Anderson Video - Thin Lens and Image Formation

Professor Anderson
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We're gonna go back to our three rules that we had before and see how to apply those. Let's start with a simple picture. Here's our optic axis. Let's put our thin lens right here. And, that thin lens has a focal position, F, on either side and it's symmetric. Okay? If it's a symmetric lens and you have symmetric focal positions, and this is part of being thin lens. All right, let's put our object out here somewhere. How about right there? That's our object. And now, we want to figure out where the image is. Okay. How do we form that image? To do that, we go back to our three rules and it's the same three rules that we use for the mirrors. Except now, we're gonna use a lens All right. Rule number one is: Parallel rays go through the focus -- same as we had before. 2, like we said, is really that one in reverse rays through focus goes parallel. Okay? And the last one, number three, is rays through the center. Do not bend. Same rules that we had before. We got to identify where the center is. Right? We knew where it was for a curved mirror. It was the center of that radius of curvature. But here for a thin lens, the center is, in fact, right in the center of the lens. All right. so let's see how to do this. We've got our object. We need to draw some of these rays. The first one is parallel ray goes through the focus Okay. Parallel ray comes in. It's going to go through the focus. It's not going to bounce off this class and go back to this focus It's going to bend and go through this focus. Okay? So, this is ray number 1. Ray number 2 is going through the focus. It then goes parallel. All right? Going through this focus, it then goes parallel. This is ray number 2. And then finally, here we'll draw a little separator right there, Finally, we have rule number 3 which is raised through the center. Do not bend. We already have an intersection point so you really only have to do two of these three. But just for kicks, let's draw the third one to make sure it works out. Ray's through the center. Do not bend. That's ray number 3. Okay? And, these are reasonably straight. That's where the object generates an image. We know that the base of the object is still going to be on the optical axis. And so, it is inverted. In this case, it looks like it is de-magnifying That is where the image is located. Okay? So, those are the three rules for figuring out where that image is located. And it takes a lot of practice. And as you move this object in and out it gets a little bit harder and harder to do. This is a real image. In other words, if I put a piece of paper there I can form an image on it. Or, if I put a piece of film there or a CCD array, then I can form an image right there It is inverted, upside down, and it is also, in this case, it is de-magnified. But, it doesn't have to be. It depends on where the object is located, as we'll see when you move the object in closer, it can get magnified. Now, this idea of it being inverted is sort of interesting. What that means is when you have a camera and you have a lens, and you're looking at a tree, the image on the film or the CCD array is upside down. Okay? But, guess what? This is exactly how you view the real world. Your eye is a lens.When you look at a tree, the image on your retina is upside down The whole world that you're seeing around you is upside down. Your brain has figured out how to not really worry about that and correct for it. But on the retina, the back of your eyeball, everything is upside down.
We're gonna go back to our three rules that we had before and see how to apply those. Let's start with a simple picture. Here's our optic axis. Let's put our thin lens right here. And, that thin lens has a focal position, F, on either side and it's symmetric. Okay? If it's a symmetric lens and you have symmetric focal positions, and this is part of being thin lens. All right, let's put our object out here somewhere. How about right there? That's our object. And now, we want to figure out where the image is. Okay. How do we form that image? To do that, we go back to our three rules and it's the same three rules that we use for the mirrors. Except now, we're gonna use a lens All right. Rule number one is: Parallel rays go through the focus -- same as we had before. 2, like we said, is really that one in reverse rays through focus goes parallel. Okay? And the last one, number three, is rays through the center. Do not bend. Same rules that we had before. We got to identify where the center is. Right? We knew where it was for a curved mirror. It was the center of that radius of curvature. But here for a thin lens, the center is, in fact, right in the center of the lens. All right. so let's see how to do this. We've got our object. We need to draw some of these rays. The first one is parallel ray goes through the focus Okay. Parallel ray comes in. It's going to go through the focus. It's not going to bounce off this class and go back to this focus It's going to bend and go through this focus. Okay? So, this is ray number 1. Ray number 2 is going through the focus. It then goes parallel. All right? Going through this focus, it then goes parallel. This is ray number 2. And then finally, here we'll draw a little separator right there, Finally, we have rule number 3 which is raised through the center. Do not bend. We already have an intersection point so you really only have to do two of these three. But just for kicks, let's draw the third one to make sure it works out. Ray's through the center. Do not bend. That's ray number 3. Okay? And, these are reasonably straight. That's where the object generates an image. We know that the base of the object is still going to be on the optical axis. And so, it is inverted. In this case, it looks like it is de-magnifying That is where the image is located. Okay? So, those are the three rules for figuring out where that image is located. And it takes a lot of practice. And as you move this object in and out it gets a little bit harder and harder to do. This is a real image. In other words, if I put a piece of paper there I can form an image on it. Or, if I put a piece of film there or a CCD array, then I can form an image right there It is inverted, upside down, and it is also, in this case, it is de-magnified. But, it doesn't have to be. It depends on where the object is located, as we'll see when you move the object in closer, it can get magnified. Now, this idea of it being inverted is sort of interesting. What that means is when you have a camera and you have a lens, and you're looking at a tree, the image on the film or the CCD array is upside down. Okay? But, guess what? This is exactly how you view the real world. Your eye is a lens.When you look at a tree, the image on your retina is upside down The whole world that you're seeing around you is upside down. Your brain has figured out how to not really worry about that and correct for it. But on the retina, the back of your eyeball, everything is upside down.