 Hi, I'm Zor. Welcome to Indizor Education. I would like to add another particular kind of lenses to whatever the categories of lenses we have already talked about. It's called Fresnel lenses. Sometimes it's pronounced Fresnel sometimes. I think Fresnel is more French because he's a French guy. His full name is Austin Jean Fresnel. He's a physicist in France. Somewhere in... I think it's 1800s, I believe. I don't remember exactly. So what was his very important contribution to lenses? Well, as we know, lenses are some vices which can actually do a very simple thing. This is a simple lens. And if you have lights coming, parallel lights coming from this side, they will concentrate in one particular point called the focal point and then it will go further. Now, why? Well, because of a very simple property of a prism, if you remember, if you go this way, it will go this way. We have already talked about this. Okay. So now, from... this looks like a prism, right? This particular piece. And this piece. And this piece. And this piece. And this piece. And this piece. So, let's examine how light actually goes through the prism. When it goes here, it's perpendicular in this particular prism, right? So it doesn't really change the direction. It changed the speed because of the difference in substance. This is the glass, this is the air. But where is it exactly bending? Well, it's bending on this boundary. So whenever it goes into this particular piece, let's call it a small prism, again, it doesn't change anything, doesn't change direction when it crosses this particular side. But whenever it goes this way, it will bend. It will bend. It will bend. So only on the surface of the lens, it actually does this change of direction. Now, if you would like to make a large lens which has a lot of light actually coming through... Well, it's kind of bulky. It's a big piece of chunk of glass which you have to polish, etc. Well, incidentally, if you put the point source of light here and it will direct the rays this way, the rays will go the opposite way and it will be parallel to this. So the idea was to use the lens as a source of light in lighthouses. At that time it was extremely important. No GPS. Okay, so again, exactly the same thing. The real change of direction happens on the surface of the prism. And then after that it goes parallel. So the only problem was to properly shape this surface so that the light goes parallel. Well, in the beginning people were actually shaping as part of the sphere and we were talking about this is not precise. The precise surface which does exactly this type of a point source to a parallel light, it's a very complicated curve. But in any case, whenever people did it, the whole lens became very bulky. So what's actually Fresnel's contribution to this? Very important. He says, look guys, this piece, this piece of lens is not really used at all. What we need is just these prisms at the very edge of this curved surface. So let's make another construction. I will take this prism here and then this prism here and this prism here, etc. So all these prisms, these are this way, and prisms will be this way, like teeth. Now what we actually need, but what's really very important is to have the curvature of these parts and curvature of these parts in such a way that the light coming here would go to this point. Light coming here will go to this point, light coming here will go to this point. So all we need to do is to properly curve these teeth, so to speak. It's significantly less bulky, but it does exactly the same, well, approximately the same. The finer the teeth are, the better approximation to this curve will be with these little pieces of these prisms. So the prism is not triangle again, the prism on this side, on the top side would look like this and on the bottom side it will look like this. But these curvatures should correspond to these curvatures and the middle one as well. Not exactly, they should be a little bit less bending than this particular curvature because it's closer. So whenever we just have this particular piece cut it out and move here, then the focus will be here, right? So we need less curvature here, so it will go this way. So this one would be a little bit less curved than this one. But in any case, the curvature can be calculated or can be experimentally determined. And the finer the teeth are, the better the focus will be. And this is called Fresnel lens, Fresnel's maybe lens. So this is called, by the way, positive Fresnel lens. Now, this is exactly what's used since that time and not only in lighthouses, it's used in many, many, many different places. The car lights actually have this kind of curvatures to put the light rays parallel forward and in many other cases. So whenever you need a really big curved lens, people are using Fresnel lens. So these are, so this is a positive Fresnel lens. Now, there is a negative Fresnel lens, which I'm going to talk about right now. Instead of going through, the light would reflect. And it looks like a parabolic lens. Basically, the functionality is like a parabolic lens. But it's not really parabolic, it will be flat. I'll talk about this. Now, why am I actually going into this direction? Is it important? Well, because it will help me to explain how hologram is working. Because in hologram, it's not the Fresnel lens per se, but it's something very functionally similar. And we will talk about this whenever we will talk about holograms. So let's talk about reflecting. So this is refraction when the light goes through and you need something like a glass or whatever. And the next one, the negative one, will be a reflection of the light. Now, we talked about parabolic lens. It has focus, focal point. And if you put the light here, it will direct parallel rays of light. So that's the functionality of parabolic lens. Well, again, I'm saying parabolic. In many cases, it's a part of the sphere. Approximately, it's parabolic. It doesn't really matter. With parabola, it's really exact. And we did some calculations. Okay, now, it's, again, it's big, it's bulky. How can I make it flat, basically? We will use exactly the same thing. Again, what's important? Important is this piece which is supposed to be curved somehow. So let me just do it differently. I'll do a flat surface and I will put these mirrors, if you wish, same as these spaces. I'll put it on a flat surface. Again, the finer teeth I will make, the better will be parabolic functionality of this flat negative Fresnel's lens. But again, if you put the source of light here, from every lens, it will supposed to go this way. So functionality will be very similar. And vice versa, if you put the parallel lights from here, the parabolic lens will collect it into one point. So there is a focal point. There is a focal distance, obviously. And the functionality is the same, but it's flat, which means it's much easier to make. And now the problem is these teeth should be very, very tiny. I actually have seen plastic made as a positive Fresnel's lens. Teeth are really like grooves on the old vinyl disc. So the grooves are really tiny, right? So that's approximately the size of the teeth on Fresnel's lens, a positive Fresnel lens made of plastic. Now, again, this is something as a principle that you can actually put all these small mirrors, if you will, in a special position and as fine as part of the size is concerned as positive in such a way that it will act like a parabolic lens. And again, I will use it as a principle, not as a real construction, but as a principle I will use it when I will try to explain how hologram is actually made. This is a very important principle, a negative Fresnel's lens principle. That's it. It's a very short lecture today. I do suggest you to read on Physics 14's course, which is presented on Unisor.com. This lecture is supplemented with textual material, like a textbook, and it has a couple of pictures, much better than whatever I have just drawn. And the whole lecture is just part of this, some kind of properties of light which we were talking about when we were talking about lenses in general. A particular kind of lenses, which is very, very practically useful. So, I think the glory belongs to this guy, Augustine Jean Fresnel, but there were other people who contributed to the creation of this thing and what's very important is basically manufacturing. How can you make these tiny teeth properly positioned, properly angled, etc. But that's the technicality which is not part of this course. So, thank you very much and good luck.