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Anderson Video - Lenses

Professor Anderson
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Let's talk about lenses now. Now that we understand Snell's law and this idea of the index of refraction. How does this apply to lenses? Well, let's think about the following picture. Let's say I have a piece of glass and I curve it like so. What's gonna happen to the light that goes through this piece of glass? All right, we know that a light ray that is normal to the surface doesn't bend at all. Right? If it's normal to the surface, theta i is zero. Theta t is therefore zero. So it will continue straight on through and head off in that direction. Actually, that's a solid line in there. What about a light ray that comes in near the top of the lens? Well this glass is curved right there and so it's going to bend down just a little bit. Then it sees another curve on the other side. So it's going to bend down a little bit more. It takes a path like that. A light ray on the bottom side sees a curve. It bends a little bit there and then it bends more. It all goes through like so. Each ray obeys Snell's law. If you design this glass just right, you can get all those rays to come to the focus, f. And this of course becomes a thin lens. So it's kind of cool when you think about it, because glass you can make from silica, right? You take a bunch of sand, purify it a little bit, melt it down, carve it into this shape. And all of a sudden it does something very special to the light that goes through it. And now you can use that glass to help people see better. Or make a telescope. Or make a microscope. You can make all these really cool elements just by carving this glass appropriately. All right, this is what a lens looks like. There are a bunch of different types of lenses. And let's identify a few them. So this is curved on the first side, curved on the second side. And therefore it is called bi-convex. If it is curved the other way on the first side and curved the other way on the second side, then it is called bi-concave. Remember, cave is the one that you can crawl into. So if you can crawl into this cave, it's concave. Bi-concave. But they don't have to be curved on both sides. You can just have it curved on one side. So if I curve it on one side, like this, this is called plano-convex. Plane on one side, convex on the other. And likewise, if I do it the other way, then it's called Plano-concave. These are four of the typical lenses. There is a table in your book. Figure 23.31. That talks about a few other kinds of lenses. Now if it's a thin lens, then we are not worried about the thickness of the lens. We don't have to really worry about what's happening in the interim. It really only depends on what's happening out here at the focal position. Once you get into advanced optics, you start talking about thick lenses. Where there is a substantial amount of glass in between the two curvatures. And then you have to worry about the propagation in between them. Whenever you're designing an optical element, like for a 35 millimeter camera. You really have to take into account the curvature and the thickness of the glass itself. If you have a nice 35 millimeter telephoto lens, there will be something like 30, 40 elements in that lens. Okay, you'll have all these different lenses one after another. And the goal is to create a good image. It's not easy to do that with just one lens. You need a whole bunch of lenses to get color correction, to get rid of spherical aberration, all sorts of those problems. Okay, so let's talk a little bit more about the lens and how we might form images with the lens.