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# Parabolic mirrors 2

## Video transcript

let's draw a bunch of parabolic mirrors and what I want to do in this video is do a bunch of examples of objects in front of parabolic mirrors and think about what the images of those objects will be based on how far those objects are and besides just giving us a better understanding of parabolic mirrors this will also it'll hopefully also give us a sense of how do we how do we manipulate or how can we conceptualize these light rays which will be a pretty useful tool when we tackle other types of reflective or refractive devices like lenses so that's a parabolic mirror I've drawn its principal axis right over here and let me just copy and paste this just so that I actually let me draw the focal point too so this is the focus right over here so let me just draw the focus right over there and this is the center of curvature it's twice the distance from this point as the focus so that is the let me make it as close as possible so that is the center of curvature right over there and let me copy and paste it so we can reuse this later on in the video I don't have to keep drawing it so copy it all right so I've copied that now let's put an object and I think we did this in the last video let's put an object beyond the center of curvature so let's put an object here and the convention is to use upward pointing arrow this isn't a light ray it's used to show an object and we use the tip of the arrow to really kind of show the top of the object and that's usually where we trace our our light rays from but it doesn't have to be there you could do the middle you could do the bottom and you could figure out what the image of the objects going to be so let's do that and when you're dealing with parabolic mirrors it's easiest to have to show just two light rays one that goes parallel to the principal axis and one that goes through the focus because you know what's going to happen to each of those when they reflect you don't have to do any math there so let's have the parallel ray that's the parallel ray when it reflects the the parallel incident ray when it reflects it will go through the focus it will go through the focus and then let's have an incident ray that goes through the focus an incident ray that goes through the focus and when it reflects it will be parallel it will be parallel and this is the example we actually saw in the last video and so whatever light is being emitted from this point over here in that direction it will come back and converge again at this point and we could actually do it at every point along the we could do it halfway this halfway point of the arrow just to make it clear this halfway point of the arrow same thing you have a parallel it's something parallel will go will reflect a parallel incident ray will reflect through the focus and I'll just do it for this one right over here it will reflect through the focus and then if you have something that goes through the focus then incident ray that goes through the focus it will reflect parallel it will reflect parallel so this point will correspond to this point over here I think that makes it clearer that this image the image of this object when it's reflected by this parabolic mirror will look will look will look just like that so will actually form a real image and it will form a real image that is smaller than this original image it's not so clear the way I did it over here but you could put push this even further back out and it'll be clear that this is going to be a smaller real image than that right over there now let's do a couple of more examples so let me just paste my drawing so I don't have to redraw it let's see what happens let me write it so here the image just so we can keep track of things here the image the image is real image is real and smaller and smaller than the actual object when the actual object is beyond is beyond the center of curvature and actually let me let me make it a little bit clearer by drawing let me do another example like that where I do something big way out here just to make it clear so once again we go parallel reflect through reflect through the focus and then we can go through the focus we go through the focus and then reflect out like that and there you see now it's much clearer that the image that the image is going to be much smaller and of course inverted relative to the actual object now let's do this again but this time let's place the object at the center of curvature so let's place let's place the object let's place the object right over here so right at that distance that twice the distance from from the vertex of the parabola to the focus so we do a parallel line these lines are the hardest things to do so parallel incident ray parallel to the principal axis this is the principal axis right here principal axis that's what this line is right over here it's kind of the line of symmetry of the parabola when it reflects it will reflect through the focus it will reflect through the focus and then let's take another ray that goes the incident ray goes through the focus and when it reflects it will reflect parallel it will reflect parallel and my drawing isn't the neatest drawing on the planet and actually let me draw it a little bit better than that well that's pretty good let me just so that's the incident ray that was parallel and then an incident ray that goes through an incident ray that goes let me them having trouble drawing these an incident ray that goes through the focus will then come out and reflect right over there and they'll converge and the way I've drawn it my drawing isn't ideal but the way but the reality is is that they'll converge so that the image will just be in an inverted same size version as this thing up here because it's symmetric let me see if I can read read read are this whole thing so it comes out neater so so far that looks good so then you want to reflect you want to reflect like that you got you're coming through the focus and then you have another ray that goes through the focus and this whole thing should be symmetric and then when it reflects it comes back out like that so that makes it a little bit clearer so this is the object and now it's image it's just an inverted version of this object the image kind of comes into focus or I guess you it the the the Rays converge at the same distance from the actual mirror as the actual object and it's going to be the same size just inverted so that's so here the image here the image is real and the same size and the same size as the object let's do a couple more of these I think you get the hang of it and you might want to try them out you might want to pause the video and try it out on paper because really and I think nothing beats practice so let's let's take our object let's stick our object between the center of curvature and the focus and the focal point so if we put our object there we could have a light ray that goes parallel to the principal axis and then it will reflect out through the focus and then you could have another point it goes through another ray it goes through the focus and then it reflects and then it will reflect out it will reflect out it will reflect out and let me draw it better than that actually this is that's I should probably have used a more precise tool when I did all of this so let me draw it let me draw it right over here so I'll have the parallel one and then it goes through the focus just like that when it gets reflected I really should have had a line tool for this to have neater drawings and then array that goes through the focus that goes through the focus will be reflected out parallel would be reflected out parallel and at least for the light that comes from that tip they will reconverge at that tip and if you did it for every point on this arrow the image would be an inverted arrow that is bigger than the original and it is beyond it's almost the opposite of the first example that we showed and so now the image is bigger than the original so the image is real and it is bigger and the image and and the image will will will it where it converges is going to beyond be beyond the centre of curvature and you could imagine if this was the object right here then this would be the image over here if you just trace the lines backwards so there's kind of a symmetry here between this example and the first one we did up here now let's just do a couple more let's imagine if the object is actually at the focal point it's actually at the focus so let's draw an object there let's think about what would happen so if we're at if we're at the focus array that comes out parallel will will go through the focal point and come out just like that and then here we're going to you can't we if we can't have a ray that just goes well actually we could have a ray that goes through well that that become you can't go into the object so here I'll do a slightly different ray I'll do a ray that intersects that intersects the parabolic mirror right over there and the reason why I want to do there is because there the parabolic Miller mirror is essentially flat and essentially vertical so you can kind of imagine that the incident ray is going to be the same thing as the reflected ray so you could draw a ray that comes in like that so this is a departure from what we did before and then the reflected ray will come out like that so what happens when an object is at the focal point is that all of the light all of the light that's coming off of this object in any direction all of the light is coming off of this object in any direction will all be made it will all be made parallel and so it won't converge so it won't converge so it won't be able to form a real image and it's not it doesn't look like it's diverging from some from some point in the mirror so it won't even form a virtual image so here there will actually be no image no image when the object is actually at the focal point and then the last case as you can imagine is if an object is closer than the focal point so let's draw that so let's put an object at the focal point so right over here and here just just for the sake of argument one I can draw I can always draw a parallel and anything that any light that goes parallel will then look to come out in a direction that would go through the focal point so it would go through the focal point it would come out in that direction although the object itself is blocking but it would look to go in that direction it would be reflected in that direction and then you can imagine a ray of light that would have been coming from the focal point or would have been coming in from the same direction so you can imagine coming from the same direction as a focal point would be reflected parallel in a parallel direction to the principal axis in a parallel direction now these two light rays are not converging but they look like they're diverging from some point behind the mirror they'll look like they're diverging from some point behind the mirror so in this case we are forming a virtual image we are forming a virtual a virtual image and the virtual image will actually look something like this and so it'll be larger it'll be larger than the original virtual image so it's kind of a magnifying if you were to go to what do they call it a funhouse at the circus or the amusement park or whatever and if you were to get close enough to a parabolic mirror it would show a magnified a magnified version of you a virtual version of you actually let me draw that a little bit bigger just because it might not be clear so let me draw so if this is the mirror that is the focal point this right here is the principal axis this is may be you may be it whatever object you can draw a ray that goes parallel it will reflect in the direction of the focal point so it'll reflect out like that it'll be black blocked by the object though and then something that looks like it would have come from the focal point from the same direction as a focal point would then be reflected parallel to the principal axis so these two rays once again they are diverging but they look like to the human brain to the human eye they look like they came from that point over there and so this would correspond to that point on the virtual image that point on the virtual image so hopefully that gives you some practice but the most important thing it gives you some practice dealing with these kind of arbitrary rays that we're showing emanating from the tip of this hour we could do it for the whole arrow but the reason what we're picking these Ray's in these directions is that they're easy to work with somewhat they go through the focus they'll come out parallel if the incident ray is parallel it'll come out through the focus