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Like we did with parabolic mirrors, what I really want to do in this video

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is just for put objects at different distances relative to this convex lens

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and just think about what its image will look like

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And the whole point of doing that is going through all the different situations but

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more is getting practice of how to think about it

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So let's first put an object out here

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That's more than two focal lengths away from the lens

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I'll put the object right here

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We'll do our classic arrow

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Actually I'll make a point here. When we dealt with parabolic mirrors

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we talked about the distance of two focal lengths being our center of curvature

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Over here we're just gonna call it 2 focal length, because it's really not

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the center of curvature--

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or this distance really isn't the radius of curvature of

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each of these curves. So we're just gonna call it 2 focal lengths

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So with that said, let's actually try to figure out what the image of this thing would look like

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as the light from it gets refracted through this lens

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So like always, it's useful to draw one ray

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Every point of this object is emitting rays in every direction

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because it's diffusely reflecting light

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So we can just pick rays that are convenient

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So we can go from the tip of the arrow

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and go parallel to our principal axis just like that

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I'm not gonna show all the internal refraction within this lens right here

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But we know that if we enter the lens, parallel to the principal axis

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when we get refracted, we will go through the focal point on the other side of the lens

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And on the left side of the lens

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we'll do another ray that goes through the focal point on the left side

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and then comes out parallel

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The incident ray goes through the left focal point

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and when it gets refracted, it will now be parallel

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And so the light that came from that point of the object will reconverge right over here

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So if you did this for every point of this object

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if you did a point in the middle right over here, it would reconverge right over here

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If you did this point right over here, it would reconverge right over there

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So the image of this object is going to look like this

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So it's going to be a real image. The rays actually converge here. So it's a real inverted image

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It was pointing up before. Now it's pointing that down

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And in this situation, it's actually going to be smaller than the original

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So, real, smaller, inverted image

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Let's do a couple of other scenarios

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Let me copy and paste this before starting this video to save on time

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Let's do a situation now where the object is at the 2 focal distances. I guess we can call that

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Let's put the object right over here

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We can do the exact same thing

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You might want to do it on paper on your own to get some practice doing it

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We'll do one ray that's parallel

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When it gets refracted, it will go through the focal point on the other side

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And then we'll do another ray that goes through the focal point on the left side

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and then it will become parallel

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And they can reconverge or they converge right over there

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So you can see that this is actually a parallelogram

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This distance right there is going to be the same thing as that distance over here

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It is actually--I don't want to say symmetry. You can't flip it over

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But this is a--and this distance right over here is going to be the same

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thing as this distance over here. I won't go into all the geometry

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Anyway, this would be an inverted image of exactly the same size at the exact same distance

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Actually I didn't talk about distance in this one over here

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Over here, it's a real image; it's smaller and it's also going to be closer in

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than this one was. It's gonna be closer to lens

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But here the image is going to be the same size as the original object

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It's going to be inverted, but it's going to be at the same distance from the lens

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just on the other side. Once again this is a real image

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Let's do another one

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Copy and paste

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So let's stick something between one focal length and two focal lengths

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So what's put my object right over there

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So once again, let's go parallel

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then we will refract through the focus on the other side

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And then let's go through the focus on the left side

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And then we will refract and go parallel

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So here, we will have--remember, I could use any point. Here I just used the tip

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because I know the base will converge over there

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If I took 2 points, it would go converge right back there

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And then if I did with a point right here

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and I did that same exercise, it would go right over there

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And so the whole image would show up over here

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So here, it's real; it's inverted; and it's larger

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and it is now further away from the lens than the object on the other side

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This is really kind of the reverse of the first example

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The first example, the object was larger and more than two focal lengths away

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and the image was in this range

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Now the object is here and now the image's on the other side. So they're kind of--

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that's really just the other side of that first examples

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Let's do a couple more

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So let's put the object at the focal point and see what would happen

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And sometimes people memorize this type of things for physics exams

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You don't need to. All you have to do is remember just think about 2 rays

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usually from the tip of the arrow that gives you a sense what the image will look like

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and you do one parallel and one that goes through the focal point

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Well, with that said

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we're gonna do something slightly different when something is sitting at the focal point

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When something is sitting at the focal point

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one is we can do the parallel

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It will be refracted through the focal point on the other side

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And then instead of doing a ray that goes through the focal point on this side

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because actually you can't. You're sitting on the focal point right there

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Let's do a ray that does not get refracted. We did a similar thing with the parabolic mirrors

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What I want do is a ray that'll go right to the center of the lens

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where it won't get refracted

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It's just go straight through the center of the lens

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So what you have here is, both of these rays that were diverging from this point from this tip

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they don't reconverge anywhere

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And they don't even look like they're diverging from another point

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if someone's eyeball is right over here

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They're just going to see these as 2 parallel rays of light

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So no image will form. Not a real image or virtual image

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So we can say no image is going to form

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Now the last case is, let's put the object less than one focal distance away

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Let's put the object right over here. And think about what happens

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Once again, the light ray from this tip

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where to go parallel. It will be refracted through the focal point on the other side

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And then let's do another light ray, going

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in a direction as if it were coming the direction of the focal point on this side

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So it comes from that direction

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The light ray would go like that

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And then it would come out on the other side parallel

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So clearly, these two light rays are not converging

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So no real image's going to form

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But they do look like they're diverging from some point

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Continue these lines. They both look like they're coming from a point right over there

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So what's going to happen? If someone's eyes are processing these light rays

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they're gonna see the tip of this arrow all the way up here

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They're gonna see the base of this arrow down here

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And essentially, they're going to see a magnified virtual image of the actual arrow

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Anyway, hopefully you found that interesting