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We've talked a
lot about mirrors,

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in particular parabolic
mirrors, that reflect light.

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What I want to do now
is talk about lenses,

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or talk about what a lens is.

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And think about how they
transmit or refract light.

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So a simple lens, and
we've all seen them.

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Maybe it's made of glass,
maybe something else.

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And I'm going to focus
on convex lenses first.

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So remember, concave means
it opens inward, like a cave.

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Convex means it kind
of opens outward.

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And in a convex lens,
it'll be symmetric.

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So let me see if I can draw it.

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One side of the lens
will look like that.

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And this one, you could
kind of view this.

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And oftentimes, most
lenses, the simpler lenses,

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are made this way.

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So this is kind of the
surface of a sphere,

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or part of the
surface of a sphere.

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Let me see if I can draw
that a little bit better.

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So part of the surface of a
sphere, and it's symmetric.

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So it has some center, right
over here, just like that.

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And then you have
another surface

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of a sphere that's
exactly the same.

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I'm doing my best to draw this
convex lens, just like that.

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That is a pretty good job here.

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And let me copy and paste
it so I can actually

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use this drawing in the
future, before I mark it up.

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All right.

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So I've copied it.

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So let's think
about what's going

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to happen as light
goes through this lens,

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as it's transmitted
through it and maybe gets

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diffracted by it.

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So we're assuming this is air
out here, and this is glass.

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Something that has a higher
index of refraction, something

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in which light travels slower.

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So you can imagine
that some light that

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is going parallel-- I
guess you could view it

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to the principal
axis of the lens.

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This would be the principal
axis of the lens right here,

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just like we talked
about the principal axis

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of our parabolic mirrors.

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But if you imagine light
that's going parallel to that,

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right when it hits this
surface over here-- Remember,

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the perpendicular
at this point is

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going to look like this because
the lens is actually curved.

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And remember, it's moving
faster on the outside.

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So the right side is
going to be able to stay

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outside a little bit longer.

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Or actually I should
say, the top side

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of the light-- if you
imagine the car analogy--

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is going to be able to
stay out of the lens

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a little bit longer
than the bottom side,

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or the bottom wheels.

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Or if we go in the
direction of the light,

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the left side of the car
is going to be able to--

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And just so we can visualize the
car, there's the left wheels.

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Those are the right wheels.

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The left wheels are going
to be able to stay out

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a little bit longer and travel
faster a little bit longer.

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So this is the
perpendicular again.

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So it will it be
refracted downwards

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like that, a little bit.

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And then once you get
to this interface,

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now you're going to move into
a faster medium, into the air

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again.

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And let me draw our
perpendicular over here.

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And you could imagine that
the right side of this ray

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is going to-- Actually,
the left side of this ray

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is going to come out first.

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And since the left side of
this ray, or the left side

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of these tires are
going to come out first,

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or maybe the top tires are
going to come out first,

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they're going to be
able to travel faster.

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And so you'll be deflected
even more downwards.

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So it will look
something like this.

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And the light ray would
do something like that.

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Now there is a point
out here someplace

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that whenever I take
any ray that is parallel

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to the principal
axis of the lens,

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it will be refracted through
the lens to that same point.

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So here, we're going
to be refracted

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a little bit like that.

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And there we'll
be refracted more.

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And then we're going to
go to that same point.

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So that's another ray.

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And then this is
another parallel ray.

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It'll be refracted a
little bit over here,

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and then a little bit more.

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And it'll go to that same point.

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And I think you could guess what
I'm about to call this point.

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I wish I could draw my lines
a little bit straighter.

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It's refracted a
little bit, and then

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refracted a little bit more, and
goes straight into that point.

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This point, where all of the
parallel rays-- Sometimes

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you'll hear them talked
of as collimated rays.

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Those are rays of light
that are roughly parallel.

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They all converge at this point
on the other side of the lens.

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They're essentially all
being focused on that point.

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And this right here you can
view as the focus of the lens.

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Or you can view this
length from the lens

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to that point as
the focal length.

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Now this lens is
completely symmetric.

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Anything you can
do from one side,

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you end up getting
focused on the right side.

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If you had collimated
rays, or parallel rays,

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coming from the right side,
the same thing would happen.

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But it would just be
on the other side.

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So that ray would go like that.

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And then it would be
refracted some more.

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And maybe it would go to
this point, right over here.

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And so you actually have
two foci for a lens.

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Two actual points where,
if parallel rays are coming

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from one side,
they'll be focused

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on the point on the other side.

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And if parallel arrays are
coming from the left side,

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they'll be focused
at the focal length

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or at the focus point
on the right-hand side.

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And this goes the
other way around.

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Let me draw another lens.

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And actually, one
thing that we're

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going to assume while
we're dealing with lenses,

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and this is kind of a
simplifying assumption,

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is called a thin
lens assumption.

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There is a difference
in distance

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it travels, depending on where
the light travels in the lens.

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For example, here there's
less distance than over here.

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And in an introductory
physics-- and we're

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going to do that
here, as well-- we're

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just going to ignore that
difference in distance,

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because that would lead to some
differences in how the light is

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refracted and transmitted
and all of that.

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Because it has to
travel a smaller

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distance here than over here.

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So we're going to ignore
those differences,

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and we're just going to make
the thin lens assumption.

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But using a thin
lens assumption,

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let's think a little
bit about what's

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going to happen with the light.

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And in the next
few examples, I'm

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not going to worry about
this kind of two-step.

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I'm just going to say,
look, it just in general

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gets refracted in that direction
when it exits the lens.

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So let me just draw a
simple lens right over here.

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It is symmetric.

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And it has two focal
points, one on this side,

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so that is one focal point.

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And then it has another focal
point, the exact same distance,

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on the other side.

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This lens is symmetric.

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So let's think about
what this lens will

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do to the images of
different objects.

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So let me draw its
principal axis again.

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So both focal points lie
along that principal axis.

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Now let's stick an object out
here, beyond the focal length.

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So let's think about
what's going to happen.

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So first, remember, we can
pick any point on this object.

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Light is being diffusely
reflected off of every point.

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I like to pick
points that are going

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to do something that's
kind of predictable.

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So let's pick a point.

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Well, let's take the tip.

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And take a ray that does
something that's predictable.

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So let's take a ray that is
parallel to the principal axis.

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I mean, I could
draw this two steps

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so it gets refracted once.

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And then it'll get
refracted again

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through the focal point on
the other side of the lens.

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So then it gets refracted
through there, just like that.

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And then, I could
take another ray

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from the tip of
that arrow that goes

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through the focal
point on this side.

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So it goes through the
focal point on this side.

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And so that is going to
get refracted like this,

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and then get refracted again.

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So it comes out on the
other side of the lens,

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going parallel.

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And hopefully this
makes sense to you,

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because it's kind
of a symmetric deal

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that we're dealing
with over here.

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Something coming in
parallel on the right side

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will go through the focal point.

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Then something going
through the focal point

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will come out on the
other side parallel.

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So whatever light is coming out
radially outward onto this side

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and going through the lens
will converge at this point,

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right over here, on the
other side of the lens.

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And so you could do even
light that goes straight

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through the lens would
end up right over there.

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It actually won't
be refracted at all.

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It'll just be able to go
straight through the lens.

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And so the image
that gets formed

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on the other side of the
lens will look like that.

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So in this example,
it looks like we

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have an inverted real image.

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And once again,
it's a real image

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because the light is actually
converging at that point.

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You would actually be able
to put some type of a screen

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and project the image there.

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In the next video,
we're just going

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to practice this idea of
drawing these rays to figure out

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what type of images we'll get,
depending where the object is,

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whether it's at the focal
point, beyond the focal point,

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beyond two times
the focal point,

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or within the focal point.

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And the best thing
there is we'll just

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get a lot of practice doing
this, drawing these rays

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and thinking about how
they'll get refracted.

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