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.