Anderson Video - Thins Lens Equation

Professor Anderson
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The thin lens equation is exactly the same as the mirror equation. It's the following: 1 over do plus 1 over di equals 1 over f. There's only one difference which is the sign of these items. So, the way they're measured is the following: This is our focal length f. we've drawn a positive focal length, f, because it's a positive lens. When we put our object out here, that distance from the center of the lens is do. This is a positive number. Okay? When do is to the left, it's a positive number. We know that it's going to form an image over here somewhere. Okay? We can use our ray-tracing techniques to figure out where that is. That distance from the lens to the image is di. And in the case of a mirror, remember it was positive to the left and negative to the right. But for a lens, this is also positive. Okay? So, all the numbers in this picture are positive 1 over do plus 1 over di equals 1 over f. All right. Let's see how that applies for a real example. Let's say you want to take a picture of a tree. And, we're going to say that the distance from your camera lens to the tree is 2 meters. And, let's say that the focal length of your camera is pretty short maybe it's about like that. So, that's 10 centimeters. Okay? What is di equal to? All right. How do we do that? Well, here's our lens equation. We can just take that equation and rewrite it. And then, we can solve for di, so we have 1 over do plus 1 over di equals 1 over f. All right. So, 1 over di equals 1 over f minus 1 over do. And, I can rewrite this slightly if i multiply up by do. Multiply up by f, divide by the common denominator and now I can flip it. So, what is di? It's equal to fdo divided by do minus f. And now, we have all those numbers. 10 centimeters is, of course, not si units, so we need to make that si units. What do we get? We get 0.1 times do, which we said was 2. We're going to divide by 2 minus 0.1 and so we get 0.2 divided by 1.9 And so, di is very close to 0.1, but it's a little bit bigger than that. Sean can you punch in those numbers? I'm going to say it is 0.11 That's my guess. Let's see what it turns out to be. 0.2 divided by 1.9. >> (student speaking) 0.105 >> 0.105 All right. So, we'll clear that up, 0.105 Very close to the focal length of that lens. Okay? And ,that was with a tree that was only two meters away. Anything further away, the image distance gets closer and closer to the focal length of the lens. And, this is why point and shoot cameras or your smartphone camera can basically have things in focus very far distances out because it's all at an image distance that's nearly the same as the focal length of that little lens. Okay?
The thin lens equation is exactly the same as the mirror equation. It's the following: 1 over do plus 1 over di equals 1 over f. There's only one difference which is the sign of these items. So, the way they're measured is the following: This is our focal length f. we've drawn a positive focal length, f, because it's a positive lens. When we put our object out here, that distance from the center of the lens is do. This is a positive number. Okay? When do is to the left, it's a positive number. We know that it's going to form an image over here somewhere. Okay? We can use our ray-tracing techniques to figure out where that is. That distance from the lens to the image is di. And in the case of a mirror, remember it was positive to the left and negative to the right. But for a lens, this is also positive. Okay? So, all the numbers in this picture are positive 1 over do plus 1 over di equals 1 over f. All right. Let's see how that applies for a real example. Let's say you want to take a picture of a tree. And, we're going to say that the distance from your camera lens to the tree is 2 meters. And, let's say that the focal length of your camera is pretty short maybe it's about like that. So, that's 10 centimeters. Okay? What is di equal to? All right. How do we do that? Well, here's our lens equation. We can just take that equation and rewrite it. And then, we can solve for di, so we have 1 over do plus 1 over di equals 1 over f. All right. So, 1 over di equals 1 over f minus 1 over do. And, I can rewrite this slightly if i multiply up by do. Multiply up by f, divide by the common denominator and now I can flip it. So, what is di? It's equal to fdo divided by do minus f. And now, we have all those numbers. 10 centimeters is, of course, not si units, so we need to make that si units. What do we get? We get 0.1 times do, which we said was 2. We're going to divide by 2 minus 0.1 and so we get 0.2 divided by 1.9 And so, di is very close to 0.1, but it's a little bit bigger than that. Sean can you punch in those numbers? I'm going to say it is 0.11 That's my guess. Let's see what it turns out to be. 0.2 divided by 1.9. >> (student speaking) 0.105 >> 0.105 All right. So, we'll clear that up, 0.105 Very close to the focal length of that lens. Okay? And ,that was with a tree that was only two meters away. Anything further away, the image distance gets closer and closer to the focal length of the lens. And, this is why point and shoot cameras or your smartphone camera can basically have things in focus very far distances out because it's all at an image distance that's nearly the same as the focal length of that little lens. Okay?