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Current time:0:00Total duration:6:00

Convex parabolic mirrors

Video transcript

all the parabolic mirror examples we've been doing so far have been concave and that just means and you might know already that what concave means but just to make it clear they were we were kind of they were opening out towards the objects and in most of the cases out towards the out towards the where the images were formed so what we cared about the inside we cared about the inside surface of the mirror right here now the way I always remember concave is it kind of forms a cave you could view this part right here is the inside of the cave and we had a bunch of examples where we had focal points and then this would 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 that's 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 convex parabolic mirror and here we care about the other side of the mirror we care about we care about the side that's kind of not the kind of the outside of the bowl if you want to view this as the parabolic Mueller mirror is a bowl so let's think about that as a little bit so let's imagine that once again you 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 that is you can almost you that is 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 concave looks like it's caved in here it's jetting out towards us and let's think about what would happen if I put an object 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 you can just for once again from we can do raise to go to any direction from any of these points because there being 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 ones the useful diffuse 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 so let's do one that's parallel so if something is parallel to the principal axis and I'm not doing the math over here but if it reflects on the outside of this parabolic mirror it will reflect in a way that it's light so it looks like it's coming from the focus so obviously the focus is on the other side of this mirror but it would reflect in a way that it looks like it'll cut 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 so 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 it project that image onto print 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're there they're diverging from a single point they look this ray looks like let me make it clear this one that just got reflected out parallel it looks like it's coming from 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 does it look like they're coming from there but the actual image will look like that we can 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 that goes straight to that goes straight to the actual mirror we'll then go flecked it straight back so it would look like it would look like it's coming from appointed the mirror back over here now we could do other things we could we could we could draw stuff so that you can 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 the thing that or I guess the thing that hopefully you realize from this video is when you're dealing with the convex parabolic Miller on the outside 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 it's also going to be a smaller it's also going to be a smaller image and you see these types of mirrors all the time especially around corners you know if you see a corner let's let me draw a hallway with corners you'll sometimes see you'll sometimes see mirrors let me do it the other way well 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 and this is not the best of drawing but I think you've seen these convex mirrors mirrors that look like mirrors that look something like this sometimes you'll also see them at the aisles of stores at the head of aisles of stores in this way the store owners have a good field of view and they can see if anyone is anyone is a shoplifting anyway hopefully you found that interesting