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All the parabolic
mirror examples

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we've been doing so
far have been concave.

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And that just means,
you might know already

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what concave means, but
just to make it clear,

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they were opening out
towards the objects,

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and in most of the
cases, out towards where

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the images were formed.

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So what we cared about the
inside surface of the mirror

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right here.

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And the way I always
remember concave

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is the kind of forms that cave.

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You could view this part right
here as the inside of the cave.

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And we had a bunch of examples
where we had focal points.

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And then this one here
was our principal axis.

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And we had objects.

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And I showed you how the light
would reflect off of the mirror

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and go through the focal points.

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So thus we did a
bunch of examples

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like that in the last
couple of videos.

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What I want to do in this
video is a quick example

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of using a convex
parabolic mirror.

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So let's do a convex
parabolic mirror.

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And here we care about the
other side of the mirror.

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We care about the side that's
the outside of the bowl,

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if you want to view the
parabolic mirror as a ball.

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So let's think about
that as a little bit.

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So let's imagine
that once again we

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have something that's
the shape of a parabola.

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It has this-- let me draw
a better version of it--

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so it has the shape
of a parabola.

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This is the principal
axis right over here.

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You could almost view that
as the line of symmetry.

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This is still the focal point.

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That right there
is still the focus.

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But now we're going to assume
that the reflective surface is

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on the outside.

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It's on the outside.

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So the reflective
surface is kind

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of jutting out towards us
as opposed to caving in.

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That's another way to
remember it-- concave,

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looks like it's caved in.

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Here, it's jutting
out towards us.

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And let's think about
what would happen

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if I put an object over
here on the outside assuming

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that this is a
reflective surface.

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So if I put an object over
here, what is going to happen?

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So let's just do
the same exercise.

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But what we're
going to do is we're

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going to have one parallel ray.

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We could do rays that go
in any direction from any

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of these points because there's
some light source over here.

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They never draw
the light source,

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but it reflects diffusely
off of this object.

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So this object is emitting
light rays in every direction.

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But the useful
diffused light rays

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being emitted by this object
are the ones that are parallel

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to the principal
axis and the ones

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that would go through the focus.

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Let's do one that's parallel.

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So if something is parallel
to the principal axis--

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and I'm not doing
the map over here--

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but if it reflects
on the outside

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of this parabolic mirror,
it will reflect in a way

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so it looks like it's
coming from the focus.

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So I would see the focus as on
the other side of this mirror,

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but it would reflect
in a way that it

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looks like it's
coming from the focus.

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So that ray will
reflect like that.

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And then if we have another ray
from the head of this object,

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from the tip of that
arrow, and that ray

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is going in the
direction of the focus--

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so the focus is there-- so
let me draw the direction.

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So let's say I have
an incident ray going

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in the direction of the focus.

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When that gets reflected,
it will reflect parallel

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to the principal axis.

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And so what type of image
is going to be formed here?

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Clearly, these two rays
will never converge.

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So we can't form a real image.

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We cannot project that image
onto a screen or cloth and then

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see it.

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These two rays are converging.

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But if one were to
observe the rays,

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they look like they are
diverging from a single point.

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This ray looks like,
let me make it clear,

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this one that just got
reflected out parallel looks

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like it's coming from
if you go straight

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back behind the mirror.

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And then this one
that's coming out

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looks like it's coming
out of this point there.

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So it looks like
they're diverging

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from this point on the
other side of the mirror.

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And not only doesn't look like
they're coming from there,

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but the actual image
will look like that.

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We could do it with other
points on this arrow if we want.

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If you take the bottom of
the arrow, that's maybe

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the easiest, light that goes
straight to the actual mirror

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will then be reflected
straight back.

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So it would look
like it's coming

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from a point at the
mirror back over here.

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And we could do other things.

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We could draw stuff
so that you could

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see what the whole image-- we
could take points over here,

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and you would say
that that would

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correspond to a
point over there.

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But I guess the thing
that hopefully you'll

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realize from this
video is when you're

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dealing with a convex
parabolic mirror,

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the outside is a
reflective surface.

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You're not going to
form a real image,

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you're going to form
a virtual image.

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This is a virtual
image, just like you

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would see in your
bathroom mirror,

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although that's probably
not parabolic, I'm guessing.

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And it's also going
to be a smaller image.

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And you see these types
of mirrors all the time,

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especially around corners.

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If you see a
corner-- let's let me

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draw a hallway with
corners-- you'll

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sometimes see mirrors-- let me
do it the other way-- you'll

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sometimes see mirrors so that
people-- well, the mirror might

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be out here-- so that
you can see people

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as they're coming
around the corner.

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And the reason why
these mirrors are useful

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is that they reflect light
from a lot of directions.

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And so you can kind
of see around corners.

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This is not the best
of drawing, but I

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think you've seen these
convex mirrors, mirrors

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that look something like this.

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Sometimes you'll also see
them at the aisles of stores,

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at the head of aisles of stores.

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And this way, the store owners
can have a good field of view.

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And they can see if
anyone is shoplifting.

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Anyway, hopefully, you
found that interesting.