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# Convex lenses

## Video transcript

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 out of glass maybe something else is each surface and I'm going to focus on convex lenses first so remember concave means it kind of 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 so it'll be 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 and I could do part of the surface of a sphere and it's symmetric so it has some center or right over here just like that and then you have another surface of a sphere that's exactly the same doing my best to draw this convex lens just like that that is pretty that's a pretty good job here 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 is light goes through this lens as its transmitted through it or me and maybe gets diffracted by it so we're assuming this is air out here this is glass something that has a higher index of refraction something in which light travels slower so you could imagine that some light that is going parallel that is going parallel I guess you could view 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 millers mirrors but if you imagine light that's going parallel to that right when it hits this surface over here remember the 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 no the top side of the light if you imagine the car analyses our 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 with the direction of the light the left side of the cars are 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 stand a little bit longer and travel faster a little bit longer and so it will so this is the perpendicular again so it will be refracted 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 into a faster medium into the air again and let me draw our perpendicular over here so let me draw a perpendicular over here and you can imagine that the right side the right side of this Ray is going to the right side of this actually so let me be good 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 it'll look something like it will look something like this and the light ray and the light ray 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 any ray that is parallel to the principal axis of the lens any ray that is parallel to the principal axis of the lens it will be refracted through the lens to that same point to that same point so here we're going to be refracted a little bit like that and there will be refracted more and then we're going to go to that same point and that'll 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 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 I frakked a little more and goes straight to that point this point where all of the parallel rays sometimes you'll hear them talked of is collimated rays those rays of light that are roughly parallel they're all with 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 this right here you can view as the focus of the of the lens or you could view this length from the lens to that point as the focal length now this lens is completely symmetric anything you could do from one side you end up getting focused on the right side if you had Cola mitad rays or parallel rays coming from the right side get 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 would go to this point it would go to this point right over here and so you actually have two foci for parallel for a start for a lens two actual points where if if parallel rays are coming from one side they'll be focused on the point on the other side and the parallel rays are coming from the left side they'll be focused on at the folk 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 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 it's called the thin lens assumption there is a difference in distance it travels depending on where the light travels in in in the lens for example here there's less distance then over then 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 is refracted and transmitted all of that because NASA travels a smaller distance here then over here so we're going to ignore those differences 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 when it exits the lens so let me just draw a simple lens right over here a simple lens 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 and 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's let me draw its principal axis again so both focal points lie along that principal axis now let's take an object let's take 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 let's 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 and then I mean I could draw this to step 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 a 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 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 it was 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 it looks like we have an inverted real image in verted real image and once again 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 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