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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 for 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 going through all the different situations but more is 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 I'll put the object right here We'll do our classic arrow Actually I'll make a point here. 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 gonna call it 2 focal length, because it's really not the center of curvature-- or this distance really isn't the radius of curvature of each of these curves. So we're just gonna call it 2 focal lengths So with that said, let's actually try to figure out what the image of this thing would look like as the light from it gets refracted through this lens So like always, it's useful to draw one ray Every point of this object is emitting rays in every direction because it's diffusely reflecting light So we can just pick rays that are convenient So we can go from the tip of the arrow and go parallel to our principal axis just like that I'm not gonna show all the internal refraction within this lens right here But we know that 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 And on the left side of the lens we'll do another ray that goes through the focal point on the left side and then comes out parallel The incident ray goes through the left focal point and when it gets refracted, it will now be parallel And so the light that came from that point of the object will reconverge right over here So if you did this for every point of this object if you did a point in the middle right over here, it would reconverge right over here If you did this point right over here, it would reconverge right over there So the image of this object is going to look like this So it's going to be a real image. The rays actually converge here. So it's a real inverted image It was pointing up before. Now it's pointing that down And in this situation, it's actually going to be smaller than the original So, real, smaller, inverted image Let's do a couple of other scenarios Let me copy and paste this before starting this video to save on time Let's do a situation now where the object is at the 2 focal distances. I guess we can call that Let's put the object right over here We can do the exact same thing You might want to do it on paper on your own to get some practice doing it We'll do one ray that'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 they can reconverge or they converge right over there So you can see that this is actually a parallelogram This distance right there is going to be the same thing as that distance over here It is actually--I don't want to say asymmetry. You can't flip it over But 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 the geometry Anyway, this would be an inverted image of exactly the same size at the exact same distant 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 gonna be closer to lens But here the image is going to be the same size as the original object It's going to be inverted, but it's going to be at the same distance from the lens just on the other side. Once again this is a real image Let's do another one Copy and paste So let's stick something between one focal length and two focal lengths So what's put my object right over there So once again, let's go parallel then we will refract 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 So here, we will have--remember, I could use any point. Here I just used the tip because I know the base will converge over there If I took 2 points, it would go converge right back there And then if I did with a point right here and I did that same exercise, it would go right over there And so the whole image would show up over here So here, it's real; it's inverted; and it's larger and it is now further away from the lens than the object on the other side This is really kind of the reverse of the first example The first example, the object was larger and more than two focal lengths away and the image was in this range Now the object is here and now the image's on the other side. So they're kind of-- that's really just the other side of that first examples Let's do a couple more So let's put the object at the focal point and see what would happen And sometimes people memorize this type of things for physics exams You don't need to. All you have to do is remember just think about 2 rays usually from the tip of the arrow that gives you a sense what the image will look like and you do one parallel and one that goes through the focal point Well, with that said we're gonna do something slightly different when something is sitting at the focal point When something is sitting at the focal point one is we can do the parallel It will be refracted through the focal point on the other side And then instead of doing a ray that goes through the focal point on this side because actually you can't. You're sitting on the focal point right there Let's do a ray that does not get refracted. We did a similar thing with the parabolic mirrors What I want do is a ray that'll go right to the center of the lens where it won't get refracted It's just go straight through the center of the lens So what you have here is, both of these rays that were 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 is right over here They're just going to see these as 2 parallel rays of light So no image will form. Not a real image or virtual image So we can say no image is going to form Now the last case is, let's put the object less than one focal distance away Let's put the object right over here. And think about what happens Once again, the light ray from this tip where to go parallel. It will be refracted through the focal point on the other side And then let's do another light ray, going in a direction as if it were coming the direction of the focal point on this side So it comes from that direction The light ray would go like that And then it would come out on the other side parallel So clearly, these two light rays are not converging So no real image's going to form But they do look like they're diverging from some point Continue these lines. They both look like they're coming from a point right over there So what's going to happen? If someone's eyes are processing these light rays they're gonna see the tip of this arrow all the way up here They're gonna see the base of this arrow down here And essentially, they're going to see a magnified virtual image of the actual arrow Anyway, hopefully you found that interesting