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Convex parabolic mirrors

Convex Parabolic Mirrors. Created by Sal Khan.

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Video transcript

All the parabolic mirror examples we've been doing so far have been concave. And that just means, you might know already what concave means, but just to make it clear, they were opening out towards the objects, and in most of the cases, out towards where the images were formed. So what we cared about the inside surface of the mirror right here. And the way I always remember concave is the kind of forms that cave. You could view this part right here as the inside of the cave. And we had a bunch of examples where we had focal points. And then this one here was our principal axis. And we had objects. And I showed you how the light would reflect off of the mirror and go through the focal points. So thus we did a bunch of examples like that in the last couple of videos. What I want to do in this video is a quick example of using a convex parabolic mirror. So let's do a convex parabolic mirror. And here we care about the other side of the mirror. We care about the side that's the outside of the bowl, if you want to view the parabolic mirror as a ball. So let's think about that as a little bit. So let's imagine that once again we have something that's the shape of a parabola. It has this-- let me draw a better version of it-- so it has the shape of a parabola. This is the principal axis right over here. You could almost view that as the line of symmetry. This is still the focal point. That right there is still the focus. But now we're going to assume that the reflective surface is on the outside. It's on the outside. So the reflective surface is kind of jutting out towards us as opposed to caving in. That's another way to remember it-- concave, looks like it's caved in. Here, it's jutting out towards us. And let's think about what would happen if I put an object over here on the outside assuming that this is a reflective surface. So if I put an object over here, what is going to happen? So let's just do the same exercise. But what we're going to do is we're going to have one parallel ray. We could do rays that go in any direction from any of these points because there's some light source over here. They never draw the light source, but it reflects diffusely off of this object. So this object is emitting light rays in every direction. But the useful diffused light rays being emitted by this object are the ones that are parallel to the principal axis and the ones that would go through the focus. Let's do one that's parallel. So if something is parallel to the principal axis-- and I'm not doing the map over here-- but if it reflects on the outside of this parabolic mirror, it will reflect in a way so it looks like it's coming from the focus. So I would see the focus as on the other side of this mirror, but it would reflect in a way that it looks like it's coming from the focus. So that ray will reflect like that. And then if we have another ray from the head of this object, from the tip of that arrow, and that ray is going in the direction of the focus-- so the focus is there-- so let me draw the direction. So let's say I have an incident ray going in the direction of the focus. When that gets reflected, it will reflect parallel to the principal axis. And so what type of image is going to be formed here? Clearly, these two rays will never converge. So we can't form a real image. We cannot project that image onto a screen or cloth and then see it. These two rays are converging. But if one were to observe the rays, they look like they are diverging from a single point. This ray looks like, let me make it clear, this one that just got reflected out parallel looks like it's coming from if you go straight back behind the mirror. And then this one that's coming out looks like it's coming out of this point there. So it looks like they're diverging from this point on the other side of the mirror. And not only doesn't look like they're coming from there, but the actual image will look like that. We could do it with other points on this arrow if we want. If you take the bottom of the arrow, that's maybe the easiest, light that goes straight to the actual mirror will then be reflected straight back. So it would look like it's coming from a point at the mirror back over here. And we could do other things. We could draw stuff so that you could see what the whole image-- we could take points over here, and you would say that that would correspond to a point over there. But I guess the thing that hopefully you'll realize from this video is when you're dealing with a convex parabolic mirror, the outside is a reflective surface. You're not going to form a real image, you're going to form a virtual image. This is a virtual image, just like you would see in your bathroom mirror, although that's probably not parabolic, I'm guessing. And it's also going to be a smaller image. And you see these types of mirrors all the time, especially around corners. If you see a corner-- let's let me draw a hallway with corners-- you'll sometimes see mirrors-- let me do it the other way-- you'll sometimes see mirrors so that people-- well, the mirror might be out here-- so that you can see people as they're coming around the corner. And the reason why these mirrors are useful is that they reflect light from a lot of directions. And so you can kind of see around corners. This is not the best of drawing, but I think you've seen these convex mirrors, mirrors that look something like this. Sometimes you'll also see them at the aisles of stores, at the head of aisles of stores. And this way, the store owners can have a good field of view. And they can see if anyone is shoplifting. Anyway, hopefully, you found that interesting.