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# Convex lens examples

## Video transcript

like we did with parabolic mirrors what I really want to do in this video is just put objects at different distances relative to this convex lens and just think about what its image will look like and the whole point of doing that is one look just going through all of the different situations but more just getting practice of how to think about it so let's first put an object out here that's more than two focal lengths away from the lens so I'll put the object I'll put the object right here and we'll just do our classic arrow and actually I'll make a point here when we did when we dealt with parabolic mirrors we talked about the distance of two focal lengths being our center of curvature over here we're just going to call it two focal lengths because it's really not the center of curvature of the or the or or this distance really isn't the radius of curvature of each of these curves we're just going to call it two focal lengths so with that said let's just actually try to figure out what the image of this thing will look like as the light from it gets refracted through this lens so like always it's useful to draw one ray remember every point on this object is emitting Ray's in every direction because it's diffusely reflecting light so what we do is we just pick rays that are convenient so we could go from the tip of this arrow and go parallel go parallel to our principal axis just like that and I'm not going to show all of the internal refraction within this lens right here but we know that if we if we enter the lens parallel to the principal axis when we get refracted we will go through the focal point on the other side of the lens so we will go through the focal point on the other side of the lens and we'll do the same and now on the on the left side of the lens will do another ray that goes through the focal point on the left side and then comes out parallel so let's do that I'll do that in another color so it comes out let me so it comes the incident the incident ray goes through the left focal point and when it gets refracted it will now be parallel it will it will now be parallel and so the light that came from point in the object will reconverge I guess we could say will converge right over here and so if you did this for every point on this object if you did a point in the middle right over here would reconverge right over here if you did this point right over here it would reconverge right over there and so the image of this object is going to look like this is going to look like this so it's going to be a real image the Rays actually converge here so it is a real it is a real inverted image it was pointing up before now it's pointing down and in this situation it's actually going to be smaller than the original it's a real smaller inverted image let's do a couple of other scenarios let me let me I copy and pasted this before starting this video to save on time so let's do a situation now where the object is at this at the two focal distances I guess we could call it so let's let's put the object right over here let's pull it out do it in blue this time but we do the exact same thing you might want to do it on paper for your on your own just to get some practice doing it but we'll do one ray that is parallel one ray that is parallel and when it's parallel when it gets refracted it will go through the focal point on the other side and then we'll do another ray that goes through the focal point on the left side and then it will become parallel and then it will become parallel and they could re converge or they converge right over there and so you can see that this is actually a this is this is actually a parallelogram this distance this distance right there is going to be the same thing as that distance over here there's actually I don't want to say symmetry you can't flip it over but these this is a and this distance right over here is going to be the same thing as this distance over here I won't go into all of the geometry but where and if you do this with really straight lines it would just come out that way but this will just be an inverted image that's exactly the same size at the exact same distance actually I didn't talk about distance in this one over here over here it's a real image it's smaller and it's also going to be closer in than this one was it's going to be closer to the lens this is going to be really the same image or the same SOT the image is going to be the same size as the original object but it's going to be inverted but it's going to be at the same distance from the lens just on the other side and once again this is a real image let's do another one let me let me copy and paste so let's stick something between one focal length and two focal lengths so let's put something right over let's put my object let's put my object right over there so once again let's go parallel we go parallel then we will refract through the focus on the other side I can do a better job than that we can go through the focus on the other side and then let's go through the focus on the left side and then we will refract and go parallel and we will refract and go parallel so here we will have we will have remember I could do this with every point I'm just doing it with the tip because I know the base will that will converge over there if I just took two points it would it would converge right back there and then if I did that with a point right over here if I did that same exercise it would go right over there and so the whole image the whole image would show up over here so here it's real it's inverted it is now larger and it is and it is now further away from the lens than the object just on the other side so this is really kind of the reverse of the first example the first example the object was large and more than two focal lengths away and the image was in this range now the object is here and now the image is on the other side so they're kind of there there it's really just the other side of that first example so let's do let's do a couple more let's do a couple more so let's put the object at the focal point let's put the object at the focal point see what happens and sometimes people memorize this type of things for physics exams for optics again today you don't need to all you have to do is remember just just think about two rays usually from the tip of the arrow that because that gives you a sense of what the image will look like and you one parallel and one that goes through the focal point and well with that said we're going to do something slightly different when something is sitting at the focal point when something is sitting at the focal point one is we could do the parallel ray so the parallel ray it will be refracted through the focal point on the other side and then instead of and instead of going something that doing a ray that goes through the focal point on this side because it's actually you can't you're sitting on the focal point right there let's do a ray that does not get refracted and we did a similar thing with the parabolic mirrors what I want to do is array or actually the parabolic Muellers we did a ray that went right at the center but over here will go right to the center of the lens where it won't get refracted so it's just going to go straight through it's just going to go straight through the center of the lens and so what you have here is both of these rays that were that we're diverging from this point from this tip they don't reconverge anywhere and they don't even look like they're diverging from another point if someone's eyeball if someone's eyeball is right over here they're just going to see these as two parallel rays of light so no image will form not a real image or a virtual image so we can say we can say no no image is going to form now the last case is let me draw this I'm running out of space let me just paste it over here so the last case let's put the object less than one focal distance away so let's put the object let's stick let's put the object right over here and think about what happens so once again if a light ray from this tip we're to go parallel it will be refracted through the focal point on the other side and then let's do another light ray go in a direction as if it were coming from the direction of the focal point on this side so if it were to come from that direction the light ray would go like that and then it would come out on the other side parallel so it would come out on the other side parallel so clearly these two light rays are not converging so no real image is going to form but they do look like they're diverging from some point they do look like they're diverging from let me continue these lines they do they both look like they're coming from a point they look like they're coming from a point right over there so what's going to happen well if someone's eyes are processing these light rays they're going to see the tip of this arrow all the way up here they're going to see the base of this arrow they're going to see the base of this arrow down here and essentially what's going to happen essentially what's going to happen is they're going to see a magnified they are going to see a magnified version they are going to see a magnified virtual image I should say then we're going to see a magnified virtual image of the actual arrow anyway hopefully you found that hopefully you found that interesting