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In this video, I
want to expose you

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to a special class of mirrors
called parabolic mirrors.

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Or sometimes called
parabolic reflectors.

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And what's neat about
parabolic mirrors--

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and I'll draw a cross
section of one right here.

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And if you're familiar
with the algebra,

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they are essentially-- the
cross section, especially,

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is in the shape of a parabola.

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So let me draw a
parabola right here.

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So it's in the
shape of a parabola.

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Just like that.

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And what's neat about
a parabolic mirror--

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and I'm not going to go
into the math right here.

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I just want to give
you the general idea.

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And let me just draw
its principal axis.

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So this is the line of
symmetry of the parabola.

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So this is its principal
axis right over here.

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It divides it in two.

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This is just a cross section.

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You could imagine
if this was spun

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around that principal
axis, you would

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get something that
would look like this.

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You would get something
that would look like a bowl.

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But it's actually the
shape of a parabola.

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It's not an actual sphere shape.

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So if you rotate
this around, you

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would get a circle
around the edge.

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So this would be a
circle right over here.

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But this shape down here
is not a hemisphere.

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It's not spherical.

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It's actually a parabola.

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And the reason why we
care about a parabola,

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or what's neat about
parabolic mirrors,

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is if I have parallel
light rays coming

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into a parabolic
mirror-- I'll do

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my best to draw a
parallel light ray.

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So parallel to its central axis.

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So if I have a light ray
that comes like that,

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it will reflect off
of the-- it's parallel

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to this principal axis--
it will reflect like that.

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And I'll tell you what's
neat about this in a second.

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Now let me draw
another parallel ray.

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Let's say I have a
parallel ray that's

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coming in right over there.

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So it hits the parabolic
mirror at that point.

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It's going to reflect--
so it comes in like that.

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And if I have another ray
that comes in like this,

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it will reflect so that
the reflection goes right

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over there.

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So what's neat about this?

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Well, what's neat is
any light ray that

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comes in parallel-- any incident
light ray that's parallel

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to the principal axis of
this parabolic mirror--

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the reflected ray is going
to go through the same point.

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I don't care where
you hit the mirror.

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As long as it was parallel
to the principal axis,

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the reflected ray is
going to hit this point.

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And this point right
here is the focus.

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This is the focus of
the parabolic mirror.

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Now, what's neat about this?

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Well, let's say
that you were trying

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to capture heat from the sun.

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You were trying to concentrate
the electromagnetic radiation

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from the sun.

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So what you could
imagine-- you could

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go to the middle of the
desert-- and people do do this--

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and you set up of
parabolic mirrors

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like this that are
pointed at the sun.

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And the sun's rays come in.

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And the sun is so far away,
they're essentially just coming

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in parallel because they
are radiating from the sun.

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But the sun is 93
million miles away.

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So the rays for our purposes are
essentially coming in parallel.

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And what's neat
about them is, is

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when they hit the surface
of the parabolic mirror,

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they all get reflected
to one point.

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So if you have a
ray coming in there,

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it's going to get
reflected there.

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If you have a ray
coming in like that,

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it's going to get
reflected like that.

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And so all of the energy can be
focused on a point like that.

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And so could imagine you might
have a water pipe running

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into the screen here.

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And so all of that
light energy would

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be used to heat up
that water pipe.

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So it's a pretty neat way
to concentrate energy.

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Another thing you
might want, maybe

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instead of taking
in energy, maybe you

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want to give out energy so
that all the beams of light

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are parallel.

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For example, let's say you
have a light for a car.

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If you have a light,
you could imagine

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if car headlights were just--
if I drew a car like this--

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let me scroll down a little bit.

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If I drew a car like
this-- let me draw--

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have a reasonable
attempt at a car.

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So let's say this is
a car right over here.

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I think you get the idea.

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This is the wheel housing.

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That's the wheel.

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So forth and so on.

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This isn't about the
drawing of the car.

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But you could imagine if
we just stuck light bulbs

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at the front of cars.

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So you could imagine
just a light bulb

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sitting at the front of a car.

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So that's a light bulb.

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And that would provide light
but it would provide light

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in all directions
radially outward.

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And it would be kind of useless.

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First of all, the
way I drew it here,

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it would probably show
up in the dude's eye

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who's trying to drive the car.

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But it's a lot of wasted energy.

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A lot of the light is
coming back onto the car.

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And it's pointing in all
sorts of random directions.

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It's not so useful.

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When you are driving
a car, you want

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all of the light pointed at the
road or maybe the stuff that's

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directly above the road.

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So how could you
point the light?

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Well, you could use
a parabolic mirror.

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And any car you
look at will have

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a light inside of
a parabolic mirror.

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And what does that do?

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Let's say instead
of this situation

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that I just drew--
let me clear this out.

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And I'll draw it
on a larger scale.

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Let's say I had a
parabolic mirror here.

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So I have a parabolic mirror.

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Obviously, this looks more like
a snow shovel or something.

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But I'm drawing it way huge just
so you get the general idea.

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So this is a parabolic mirror.

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And let's say we put the light
bulb now at the focal point.

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At the focus.

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At the focus of this
parabolic mirror.

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Now what's going to happen?

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Well, light that has to
go in this direction, that

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comes radially
outward, that's good.

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Because that's light that's
being useful to the driver.

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It's actually
illuminating the road.

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But light that's going
backwards-- light that's

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radiating outward from that
focus of the parabola--

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it's going to do the exact
opposite of that solar energy

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collector.

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It's going to be
reflected out parallely.

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Or a parallel way.

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And so all of the
light-- because

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of this parabolic reflector,
or parabolic mirror-- all

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of the light that this
light source is generating,

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or most of it, is going
to be emitted parallel

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to the principal
axis of the parabola.

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And actually you
could point the light.

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If you actually moved
this parabola around,

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you can point which
direction the light's in.

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So it's actually a pretty
useful thing to have.

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Now the other thing
about parabolic mirrors

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is that they actually
form real images.

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In the last video, we
talked about the notion

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of a virtual image.

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You think something
is there because it

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looks like the light is
converging at some point.

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But that point isn't even there.

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It's actually from some other
point getting reflected.

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But a real image-- let
me draw it over here.

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So let me draw a
parabolic mirror.

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Let me draw big
parabolic mirrors

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to make the diagram clear.

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And let me draw
its principal axis.

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This is a side profile of it.

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Let me draw its principal
axis, just like that.

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And let's put an object.

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So I'm going to define a couple
of interesting points here.

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So first of all, we
have our focal point.

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I'll call that F.

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And then there's something
called the center of curvature.

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And the curvature I always
imagine as a sphere.

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But for the center of curvature
of a parabolic mirror,

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it's actually going to be
two times the focal length

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of this distance right here.

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Let me make it clear.

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I'll call that-- this
distance right here

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is F. Then this
distance right here,

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to the center of curvature,
we'll just call that point C.

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But this distance over here
is going to be F as well.

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Or it's going to be 2F
from-- you could imagine

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that vertex, or that minimum
point of the parabola,

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depending on how
you want to view it.

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Now, what I want to do is
put a couple of objects

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in front of this
parabolic mirror.

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And just think
about what happens

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to the light rays
of that object.

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So let's first put
an object here.

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So I'm just going to draw
the object as an arrow.

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And maybe some light
is shining on it

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from who knows what direction.

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But it's going to reflect
that light diffusely.

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Assuming it's not shiny.

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And I'm just going to
pick points on this object

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to radially emit
light outward from.

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Or reflect light outward from.

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And see what happens
to those light rays.

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And for the sake of simplicity,
whenever you do something

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with a parabolic mirror,
it's good to emit

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one radial ray that's parallel
and one that goes to the focus.

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Because we know what they're
going to do after that.

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So let's do one that's parallel.

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And of course,
these are just two

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of the gazillions
of light rays that

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are being emitted from
every point of this object.

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But we're just doing
this to understand

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what will the image of this
object actually look like.

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So let's do one parallel.

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It hits the surface of
the parabolic mirror.

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And then it reflects and
goes through the focus.

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We know that already.

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And then let's make another
light ray go through the focus.

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Let me draw it a little
bit better than that.

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Another light ray going
through the focal point.

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Just like that.

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And then it reflects.

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And it'll be reflected
in a parallel way.

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So what just happened here?

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Those two rays that were emitted
by the same point on this arrow

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object, they radially
emit outward.

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They reflect on this parabolic
mirror at two different points,

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but then they converge again.

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They converge right over there.

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And actually if you put-- and we
could do that with every point.

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If you did the stuff that
leaves that point-- actually

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both of those are going
to go and come back--

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go through the focal point and
then come back right over here.

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They'll keep going.

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But you could
imagine, you could use

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with every point on this arrow.

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And what you're
going to do is get

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an image that looks like this.

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This point up here
corresponds to that point.

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This point corresponds
to that point.

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And so if you were to put
a screen right over here--

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this is a screen.

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It could just be a, I don't
know, white tablecloth.

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Or if there was a
wall right over here.

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Then it would actually
show the image.

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You would actually be
projecting the image

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onto this wall right over here.

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It would actually be
a projected image.

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And that projected image
that we're talking about,

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where the light is converging--
so the light comes radially

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outward from each
point of this arrow.

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And then it converges on
a point on the screen.

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That image that gets formed,
we call that a real image.

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It's real image.

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This is a real image.

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And you might want
to compare that

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to what we call a virtual image.

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A virtual image is
an image that looks

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like it's coming from someplace.

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Because it looks like things
are diverging from some point.

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But they've really been
reflected off of some surface.

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So what we think is
there, really isn't there.

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A real image is an image
that's actually projectable.

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We could put a screen
right over here

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and then these guys are going
to be hitting the screen

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and essentially defusing
the exact same light

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as this point of
the actual object.

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And because of that, the screen
will look just like the object.

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This is a projectable image.

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Anyway, hopefully you
found that useful.

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I realize I've gone
longer than I like to

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with some of these videos.

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We'll talk a little bit
more about parabolic mirrors

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in the next video.