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In this video we're
going to try to learn

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a little bit about reflection.

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Or I guess you could say we are
going to reflect on reflection.

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I think most of us have
a sense of what this is,

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but we'll try to get a little
bit more exact about it.

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So there are actually
two types of reflection,

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and everything that reflects
is doing one or the other,

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or something in between.

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So we have two types.

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Let me draw them.

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So the first type, and this
is kind of what we normally

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associate with reflection
is specular reflection.

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And in specular
reflection, let's say

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that this is the
top of a mirror.

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This is the surface of a mirror.

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If I have a light
ray coming in-- So

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let me draw a light
ray coming in.

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And just to get the
terminology right,

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this light ray coming in,
this ray, is the incident ray.

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And it's the incident
ray because it's

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the ray as it approaches
the reflective surface.

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Let me write that down.

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That right there is
the incident ray.

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It'll approach the surface.

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And you can almost imagine
that it bounces off

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at essentially the same angle,
but in the other direction.

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So then it'll hit the surface,
and then it'll bounce off,

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and it'll go just like that.

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And then we would call
this the reflected ray,

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after it is kind of
bounced off of the surface.

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Reflected ray.

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And you may have
already noticed this

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if you've played around a lot
with mirrors you would see--

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and we're going to
look at some images.

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So you can think about
it a little better.

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Next time you're in
front of the bathroom

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mirror you can think
about this, and think

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about the angle of incidence
and the angle of reflection.

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But they're actually equal.

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So let me define
them right here.

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So if I were to just
drop a straight line

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that is at a 90
degree, or that is

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perpendicular to the
surface of the actual mirror

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right over here, we would
define this, right here,

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as the angle of incidence.

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I'll just use theta.

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That's just a fancy letter to
show that the angle at which

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we're coming in, the
angle between this ray

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and the vertical right there,
that's the angle of incidence.

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And then the angle
between that vertical

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and the blue ray
right there, we call

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that the angle of reflection.

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And it's just a property
of especially mirrors when

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you're having
specular reflection.

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And you can see
this for yourself

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at all the regular mirrors
that you might experience

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is that the angle
of incidence is

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equal to the angle
of reflection.

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And actually we could
see that in a couple

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of images over here.

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So let me show you some
images of specular reflection,

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just to make it clear here.

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So you have some light from
the sun hitting this mountain.

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And we're going to talk
about diffuse reflection

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in a little bit, and
that's what's happening.

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It's being reflected diffusely.

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That's why we don't see the
actual image of the sun here.

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We just see the white.

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But then those white light
rays, and they're actually

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being scattered in every
direction, some of them

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are hitting the water.

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I'm going to try to match
up parts of the mountain.

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So you have this
part of the mountain.

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Let me do this in
a better color.

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You have this part of
the mountain up here,

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and the part of the
reflection right over there.

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So what's happening
right here is

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light is coming from that
part of the mountain,

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hitting this part of the
surface of the water.

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Let me see if I can
draw this better.

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It's hitting this part of
the surface of the water,

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and then it's getting
reflected, specular reflection,

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to our eyes.

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And it's actually
coming straight at us,

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but I'll draw it
at a slight angle.

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And then it's just coming
straight to our eyes like this.

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If our eye was-- Let's
say our eye was here.

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It's actually coming straight
out at us so I actually

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should just draw
a vertical line,

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but hopefully this
makes it clear.

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And what we just said,
the angle of incidence

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is equal to the
angle of reflection,

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so if you were to
draw a vertical,

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and it might not be that obvious
here, but this angle right

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over here-- Let me draw
this a little darker color.

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This angle right over
here, that's the angle--

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Let me do that in a light color.

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This right here is
the incident angle.

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We drew a vertical.

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And the angle at
which the light ray

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is approaching the
surface of the water,

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right before it bounces,
that's the incident angle

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relative to vertical.

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And then this angle
right here-- and I

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know it's hard-- it doesn't
look like they're the same

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but that's just because
of the perspective

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that we're dealing with.

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This is the angle of reflection.

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And they're actually
going to be equal.

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And you could also
make a similar case.

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And sometimes my brain has
easier thinking about this.

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If this angle is
equal to that angle--

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and this is what's defined
to be the angle of incidence

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and the angle of
reflection-- we also

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know that this
angle, right here,

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is going to be equal to
that angle right there.

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And my brain sometimes
thinks that because that's

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kind of the angle between the
ray and the actual surface,

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but they're really
the same notions.

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And obviously it's
a different angle,

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but if this is equal to that
then this is equal to that

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because these two are
going to add to 90,

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these two are
going to add to 90.

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So another way you
could view it is-- So

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if we look at the
surface of the water.

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Let me draw a line along
the surface of the water.

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Another way to think about it
is that this angle, this angle

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right over here, is going
to be the same as this angle

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right over there.

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And you can also see it in this
reflection right over here.

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So the light from the sun is
going directly to the water

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here, and then getting reflected
at that point on the surface

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of the water, and then
coming over to our eyes.

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And so we could either
say that this angle is

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equal to this angle, so the
angle between the incident ray

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and the surface of the
water is equal to the angle

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of the reflected ray and
the surface of the water,

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or we could draw a
perpendicular right over here--

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I'm not doing that too well-- we
can draw a perpendicular right

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over here to the
surface of the water,

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and say that the incident
angle, the angle of incidence

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right there between the
ray and that perpendicular,

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is going to be the same
as the reflected angle.

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And it's hard to see
there, once again,

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because of the
perspective, but hopefully

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that starts to make sense.

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And I encourage you,
go to your bathroom

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and look in the mirror, and
look at objects in the mirror,

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and think about the angle
that the light from the object

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must be hitting the mirror
for it to get to your eye,

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and where it's actually
hitting the mirror.

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It's actually a pretty
interesting thing

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to do if you're looking for
things to do in the bathroom.

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Now all we've talked about
is specular reflection,

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but the other type of reflection
is diffuse reflection.

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And this is the
type of reflection

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that it may not be
as obvious to you

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that it's occurring
everywhere you look.

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Diffuse reflection.

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And in diffuse reflection,
because the surface

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isn't smooth, it's not
what we kind of associate

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as a mirrored surface.

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So I'll draw it,
I'll zoom in a bunch.

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So in diffuse reflection,
maybe the surface looks

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like that, what happens
is-- and let me be clear.

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In specular reflection
any light ray

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that comes in like that,
the reflection will come off

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at the same-- the
angle of incidence

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will always be equal to
the angle of reflection.

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This is for the situation
of, say, a mirror.

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It'll always be the same.

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If I come in at a
steeper angle, then I'll

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go out in a steeper
angle, just like that.

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That's for specular reflection.

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For diffuse reflection all
sorts of crazy things happen.

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And that's because we don't
have this really smooth surface,

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or the molecules that
make up the surface

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do crazy things to light.

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So if I come in in one
direction, right over here,

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over at that point
the light might

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reflect in that direction.

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Although if I come in at
the same angle over here,

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now all of a sudden the light
might go in that direction.

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And then if I come in at
the same angle over here,

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now all of a sudden the light
might go in that direction.

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And if I come in-- and I think
you get the general idea here--

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if I come in over
here, now the light

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might scatter in that direction.

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If I come in over here
at the same angle,

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now the light might
scatter in that direction.

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So the general idea is,
with diffuse reaction,

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the reflected rays are going in
all sorts of crazy directions,

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and they're getting
all mixed up.

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So think about here, if you
had an image here of the sun,

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and I'm not drawing
it in particular,

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but let's say that these rays
right here are coming directly

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from the sun, then
when they reflect

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it'll kind of
preserve the image.

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You'll have the reflected
image of the sun.

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But over here, if all
of these light rays

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are coming from the
sun, they're not all

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going off in the same direction.

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This will be a part of
the sun, part of the sun.

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And it's happening at a
really, really small level.

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So you're really just
capturing the light,

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but you're losing all
of the information

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from the actual image.

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And if you're wondering where
diffuse reflection occurs just

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look around your room.

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Anything that's not a mirror
is reflecting diffusely.

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It's diffusing the light.

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Do you see that here?

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The mountain right here
is diffuse reflection.

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You have light
coming from the sun,

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but that's being reflected in
all sorts of crazy directions.

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So you don't see a reflection
of the sky over here.

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The water here, that's
specular reflection

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because it's so super
smooth that it preserves--

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The angle of incidence is going
to be the angle of reflection.

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It's always going to be
the same angle because it's

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a kind of almost
perfectly smooth surface.

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The trees, that's
diffuse reflection.

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And I also want to be clear
on something like the trees.

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So on something that's
white, and white

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is the entire
spectrum of light--

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and we'll do more videos
on that in the future--

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it's reflecting the
entire spectrum.

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It's just mixing
it all up so you

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don't see an actual reflection.

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But if you look
at the trees, you

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have the entire spectrum
from the sun coming down

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on the trees, but the trees
themselves-- and you should

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watch the videos on
photosynthesis-- they're

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absorbing every other frequency
of light except for the greens

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you see.

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So they are just reflecting
the green back to us.

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And they're doing it in
a way they're diffusely

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reflecting it.

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So we actually don't
see an actual reflection

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in those trees.

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And I'll just finish up
with one kind of neat thing

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because it's kind of
like playing billiards

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here, because you can actually
have a double reflection.

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00:10:13,563 --> 00:10:16,125
That's why I even had
this image over here.

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00:10:16,125 --> 00:10:18,310
The sun is being reflected
on the water here,

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00:10:18,310 --> 00:10:19,830
and then you have a reflection.

250
00:10:19,830 --> 00:10:21,455
This is a direct
reflection of the sun,

251
00:10:21,455 --> 00:10:23,720
but this is a reflection
of the sun reflected

252
00:10:23,720 --> 00:10:25,290
on the water right over here.

253
00:10:25,290 --> 00:10:27,190
So what you have over
here is the light

254
00:10:27,190 --> 00:10:29,520
from the sun coming
to this reflection,

255
00:10:29,520 --> 00:10:31,290
reflecting at that
point on the water,

256
00:10:31,290 --> 00:10:35,640
then going to this
point on the paddle,

257
00:10:35,640 --> 00:10:38,930
and then coming to our eye.

258
00:10:38,930 --> 00:10:42,060
But once again the angle of
incidence in every situation

259
00:10:42,060 --> 00:10:45,030
here is going to be equal
to the angle of reflection.

260
00:10:45,030 --> 00:10:47,450
Although the paddle looks like
it's a little bit distorted

261
00:10:47,450 --> 00:10:49,380
here, so it's not a
completely smooth surface,

262
00:10:49,380 --> 00:10:51,240
so it makes the math
a little harder.

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00:10:51,240 --> 00:10:52,904
But when you start
thinking about this

264
00:10:52,904 --> 00:10:54,320
it becomes pretty
interesting just

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00:10:54,320 --> 00:10:56,660
to look at almost any
reflective surfaces

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00:10:56,660 --> 00:00:00,000
and to think about
the actual angles.