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Convex Lenses. Created by Sal Khan.
Video transcript
We've talked a lot about mirrors, in particular parabolic mirrors that reflect light Now I want to talk about lenses I'll talk about what lens is and think about how they refract light So a simple lens is made of glass or something else Its surface--I'm gonna focus on convex lenses first So remember, concave means kind of it opens inward like a cave Convex means it opens outward In a convex lens it'll be symmetric--I'll draw it So one side of lens will look like that And you can kind of view this--often times most simple lenses are made this way So this is kind of the surface of a sphere, part of the surface of a sphere Let me see if I can draw that a little bit better So part of the surface of a sphere and it's symmetric So it has some center right over here just like that and then you'd have another surface of a sphere that's exactly the same I'll do my best to draw this convex lens just like that That is a pretty good job here Let me copy and paste it to use this drawing in the future So I've copied it So let's think about what's going to happen if light goes through this lens It's transmitted through it or maybe get diffracted by it So we're assuming it's air out here and this is glass, something that has a higher index of refraction something in which light travels slower So you can imagine that some light that is going parallel to the principal axis of the lens This would be the principal axis of the lens right here just like we talked about the principal axis of our parabolic mirrors But if you imagine light is going parallel to that when it hits this surface over here, remember the perpendicular at this point is gonna look like this because the lens is actually curved And remember, it's moving faster on the outside So the right side is going to be able stay outside a little bit longer or I'd rather say, the top side of the light if you imagine the car analogy The car analogy is going to say, the top wheel is a little bit longer than the bottom wheel If we go at the direction of light, the left side of the car-- let's visualize the car There's the left wheels; those are the right wheels The left wheel can stay a little bit longer, travel faster a little bit longer And so--this is the perpendicular again So it will be refracted downwards like that a little bit And then once you get to this interface, now you're going to move into a faster medium into the air again Let me draw our perpendicular over here And you can imagine that the left side of this ray is going to come out first And since the left side of this ray or the left side of these tires are going to come out first or the top tires are going to come out first, they're going to be able to travel faster and so you'll be refracted even more downwards So it will look something like this The light ray would do something like that Now there is a point out here someplace that whenever I take any ray that is parallel to the principal axis of the lens it will be refracted through the lens to that same point So here it will be refracted a little bit like that Here it will be refracted more And we're gonna go to that same point of level So that's another parallel ray it'll be refracted a little bit over here and a little bit more. It'll go to that same point I think you can guess what I'm about to call this point I should draw my lines a little bit straighter Refracted a little bit and then refracted a little more, it'll go straight to that point This point where all of the parallel rays-- sometimes people will call them collimated rays that rays of light that are roughly parallel they all converge at this point on the other side of the lens They're essentially all being focused on that point And this right here you can view as the focus of the lens or you can view this length from the lens to that point as the focal length Now this lens is completely symmetric Anything you can do from one side, you end up getting focused on the right side If you have collimated rays or parallel rays coming from the right side the same thing would happen just on the other side That ray will go like that and it'll be refracted some more and maybe will go to this point go to this point right over here You actually have two foci for a lens 2 actual points where if parallel rays are coming from one side they'll be focused on the point of the other side If parallel rays are coming from the left side they'll be focused at the focus point on the right-hand side And this goes the other way around. Let me draw another lens One thing we're going to assume while we're dealing with lenses kind of a simplifying assumption, is called the thin lens assumption There is a difference in distance it travels depending on where the light travels in the lens For example, here, there's less distance than over here And in an introductory physics and we'll do that here as well we're just going to ignore that difference in distance That would lead to some differences in how the light is refracted and transmitted, all of that It travels a smaller distance here than over here So we're gonna ignore those differences. We're just gonna make the thin lens assumption Using the thin lens assumption, let's think a little about what's going to happen to the light And in the next few examples, I'm not gonna worry about this 2 steps I'm just gonna say, in general, it gets refracted in that direction when it exits the lens So let me just draw a simple lens right over here It is symmetric and it has two focal points. One of this side So that is one focal point Then it has another focal point, the exact same distance on the other side The lens is symmetric Let's think about what this lens will do to the images of different objects Let's draw its principal axis again Both focal points lie along that principal axis Now let's stick an object out here beyond the focal length What's going to happen? First, we can pick any point on this object light is being diffusely reflected off of every point I'd like to pick points that are going to do something that's kind of predictable So let's pick a point. Let's pick the tip. And take a ray that there's something predictable Let's take a ray that is parallel to the principal axis And then, I'm not gonna draw it 2 steps. Here it gets refracted once and then it gets refracted again through the focal point on the other side of the lens It gets refracted through there just like that And then I can take another ray from the tip of that arrow that goes through the focal point on the side And so that is going to get refracted like this and then get refracted again. So it comes out on the other side of the lens going parallel And hopefully this makes sense to you Because it's kind of a symmetric deal that we're dealing with over here Something coming in parallel on the right side will go through the focal point Something going through the focal point will come out on the other side parallel So whatever light is coming out radially outward onto this side and going through the lens will converge at this point right over here on the other side of the lens And so you can do even light that go straight through the lens It'll end up right over there It won't be refracted at all; it'll just go straight through the lens And so the image that gets formed on the other side of the lens will look like that So in this example, it looks like we have an inverted real image Once again, it's a real image because the light is actually converging at that point You would actually be able to put some type of a screen and project the image there In the next video, we're just gonna practise this idea of drawing these rays to figure out what type of images will get depending where the object is Whether it's at the focal point, beyond the focal point, beyond two times the focal point or within the focal point, and the best thing there is to practise doing this drawing this rays and thinking about how they'll get refracted