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Let's draw a bunch
of parabolic mirrors.

3
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And what I want to
do in this video is,

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00:00:04,080 --> 00:00:06,630
do a bunch of
examples of objects

5
00:00:06,630 --> 00:00:08,140
in front of parabolic mirrors.

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And think about what the
images of those objects

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will be based on how
far those objects are.

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And besides just giving
us a better understanding

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of parabolic mirrors, this will
also, it 'll hopefully also

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00:00:21,240 --> 00:00:23,940
give us a sense of how do
we manipulate or how can we

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conceptualize these light rays?

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Which will be a
pretty useful tool

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when we tackle other types
of reflective or refractive

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devices like lenses.

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So that's a parabolic mirror.

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I've drawn its principal
axis right over here.

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00:00:37,180 --> 00:00:39,763
And let me just copy and paste
this just so that I-- actually,

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00:00:39,763 --> 00:00:41,180
let me draw the
focal point, too.

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So this is the focus
right over here.

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So let me just draw the
focus right over there.

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And this is the
center of curvature.

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It's twice the distance from
this point as the focus.

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So that is the-- let me make
it as close as possible.

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So that is the center of
curvature right over there.

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00:00:57,899 --> 00:00:59,190
And let me copy and paste this.

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So we can reuse this
later on in the video.

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I don't have to keep drawing it.

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So copy it.

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So I've copied that.

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Now, let's put an
object-- and I think

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we did this in the last video.

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Let's put an object beyond
the center of curvature.

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So let's put an object here.

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And the convention is to use
an upward pointing arrow.

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This isn't a light ray.

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It's used to show an object.

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And we use the tip of
the arrow to really show

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the top of the object.

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And that's usually where we
trace our light rays from.

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But it doesn't have to be there.

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We could do the middle.

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You could do the bottom.

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And you could figure out what
the image of the object's

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going to be.

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So let's do that.

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And when you're dealing
with parabolic mirrors,

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it's easiest to have to
show just two light rays.

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One that goes parallel
to the principal axis.

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And one that goes
through the focus.

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Because you know what's going
to happen to each of those

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when they reflect.

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And you don't have
to do any math there.

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So let's have the parallel ray.

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That's the parallel ray.

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When it reflects-- the parallel
incident ray, when it reflects,

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it will go through the focus.

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And then, let's
have an incident ray

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that goes through the focus.

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And when it reflects,
it will be parallel.

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And this is the example we
actually saw in the last video.

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And so whatever light
is being emitted

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from this point over
here in that direction,

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it will come back and
converge again at this point.

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And we could actually do it
at every point along the--

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we could do it halfway.

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This halfway point of the
arrow, just to make it clear.

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This halfway point of
the arrow, same thing.

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You have a parallel.

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Something parallel will go,
will reflect a parallel incident

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ray will reflect
through the focus.

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00:02:36,319 --> 00:02:38,360
And I'll just do it for
this one right over here.

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It will reflect
through the focus.

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And then, if you
have something that

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00:02:41,690 --> 00:02:44,360
goes through the focus,
an incident ray that

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00:02:44,360 --> 00:02:48,840
goes through a focus, it
will reflect parallel.

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So this point will correspond
to this point over here.

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I think that makes it clearer,
that this image, the image

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of this object
when it's reflected

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00:02:57,000 --> 00:03:02,660
by this parabolic mirror
will look just like that.

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00:03:02,660 --> 00:03:05,830
So it will actually
form a real image.

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It'll form a real
image that is smaller

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00:03:09,109 --> 00:03:10,150
than this original image.

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00:03:10,150 --> 00:03:12,260
It's not so clear, the
way I did it over here.

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But you could push this
even further back out.

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And it'll be clear
that this is going

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to be a smaller real image
than that right over there.

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Now, let's do a
couple more examples.

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So let me just paste my drawing.

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So I don't have to redraw it.

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Let's see what happens.

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Let me write it.

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So here the image, just so
we can keep track of things.

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Here, the image is real and
smaller than the actual object

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when the actual object is
beyond the center of curvature.

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And actually, let me make it a
little bit clearer by drawing.

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Let me do another example
like that where I do something

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big way out here just
to make it clear.

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So once again, we go parallel,
reflect through the focus.

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00:04:00,420 --> 00:04:03,090
And then, we can go
through the focus.

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We go through the focus and
then reflect out like that.

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And there you see,
now, it's much clearer

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that the image is going
to be much smaller.

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And, of course, inverted
relative to the actual object.

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Now, let's do this again.

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But this time, let's
place the object

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at the center of curvature.

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So let's place the
object right over here.

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So right at that distance
that twice the distance

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from the vertex of the
parabola to the focus.

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So we do a parallel line.

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These lines are the
hardest thing to do.

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So parallel incident ray,
parallel to the principal axis.

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This is the principal
axis right here.

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Principal axis-- that's what
this line is right over here.

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It's kind of the line of
symmetry of the parabola.

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When it reflects, it will
reflect through the focus.

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And then, let's take
another ray that goes,

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00:05:00,330 --> 00:05:02,847
the incident ray goes
through the focus.

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And when it reflects, it
will reflect parallel.

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00:05:04,805 --> 00:05:07,440


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And my drawing isn't the
neatest drawing on the planet.

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And actually, let me draw it
a little bit better than that.

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Well, that's pretty good.

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Let me just.

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So that's the incident
ray that was parallel.

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And then, an incident
ray that goes through--

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let me-- I'm having
trouble drawing these.

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An incident ray that
goes through the focus

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will then come out and
reflect right over there.

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And they'll converge.

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And the way I've drawn it,
my drawing isn't ideal.

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But the way, but
the reality is, is

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that they'll converge so
that the image will just

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be in an inverted same size
version as this thing up here.

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Because it's symmetric.

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Let me see if I can
redraw this whole thing,

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so it comes out neater.

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So far, that looks good.

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So then, you want to
reflect like that.

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You got-- you're coming
through the focus.

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And then, you have another ray
that goes through the focus.

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This whole thing
should be symmetric.

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And then, when it reflects,
it comes back out like that.

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So that makes a
little bit clearer.

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00:06:07,800 --> 00:06:09,270
So this is the object.

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And now, its image is
just an inverted version

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of this object.

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00:06:12,430 --> 00:06:17,370
The image comes into
focus, or the rays

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00:06:17,370 --> 00:06:21,670
converge at the same distance
from the actual mirror

153
00:06:21,670 --> 00:06:23,470
as the actual object.

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And it's going to be the
same size, just inverted.

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So that's-- so here the image
is real and the same size

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as the object.

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Let's do a couple more of these.

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I think you get the hang of it.

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And you might want
to try them out.

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You might want to
pause the video

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and try it on paper because
really nothing beats practice.

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So let's stick our object
between the center of curvature

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00:06:51,720 --> 00:06:53,966
and the focus and
the focal point.

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So if we put our
object there, we

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could have a light ray that goes
parallel to the principal axis.

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And then, it will reflect
out through the focus.

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00:07:02,020 --> 00:07:04,810
And then, you could
have another point.

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It goes through another ray.

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It goes through the focus.

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And then, it reflects.

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00:07:09,540 --> 00:07:11,140
And then, it will reflect out.

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And let me draw it
better than that.

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Actually, this is--
I should probably

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00:07:20,580 --> 00:07:23,470
have used a more precise
tool when I did all of this.

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00:07:23,470 --> 00:07:27,060
So let me draw it
right over here.

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So I have the parallel one.

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And then, it goes
through the focus

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just like that when
it gets reflected.

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I really should have
had a line tool for this

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to have neater drawings.

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And then, a ray that
goes through the focus

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00:07:42,840 --> 00:07:45,300
will be reflected out parallel.

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It would be reflected
out parallel.

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And at least for the light
that comes from that tip,

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00:07:50,820 --> 00:07:53,120
they will re-converge
at that tip.

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00:07:53,120 --> 00:07:56,070
And if you did it for
every point on this arrow,

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the image would be
an inverted arrow

189
00:07:57,720 --> 00:07:59,510
that is bigger
than the original.

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00:07:59,510 --> 00:08:00,620
And it is beyond.

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00:08:00,620 --> 00:08:03,530
It's almost the opposite of the
first example that we showed.

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00:08:03,530 --> 00:08:06,560
And so now the image is
bigger than the original.

193
00:08:06,560 --> 00:08:10,140
So the image is real.

194
00:08:10,140 --> 00:08:11,820
And it is bigger.

195
00:08:11,820 --> 00:08:17,260
And the image will,
where it converges

196
00:08:17,260 --> 00:08:20,494
is going to be beyond
the center of curvature.

197
00:08:20,494 --> 00:08:21,410
And you could imagine.

198
00:08:21,410 --> 00:08:23,126
If this was the
object right here,

199
00:08:23,126 --> 00:08:24,750
then this would be
the image over here.

200
00:08:24,750 --> 00:08:26,500
If you just trace
the lines backwards.

201
00:08:26,500 --> 00:08:29,470
So there's a symmetry
here between this example

202
00:08:29,470 --> 00:08:31,600
and the first one
we did up here.

203
00:08:31,600 --> 00:08:33,070
Now, let's just
do a couple more.

204
00:08:33,070 --> 00:08:36,580
Let's imagine if the object is
actually at the focal point.

205
00:08:36,580 --> 00:08:38,679
It's actually at the focus.

206
00:08:38,679 --> 00:08:40,190
So let's draw an object there.

207
00:08:40,190 --> 00:08:42,049
Let's think about
what would happen.

208
00:08:42,049 --> 00:08:47,640
So if we're at the focus, a
ray that comes out parallel

209
00:08:47,640 --> 00:08:53,370
will go through the focal point
and come out just like that.

210
00:08:53,370 --> 00:08:56,940
And then, here we're going to--
you can't-- we can't have a ray

211
00:08:56,940 --> 00:08:57,820
that just goes.

212
00:08:57,820 --> 00:09:00,760
Well, actually we could have
a ray that goes through.

213
00:09:00,760 --> 00:09:04,141
Well, that-- you can't
go into the object.

214
00:09:04,141 --> 00:09:05,890
So here, I'll do a
slightly different ray.

215
00:09:05,890 --> 00:09:10,100
I'll do a ray that intersects
the parabolic mirror

216
00:09:10,100 --> 00:09:10,859
right over there.

217
00:09:10,859 --> 00:09:12,400
And the reason why
I want to do there

218
00:09:12,400 --> 00:09:14,290
is because there
the parabolic mirror

219
00:09:14,290 --> 00:09:17,070
is essentially flat and
essentially vertical.

220
00:09:17,070 --> 00:09:18,770
So you can imagine
that the incident

221
00:09:18,770 --> 00:09:21,411
ray is going to be the same
thing as the reflected ray.

222
00:09:21,411 --> 00:09:23,410
So you could draw a ray
that comes in like that.

223
00:09:23,410 --> 00:09:25,520
So this is a departure
from what we did before.

224
00:09:25,520 --> 00:09:28,120
And then the reflected ray
will come out like that.

225
00:09:28,120 --> 00:09:29,930
So what happens
when an object is

226
00:09:29,930 --> 00:09:35,200
at the focal point is that all
of the light that's coming off

227
00:09:35,200 --> 00:09:41,120
of this object in any
direction will all be made,

228
00:09:41,120 --> 00:09:43,330
it will all be made parallel.

229
00:09:43,330 --> 00:09:44,990
And so it won't converge.

230
00:09:44,990 --> 00:09:46,070
So it won't converge.

231
00:09:46,070 --> 00:09:47,920
So it won't be able
to form a real image.

232
00:09:47,920 --> 00:09:49,790
And it's not, it
doesn't look like it's

233
00:09:49,790 --> 00:09:53,300
diverging from some
point in the mirror.

234
00:09:53,300 --> 00:09:55,600
So it won't even
form a virtual image.

235
00:09:55,600 --> 00:10:00,060
So here, there will
actually be no image

236
00:10:00,060 --> 00:10:02,780
when the object is actually
at the focal point.

237
00:10:02,780 --> 00:10:05,510
And then, the last case,
as you can imagine,

238
00:10:05,510 --> 00:10:08,410
is if an object is closer
than the focal point.

239
00:10:08,410 --> 00:10:09,980
So let's draw that.

240
00:10:09,980 --> 00:10:13,770
So let's put an object
at the focal point.

241
00:10:13,770 --> 00:10:15,840
So right over here.

242
00:10:15,840 --> 00:10:20,060
And here, just for the sake
of argument, one I can draw.

243
00:10:20,060 --> 00:10:22,040
I can always draw a parallel.

244
00:10:22,040 --> 00:10:24,200
And anything that, any
light that goes parallel

245
00:10:24,200 --> 00:10:26,930
will then look to come
out in a direction that

246
00:10:26,930 --> 00:10:28,750
would go through
the focal point.

247
00:10:28,750 --> 00:10:30,470
So it would go through
the focal point.

248
00:10:30,470 --> 00:10:32,320
It would come out
in that direction.

249
00:10:32,320 --> 00:10:34,070
Although the object
itself is blocking.

250
00:10:34,070 --> 00:10:36,100
But it would look to
go in that direction.

251
00:10:36,100 --> 00:10:38,130
It would be reflected
in that direction.

252
00:10:38,130 --> 00:10:40,120
And then, you could
imagine a ray of light

253
00:10:40,120 --> 00:10:42,240
that would have been coming
from the focal point,

254
00:10:42,240 --> 00:10:44,890
or would have been coming
from the same direction.

255
00:10:44,890 --> 00:10:47,510
So you could imagine coming
from the same direction

256
00:10:47,510 --> 00:10:50,000
as the focal point
would be reflected

257
00:10:50,000 --> 00:10:51,730
parallel, in a
parallel direction

258
00:10:51,730 --> 00:10:52,815
to the principal axis.

259
00:10:52,815 --> 00:10:56,060


260
00:10:56,060 --> 00:10:58,710
Now, these two light
rays are not converging.

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00:10:58,710 --> 00:11:00,400
But they look like
they're diverging

262
00:11:00,400 --> 00:11:03,932
from some point
behind the mirror.

263
00:11:03,932 --> 00:11:05,390
They'll look like
they're diverging

264
00:11:05,390 --> 00:11:07,070
from some point
behind the mirror.

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00:11:07,070 --> 00:11:09,930
So in this case, we are
forming a virtual image.

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00:11:09,930 --> 00:11:15,352


267
00:11:15,352 --> 00:11:16,810
And the virtual
image will actually

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00:11:16,810 --> 00:11:18,510
look something like this.

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00:11:18,510 --> 00:11:24,162
And so it'll be larger than
the original virtual image.

270
00:11:24,162 --> 00:11:25,370
So it's kind of a magnifying.

271
00:11:25,370 --> 00:11:26,995
If you were to go
to-- what are called?

272
00:11:26,995 --> 00:11:30,717
--a fun house at the circus or
the amusement park, whatever.

273
00:11:30,717 --> 00:11:33,050
And if you were to get close
enough to parabolas mirror,

274
00:11:33,050 --> 00:11:37,960
it would show a
magnified version of you.

275
00:11:37,960 --> 00:11:39,067
A virtual version of you.

276
00:11:39,067 --> 00:11:41,150
And actually, let me draw
that a little bit bigger

277
00:11:41,150 --> 00:11:42,750
just because it
might not be clear.

278
00:11:42,750 --> 00:11:44,120
So let me draw.

279
00:11:44,120 --> 00:11:48,570
So if this is the mirror,
that is the focal point.

280
00:11:48,570 --> 00:11:51,450
This right here is
the principal axis.

281
00:11:51,450 --> 00:11:55,670
This is maybe you,
maybe whatever object.

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00:11:55,670 --> 00:11:57,600
You could draw a ray
that goes parallel.

283
00:11:57,600 --> 00:12:00,130
It will reflect in the
direction of the focal point.

284
00:12:00,130 --> 00:12:02,180
So it'll reflect out like that.

285
00:12:02,180 --> 00:12:04,397
It'll be blocked by
the object, though.

286
00:12:04,397 --> 00:12:05,980
And then, something
that looks like it

287
00:12:05,980 --> 00:12:07,521
would have come from
the focal point,

288
00:12:07,521 --> 00:12:09,450
from the same direction
as the focal point

289
00:12:09,450 --> 00:12:12,920
would then be reflected
parallel to the principal axis.

290
00:12:12,920 --> 00:12:16,080
So these two rays, once
again, there are diverging.

291
00:12:16,080 --> 00:12:19,390
But they look like, to the
human brain, to the human eye,

292
00:12:19,390 --> 00:12:22,380
they look like they came
from that point over there.

293
00:12:22,380 --> 00:12:24,690
And so this would
correspond to that point

294
00:12:24,690 --> 00:12:26,070
on the virtual image.

295
00:12:26,070 --> 00:12:28,499


296
00:12:28,499 --> 00:12:30,290
So hopefully, that
gives you some practice.

297
00:12:30,290 --> 00:12:32,040
But the most important
thing, it gives you

298
00:12:32,040 --> 00:12:34,220
some practice dealing
with these arbitrary rays

299
00:12:34,220 --> 00:12:36,986
that we're showing emanating
from the tip of this arrow.

300
00:12:36,986 --> 00:12:38,610
And we could do it
for the whole arrow.

301
00:12:38,610 --> 00:12:41,235
But the reason why we're picking
these rays in these directions

302
00:12:41,235 --> 00:12:42,760
is that they're
easy to work with.

303
00:12:42,760 --> 00:12:45,027
They go through the focus,
they'll come out parallel.

304
00:12:45,027 --> 00:12:46,610
If the incident ray
is parallel, it'll

305
00:12:46,610 --> 00:00:00,000
come out through the focus.