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Studying for a test? Prepare with these 3 lessons on Geometric optics.
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Parabolic mirrors and real images

Video transcript
In this video, I want to expose you to a special class of mirrors called parabolic mirrors sometimes called parabolic reflectors What's neat about parabolic mirrors--I'll draw a cross-section of one right here If you're familiar with the algebra, essential the cross-section is in the shape of a parabola Let me draw a parabolic mirror right here. So it's the shape of a parabola, just like that What's neat about a parabolic mirror--I'm not going into the math right here I just want to give you the general idea Let me just draw its principal axes. This is kind of the line of the symmetry of the parabola So this is its principal axis right over here, dividing it in two This is just the cross-section. You can imagine if this was spun around spun around that principal axis, you would get something that would look like this you would get something that would look like a bowl but it's actually the shape of a parabola; it's not an actual a sphere shape So if you rotate this around, you'll get a circle around the edge So this would be a circle right over here But this shape down here is not a hemisphere It's not spherical; it's actually a parabola And the reason why we care about a parabola, what's neat about parabolic mirrors is that if I have parallel light rays coming into a parabolic mirror so if I have parallel light rays, parallel to its principal axis if I had a light ray that comes like that, it will reflect like that I'll tell you what's neat about this in a second. Let me draw another parallel ray Another parallel ray that's coming in over there, hitting the parabolic mirror at that point It's going to reflect like that And if I have another ray that comes in like this it will reflect, so that the reflection goes right over there What's neat about this? What's neat is any incident light ray that comes in parallel to the principal axis of this parabolic mirror the reflected ray is going to go through the same point I don't care where you hit the mirror as long as it's parallel to the principal axis So our reflected ray's going to hit this point At this point right here is the focus This is the focus of the parabolic mirror What's neat about this? Let's say that you are trying to capture heat from the sun You are trying to concentrate the electromagnetic radiation from the sun So you can imagine you could go to the middle of the desert and people do this and you set up parabolic mirrors like this pointed at the sun and the sun's rays come in and the sun is so far way They're essentially just coming in parallel I mean, they are radiating from the sun, but the sun is 93,000,000 miles away So the rays for our purposes are essentially coming in parallel And what's neat about them is when they hit the surface of the parabolic mirror they all get reflected to one point So if you have a ray coming there, it's gonna get reflected there So if you have a ray coming like that, it's gonna get reflected like that And so all of the energy can be focused on a point like that So you can imagine you might have a water pipe kind of running into the screen here and so all of that light energy would be used to heat up that water pipe So it's a pretty neat way to concentrate energy Another thing you might want, maybe instead of taking in energy maybe you want to give out energy so that all the beams of light are parallel For example, let's say you have a light for a car If you had a light, you could imagine--let's think about car headlight Let me draw a car like this You get the idea that this is the wheel housing. That's the wheel, so forth and so on It's about the drawing of the car You could imagine if we just stuck lightbulbs at the front of cars You could imagine just a lightbulb sitting at the front of the car That's a lightbulb And that would provide light but it would provide light in all directions radially outward, kind of useless First of all, the way I drew it here would probably show up in the dude's eye who's trying to drive the car but there's a lot of wasted energy. A lot of the light is coming back onto the car and is pointing in all sorts of random directions. It's not so useful When you're driving your car, you want all of the light pointed at the road maybe this stuff is directly above the road So how could you point the light? Well, you could use a parabolic mirror and any car you look at will have a light inside of a parabolic mirror. What would that do? Let's say instead of this situation that I just drew Clear this out and I'll draw it at a larger scale Let's say I had a parabolic mirror here I'm drawing it way huge just to you get the general idea. So this is a parabolic mirror Let we put the lightbulb now at the focal point, at the focus of this parabolic mirror Now what's going to happen? Well, light that has to go in this direction would come radially outward. That's good That's light that's been useful to the driver. It's actually illuminating the road The light that's going backwards from that focus of that parabola will be reflected exact the opposite of that solar energy collector It's going to be reflected out in a parallel way Because of this parabolic reflector or parabolic mirror all of the light that this light source is generally is going to be emitted parallel Parallel to the principal axis of the parabola Actually, you could point the light. If you move this parabola around, you can point which direction the light's in. So it's actually a pretty useful thing to have Now another thing about parabolic mirrors is that they actually form real images In the last video, we talked about the notion of a virtual image You think something is there because it looks like the light is converging at some point but that point isn't even there. It's actually from some other point, getting reflected But the real image--let me draw it here. Let me draw a parabolic mirror Let me draw a big one to make the diagram clear Let me draw its principal axis It's kind of a side profile of it Let me draw its principal axis just like that Let me put in objects. I'm going to define a couple of interesting points here First of all, we have our focal point. I'll call that f And then there's something called the center of curvature Curvature is a sphere. But for center of curvature of a parabolic mirror is actually going to be two times of focal length So this distance right here--let me make it clear. I'll call that--this distance right here is f then this distance right here to the center of curvature I'll call that point c, but this distance over here is going to be f as well or it's going to be 2f from that vertex or the minimum point of the parabola depending on how you want to view it Now I want to put a couple of objects in front of the parabolic mirror And just think about what happens to the light rays of that object Let's first put an object here. I'll draw it as an arrow And that object, maybe some light is shining on it from who knows what direction but it's going to reflect that light diffusely assuming it's not shiny I'm just gonna pick a point on this object to radially reflect light outward from Let's see what happens to those light rays For sake of simplicity, whenever you do it with a parabolic mirror it's good to emit one radial ray that's parallel and one that goes to the focus because we know what they're going to do after that. Let's do one that's parallel Of course these are just two of the gazillions of light rays being emitted from every point of this object We're just doing this to understand what will be image of this object actually look like So let's do one parallel It hits the surface of the parabolic mirror and then it reflects and goes through the focus We know that already And then let's make another light ray that goes through the focus, or the focal point like that And then it reflects and it'll be reflected in a parallel way So what just happened here? Those two rays that were emitted by the same point on this arrow object they both emit radially outward They reflect on this parabolic mirror at two different points but then they converge again, right over there And actually, we could do that with every point If you deal with that point, both of those are gonna go and come back go through the focal point and then come back right over here and keep going You could imagine every point on this arrow You are going to get an image that looks like this This point corresponds to that point This point corresponds to that point and so if you were to put a screen right over here-- This is a screen. It can just be a white tablecloth or there's a wall right over here-- then it would actually show the image; it would actually projecting the image onto this wall right over here It will be a projected image and that projected image that we're talking about where the light is converging. So light comes radially outward from each point of this arrow and then it converges on a point on the screen that can-- that image that gets formed, we call that a real image This is a real image You might want to compare that to a virtual image A virtual image is an image that looks like it's coming from someplace because it looks like things are diverging from some point but they've really been reflected off of some surface. So we think it really isn't there A real image is an image that's actually projectable We could put a screen right over here and then these guys are going to be hitting the screen and essentially diffusing the exact same light They will be diffusing the exact same light as this point of the actual object And because of that, the screen will look just like the object This is a projectable image Anyway, hopefully you found that useful. I realize that I've gone longer than I'd like to with some of these videos We'll talk a little bit more about parabolic mirrors in the next video