in the direction of the transmission axis.

Alright? So let's just go ahead and just jump into a really quick example problem here. So for the situation that we just described above here, if the intensity of the unpolarized light is 100, so in other words, if this *I _{0}* is equal to 100, then what is the intensity of the transmitted light? In other words, what's the intensity of this light that makes it out of the other side? So, basically, if we want

*I*, then we're going to have to use our new equation,

*I*equals one-half of

*I*. So, in other words, it's just one half of 100, and that just equals 50 watts per meter squared.

_{0}So that's all there is to it, guys. If you have 100 watts per meter squared of intensity, then at the end, you have only 50 watts per square meter that makes it through the other side. That's it for this one, folks. Let me just go through a quick practice problem, and we'll jump into another video.