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# Parabolic mirrors and real images

## Video transcript

in this video I want to expose you to a special class of mirror is called parabolic parabolic mirrors or sometimes called parabolic parabolic reflectors and what's neat about parabolic mirrors and I'll draw a cross section of one right here and if you're familiar with the algebra they are essentially the cross section the cross section especially is in the shape of a parabola so let me draw a parabolic mirror right here so it's in the shape of a parabola just like that and what's neat about a parabolic mirror and I'm not going to go into the math right here I just want to give you the general idea is if and let me just draw its principal axis so this is kind of the line of symmetry of the parabola so this is its principal axis right over here it divides it in two and in a parabolic then this is just a cross-section you could imagine if this was spun around if it was spun around that principal axis you would get something that would look like this you would get something that would look like a bowl it looks like a bowl but it's actually the shape of a parabola it's not it's not an actual sphere shape so if you rotate this around you would get a circle around the edge so this would be a circle right over here but this shape 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 or what's neat about parabolic mirrors is if I have parallel light rays coming into a parabolic mirror so if I have do my best to draw a power a parallel light ray so parallel to its central axis so if I have a light ray that comes like that it will reflect off of the Parrot so it's parallel to this principal axis it will reflect like that now if I and I'm I'll tell you what's neat about this in a second let me draw another parallel ray let's say I have a parallel ray that's coming in it's coming in right over there so it hits the parabolic Muller at that point mirror at that point it's going to reflect so it comes in like that and if I have another ray that comes in like this it comes in like this it will reflect so that the reflection goes right over there so - neat about this what's neat is any light ray that comes in parallel any incident light ray that's parallel to the principal axis of this parallel Miller 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 was parallel to the principal axis the reflected ray is going to hit this point and this point right here is the focus this right there is the focus this is the focus of the parabolic mirror now know what's what's neat about this well let's say that you are trying to capture heat from the Sun you are trying to concentrate the the electromagnetic radiation from the Sun so what you could imagine you could go to the middle of the desert you could go to the middle of the desert and people do do this and you set up parabolic mirrors like this that are pointed at the Sun and the sun's rays come in and the Sun is so far away they're essentially just coming in parallel because they're I mean they're they are radiating from the Sun but the Sun is 93 million miles away so the Rays for our purposes are essentially coming in parallel and what's neat about them is is when they hit the surface of the parabolic Miller mirror they all get they all get reflected to one point so if you have a ray coming in there it's going to get reflected there ray coming in like that's going to get reflected like that and so all of the energy all of the energy can be focused on a point like that and so you could imagine you it 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 a 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 car if you have a light you could imagine if car if car headlights were just you know if I drew a car like this let me scroll down a little bit if I drew a car like this let me draw have a reasonable attempt at a car so let's say that this is a car right over here I think you get the idea this is the wheel housing that's the wheel so forth and so on this isn't the drawing of the car but you could imagine if we just stuck light bulbs at the front of cars so you could imagine just a light bulb sitting at the front of a car so that's a light bulb and that would provide light but it would provide light in all directions radially outward it would be kind of useless first of all it would probably the way I drew it here would probably show up in the dudes eye who's trying to drive the car but it's a lot of wasted energy a lot of the light is coming back onto the car and it's pointing in all sorts of random directions it's not so useful when you are driving a car you want all of the light pointed at the road or maybe the stuff that's directly above the road so how could you point in the light well you could use a parabolic mirror and all of your any car you look at will have a light inside of a parabolic mirror and what does that do let's say I put let's say instead of this instead of this situation that I just drew let me clear this out and I'll draw it on a larger scale just to make it let's say I had a parabolic mirror here so I have a parabolic mirror mirror obviously this looks more like a snow shovel or something but I'm drawing it way huge just so you get the general idea so this is a parabolic mirror and let's say when we put the light bulb now we put the light bulb at the focal point at the focus at the focus of this parabolic mirror now what's going to happen well light that has to go in this direction that comes readily outward that's good because that's light that's being useful to the driver it's actually illuminating the road but light that's going backwards light that's radiating outward from that focus of the parabola it's going to be reflected it's going to do the exact opposite of that solar energy collector it's going to be reflected out parallely or in a parallel way and it's just going to so all of the light because of this because of this parabolic reflector or parabolic mirror all of the light that this light source is generating or most of it is going to be emitted parallel parallel to the principal axis of the problem actually you could point the light if you actually moved this parabola around you can point which direction the lights in so it's actually a pretty a pretty useful thing to have now the other thing about parabolic mirrors is that they actually form REE 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 it's getting reflected but a real image let me draw it over here so let me draw a parabolic mirror let me draw a big parabolic mirrors to make the diagram clear and let me draw its principal axis so its principal axis this is kind of a side profile of it this is let me draw its principal axis just like just like that and let's put an object so let me I'm going to define a couple of interesting points here so that first of all we have our focal point I'll call that F and then there's something called the center of curvature and the curvature I always imagined it as a sphere but for center of curvature of a parabolic mirror it's actually going to be two times the focal length so if this distance right here 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 we call that Point C but this distance over here is going to be F as well or it's going to be 2f from you could imagine that vertex or that kind of Mac that minimum point of the parabola depending on how you want to view it now what I want to do is put a couple of objects in front of this parabolic mirror and just think about what happens to the light rays of that object so let's first let's first put an object here so I'm just going to draw the object as an arrow so I just draw the object as an arrow and that object you know 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 and I'm just going to pick a points on this object to radially emit light outward from or reflect light outward from and see what happens to those light rays so let's say and for the for the sake of simplicity whenever you do something 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 so let's do one that's parallel so and of course these are just two of the gazillions of light rays that are being emitted from every point of this object but we're just doing this to understand what will the 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 go through the focus so let's make another light ray go through let me draw it a little bit better than that another light ray going through the focal point just 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 those two rays that were emitted by the same point on this arrow object they both get you know they radially emit outward they reflect on this parabolic mirror mirror at two different points but then they converge again they converge right over there and actually if you put and we can do that with every point if you did the the stuff that leaves that point actually both of those are going to go and come back go through the focal point and then come back right over here I mean they'll keep going but you can imagine you could do this with every point every point on this arrow and what you're going to do is get an image that looks like this you're going to have an image that looks like this this point up here corresponds to that point this point corresponds to that point and so if you were to put if you were to put a screen if you were to put a screen right over here if you were to put this is a screen a screen it could just be a I don't know a white tablecloth or if there was a wall right over here then it would actually show the image you would actually be projecting the image on to this wall right over here it was a it would actually be a projected image and that projected image that we're talking about where the light is converging so the light comes radially outward from each point of this arrow and then it converges on a point on this screen that could that image that gets formed we call that a real image it's real image this is a real real image and you might want to compare that to what we called 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 that that it's they've really been reflected off of some surface so what we think is there really isn't there a real image is an image that's actually projectable we could put a screen mean 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 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 I've gone longer than I like to it some of these videos will talk a little bit more about parabolic mirrors in the next video