Convex lenses

We've talked a lot about mirrors, in particular parabolic mirrors, that reflect light. What I want to do now is talk about lenses, or talk about what a lens is. And think about how they transmit or refract light. So a simple lens, and we've all seen them. Maybe it's made of glass, maybe something else. And I'm going to focus on convex lenses first. So remember, concave means it opens inward, like a cave. Convex means it kind of opens outward. And in a convex lens, it'll be symmetric. So let me see if I can draw it. One side of the lens will look like that. And this one, you could kind of view this. And oftentimes, most lenses, the simpler lenses, are made this way. So this is kind of the surface of a sphere, or 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 have another surface of a sphere that's exactly the same. I'm doing my best to draw this convex lens, just like that. That is a pretty good job here. And let me copy and paste it so I can actually use this drawing in the future, before I mark it up. All right. So I've copied it. So let's think about what's going to happen as light goes through this lens, as it's transmitted through it and maybe gets diffracted by it. So we're assuming this is 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-- I guess you could view it 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 that's going parallel to that, right when it hits this surface over here-- Remember, the perpendicular at this point is going to 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 to stay outside a little bit longer. Or actually I should say, the top side of the light-- if you imagine the car analogy-- is going to be able to stay out of the lens a little bit longer than the bottom side, or the bottom wheels. Or if we go in the direction of the light, the left side of the car is going to be able to-- And just so we can visualize the car, there's the left wheels. Those are the right wheels. The left wheels are going to be able to stay out a little bit longer and travel faster a little bit longer. So this is the perpendicular again. So it will it 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. And let me draw our perpendicular over here. And you could imagine that the right side of this ray is going to-- Actually, 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 maybe the top tires are going to come out first, they're going to be able to travel faster. And so you'll be deflected even more downwards. So it will look something like this. And 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, we're going to be refracted a little bit like that. And there we'll be refracted more. And then we're going to go to that same point. So that's another ray. And then this is another parallel ray. It'll be refracted a little bit over here, and then a little bit more. And it'll go to that same point. And I think you could guess what I'm about to call this point. I wish I could draw my lines a little bit straighter. It's refracted a little bit, and then refracted a little bit more, and goes straight into that point. This point, where all of the parallel rays-- Sometimes you'll hear them talked of as collimated rays. Those are 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 had collimated rays, or parallel rays, coming from the right side, the same thing would happen. But it would just be on the other side. So that ray would go like that. And then it would be refracted some more. And maybe it would go to this point, right over here. And so you actually have two foci for a lens. Two actual points where, if parallel rays are coming from one side, they'll be focused on the point on the other side. And if parallel arrays are coming from the left side, they'll be focused at the focal length or at the focus point on the right-hand side. And this goes the other way around. Let me draw another lens. And actually, one thing that we're going to assume while we're dealing with lenses, and this is kind of a simplifying assumption, is called a 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're going to do that here, as well-- we're just going to ignore that difference in distance, because that would lead to some differences in how the light is refracted and transmitted and all of that. Because it has to travel a smaller distance here than over here. So we're going to ignore those differences, and we're just going to make the thin lens assumption. But using a thin lens assumption, let's think a little bit about what's going to happen with the light. And in the next few examples, I'm not going to worry about this kind of two-step. I'm just going to say, look, it just in general 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 on this side, so that is one focal point. And then it has another focal point, the exact same distance, on the other side. This lens is symmetric. So let's think about what this lens will do to the images of different objects. So let me draw its principal axis again. So both focal points lie along that principal axis. Now let's stick an object out here, beyond the focal length. So let's think about what's going to happen. So first, remember, we can pick any point on this object. Light is being diffusely reflected off of every point. I like to pick points that are going to do something that's kind of predictable. So let's pick a point. Well, let's take the tip. And take a ray that does something that's predictable. So let's take a ray that is parallel to the principal axis. I mean, I could draw this two steps so it gets refracted once. And then it'll get refracted again through the focal point on the other side of the lens. So then it gets refracted through there, just like that. And then, I could take another ray from the tip of that arrow that goes through the focal point on this side. So it goes through the focal point on this 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. Then 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 could do even light that goes straight through the lens would end up right over there. It actually won't be refracted at all. It'll just be able to 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. And 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 going to practice this idea of drawing these rays to figure out what type of images we'll 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 we'll just get a lot of practice doing this, drawing these rays and thinking about how they'll get refracted.