Parabolic mirrors and real images

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Kind: captions
Language: en

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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.

00:09:06.280 --> 00:09:08.815
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.

00:09:16.850 --> 00:09:18.060
Just like that.

00:09:18.060 --> 00:09:19.310
And then it reflects.

00:09:19.310 --> 00:09:22.580
And it'll be reflected
in a parallel way.

00:09:22.580 --> 00:09:24.000
So what just happened here?

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

00:09:30.310 --> 00:09:34.510
object, they radially
emit outward.

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They reflect on this parabolic
mirror at two different points,

00:09:38.340 --> 00:09:40.280
but then they converge again.

00:09:40.280 --> 00:09:42.750
They converge right over there.

00:09:42.750 --> 00:09:45.630
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

00:09:47.880 --> 00:09:49.860
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.

00:09:52.970 --> 00:09:54.080
They'll keep going.

00:09:54.080 --> 00:09:55.580
But you could
imagine, you could use

00:09:55.580 --> 00:09:57.694
with every point on this arrow.

00:09:57.694 --> 00:09:59.110
And what you're
going to do is get

00:09:59.110 --> 00:10:00.700
an image that looks like this.

00:10:04.560 --> 00:10:06.840
This point up here
corresponds to that point.

00:10:06.840 --> 00:10:08.870
This point corresponds
to that point.

00:10:08.870 --> 00:10:15.410
And so if you were to put
a screen right over here--

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this is a screen.

00:10:17.620 --> 00:10:20.020
It could just be a, I don't
know, white tablecloth.

00:10:20.020 --> 00:10:22.670
Or if there was a
wall right over here.

00:10:22.670 --> 00:10:25.250
Then it would actually
show the image.

00:10:25.250 --> 00:10:27.330
You would actually be
projecting the image

00:10:27.330 --> 00:10:29.740
onto this wall right over here.

00:10:29.740 --> 00:10:31.537
It would actually be
a projected image.

00:10:31.537 --> 00:10:33.620
And that projected image
that we're talking about,

00:10:33.620 --> 00:10:36.220
where the light is converging--
so the light comes radially

00:10:36.220 --> 00:10:38.580
outward from each
point of this arrow.

00:10:38.580 --> 00:10:42.060
And then it converges on
a point on the screen.

00:10:42.060 --> 00:10:46.360
That image that gets formed,
we call that a real image.

00:10:46.360 --> 00:10:47.590
It's real image.

00:10:47.590 --> 00:10:51.044
This is a real image.

00:10:51.044 --> 00:10:52.460
And you might want
to compare that

00:10:52.460 --> 00:10:53.800
to what we call a virtual image.

00:10:53.800 --> 00:10:55.350
A virtual image is
an image that looks

00:10:55.350 --> 00:10:56.683
like it's coming from someplace.

00:10:56.683 --> 00:11:00.070
Because it looks like things
are diverging from some point.

00:11:00.070 --> 00:11:02.790
But they've really been
reflected off of some surface.

00:11:02.790 --> 00:11:04.706
So what we think is
there, really isn't there.

00:11:04.706 --> 00:11:07.930
A real image is an image
that's actually projectable.

00:11:07.930 --> 00:11:10.460
We could put a screen
right over here

00:11:10.460 --> 00:11:12.920
and then these guys are going
to be hitting the screen

00:11:12.920 --> 00:11:17.620
and essentially defusing
the exact same light

00:11:17.620 --> 00:11:21.700
as this point of
the actual object.

00:11:21.700 --> 00:11:25.420
And because of that, the screen
will look just like the object.

00:11:25.420 --> 00:11:26.984
This is a projectable image.

00:11:26.984 --> 00:11:28.650
Anyway, hopefully you
found that useful.

00:11:28.650 --> 00:11:30.450
I realize I've gone
longer than I like to

00:11:30.450 --> 00:11:31.533
with some of these videos.

00:11:31.533 --> 00:11:34.220
We'll talk a little bit
more about parabolic mirrors

00:11:34.220 --> 00:11:36.550
in the next video.


Virtual image

WEBVTT
Kind: captions
Language: en

00:00:00.720 --> 00:00:03.450
Let's say I've got some
type of a book over here.

00:00:03.450 --> 00:00:05.790
So there is my book.

00:00:05.790 --> 00:00:07.535
I'll write it down, book.

00:00:07.535 --> 00:00:10.210
Let me draw the entire book.

00:00:10.210 --> 00:00:14.750
So this is my entire
book, just like that.

00:00:14.750 --> 00:00:16.780
And then I have a
mirror over here.

00:00:16.780 --> 00:00:17.620
So this is a mirror.

00:00:17.620 --> 00:00:19.619
We're just looking at the
mirror from the side--

00:00:19.619 --> 00:00:21.585
I can do a better job
of a straight line

00:00:21.585 --> 00:00:24.290
than that-- so that is a mirror.

00:00:24.290 --> 00:00:26.520
Now, what I want to do
is pick, and I'm really

00:00:26.520 --> 00:00:28.970
picking an arbitrary
point on this book.

00:00:28.970 --> 00:00:34.920
And we know that
there's light that

00:00:34.920 --> 00:00:38.169
is coming on this book--
maybe I haven't told us

00:00:38.169 --> 00:00:39.960
about the light source--
but we're assuming

00:00:39.960 --> 00:00:42.050
that the book will reflect
the light diffusely,

00:00:42.050 --> 00:00:42.960
like most books do.

00:00:42.960 --> 00:00:44.590
It is not a shiny book.

00:00:44.590 --> 00:00:48.030
And so any point on this book,
and we could pick any arbitrary

00:00:48.030 --> 00:00:50.740
point on this book, is
going to be emitting light

00:00:50.740 --> 00:00:52.130
in a whole bunch of directions.

00:00:52.130 --> 00:00:54.310
So what I'm just going to
do is pick two light rays

00:00:54.310 --> 00:00:56.220
that are being emitted from
this point on the book.

00:00:56.220 --> 00:00:57.920
It'll be more than
two, but this will

00:00:57.920 --> 00:00:59.755
help us understand
what's going on here.

00:00:59.755 --> 00:01:01.130
So let me pick
one light ray that

00:01:01.130 --> 00:01:04.260
goes like this-- it's obviously
not curving like that-- so it

00:01:04.260 --> 00:01:07.050
goes like this, and
hits the mirror.

00:01:07.050 --> 00:01:10.510
Incident angle is equal
to reflected angle,

00:01:10.510 --> 00:01:14.560
so it'll reflect off at the
same angle just like that.

00:01:14.560 --> 00:01:17.190
And let me pick another point
that is coming out radially

00:01:17.190 --> 00:01:20.650
from that same, or another ray
that is coming out radially

00:01:20.650 --> 00:01:23.110
from that same point, so
it'll come out like that.

00:01:26.360 --> 00:01:28.650
It has a larger
incident angle, so it'll

00:01:28.650 --> 00:01:32.100
have a larger reflected
angle, just like that.

00:01:32.100 --> 00:01:36.100
And now let's think
about what an observer,

00:01:36.100 --> 00:01:39.650
someone who has their
eyeball right over here--

00:01:39.650 --> 00:01:42.880
so let's say someone has
their eyeball right over here.

00:01:45.307 --> 00:01:46.890
Let me draw their
eyebrows so that you

00:01:46.890 --> 00:01:51.100
get the general idea-- let's
think about what this person

00:01:51.100 --> 00:01:55.820
right over here
will actually see.

00:01:55.820 --> 00:01:57.480
And remember all of
reality is really

00:01:57.480 --> 00:02:00.330
just a big simulation
going on in our brains.

00:02:00.330 --> 00:02:03.000
Now, this person's eye is going
to see these two light rays

00:02:03.000 --> 00:02:05.060
diverging from
some common point.

00:02:05.060 --> 00:02:07.120
If you were to look
straight at the book-- let

00:02:07.120 --> 00:02:09.520
me just do another
example-- if someone

00:02:09.520 --> 00:02:13.367
were to just look at
any arbitrary object,

00:02:13.367 --> 00:02:15.200
let's say that's an
orange right over there.

00:02:15.200 --> 00:02:16.950
And just ignore all
the stuff on the left.

00:02:16.950 --> 00:02:19.230
If I were to look at an
orange, no mirror, nothing,

00:02:19.230 --> 00:02:21.020
no reflections,
or anything, if I

00:02:21.020 --> 00:02:23.340
were to look at a certain
point on the orange,

00:02:23.340 --> 00:02:25.915
light from that point would
be diverging out radially.

00:02:29.340 --> 00:02:34.900
And if my eye were
right over there,

00:02:34.900 --> 00:02:37.530
my brain says, OK, I
have these light rays

00:02:37.530 --> 00:02:39.390
diverging from a single point.

00:02:39.390 --> 00:02:41.850
It will simulate,
or it will show

00:02:41.850 --> 00:02:45.140
me that point of an
orange in my brain.

00:02:45.140 --> 00:02:47.300
Now, The same thing is
going to happen here,

00:02:47.300 --> 00:02:51.890
even though these
two rays actually

00:02:51.890 --> 00:02:54.940
aren't diverging from
a point out here.

00:02:54.940 --> 00:02:57.770
Your brain will say, OK, I got
two things that are coming out

00:02:57.770 --> 00:03:00.440
from what looks like
a point over here.

00:03:00.440 --> 00:03:03.490
It'll really just extrapolate
these lines backwards.

00:03:03.490 --> 00:03:05.190
So it'll take that
green ray and it'll

00:03:05.190 --> 00:03:07.580
say, OK, it must be coming
from a point out there.

00:03:07.580 --> 00:03:09.970
And it'll take that
magenta ray and it'll say,

00:03:09.970 --> 00:03:13.710
it must be coming from
a point out there.

00:03:13.710 --> 00:03:16.700
Your eye is just seeing
these two light rays,

00:03:16.700 --> 00:03:18.501
it doesn't know what's
going on over here.

00:03:18.501 --> 00:03:20.750
It just says OK, they're
just converging from a point.

00:03:20.750 --> 00:03:23.820
And so in this person's
reality, or in my reality,

00:03:23.820 --> 00:03:25.870
I think that there
is an orange there.

00:03:25.870 --> 00:03:27.940
Likewise, I see
these two light rays

00:03:27.940 --> 00:03:31.050
diverging from
some common point.

00:03:31.050 --> 00:03:32.610
I will extrapolate
to figure out--

00:03:32.610 --> 00:03:35.326
or my brain will try to think
about-- where that point is

00:03:35.326 --> 00:03:36.450
in three dimensional space.

00:03:36.450 --> 00:03:38.410
It says, look,
these two rays look

00:03:38.410 --> 00:03:42.160
like they're coming from
a point back over here.

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Now, the reality is, there
is no back over here.

00:03:45.960 --> 00:03:51.180
There is nothing behind the
mirror, but to this observer,

00:03:51.180 --> 00:03:54.622
it looks like the light is being
emitted behind the observer.

00:03:54.622 --> 00:03:56.330
And so what the person
would actually see

00:03:56.330 --> 00:03:57.510
is something like this.

00:04:02.230 --> 00:04:04.439
And this is probably
not too foreign to any

00:04:04.439 --> 00:04:05.230
of our experiences.

00:04:05.230 --> 00:04:08.760
We've all looked in
mirrors-- and remember,

00:04:08.760 --> 00:04:12.220
this is the left side of
this book-- oh, sorry.

00:04:12.220 --> 00:04:13.780
This is the right
side of the book.

00:04:13.780 --> 00:04:17.390
It's the side that has
the curvy part of the B

00:04:17.390 --> 00:04:19.579
so it'll look like this.

00:04:19.579 --> 00:04:23.530
So what this observer sees is
an image that looks like this.

00:04:23.530 --> 00:04:26.180
It is what people
call the mirror image.

00:04:26.180 --> 00:04:27.640
It is flipped.

00:04:27.640 --> 00:04:29.050
The left and the
right is flipped

00:04:29.050 --> 00:04:31.150
and you can think
about why that is.

00:04:31.150 --> 00:04:34.340
I could just draw another ray
right here to make it clear.

00:04:34.340 --> 00:04:37.340
If this ray is coming like this.

00:04:37.340 --> 00:04:41.090
Now, it will reflect and
come out back like this

00:04:41.090 --> 00:04:46.870
to this observer it came from
that point right over there.

00:04:46.870 --> 00:04:48.579
So he sees a flipped
version of the book.

00:04:48.579 --> 00:04:51.078
Now the whole reason why I did
this is one, just to make you

00:04:51.078 --> 00:04:53.210
feel a little comfortable
with these reflecting

00:04:53.210 --> 00:04:54.290
lines and all of that.

00:04:54.290 --> 00:04:55.800
But one, I guess
more importantly

00:04:55.800 --> 00:04:59.610
to get you more comfortable with
the idea of a virtual image.

00:04:59.610 --> 00:05:01.730
This right here
is a virtual image

00:05:01.730 --> 00:05:03.821
and we're going to compare
it with a real image

00:05:03.821 --> 00:05:04.570
in the next video.

00:05:04.570 --> 00:05:06.028
And to some degree,
a virtual image

00:05:06.028 --> 00:05:08.550
is more intuitive because we
have so much experience with it

00:05:08.550 --> 00:05:10.840
when we think about mirrors
or reflective surfaces.

00:05:10.840 --> 00:05:12.350
So it's a virtual image.

00:05:12.350 --> 00:05:14.970
And we call it a virtual
image because the book really

00:05:14.970 --> 00:05:15.630
isn't there.

00:05:15.630 --> 00:05:16.710
It's virtually there.

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There is no actual
physical space,

00:05:18.360 --> 00:05:19.890
or we don't know if
there's any physical space

00:05:19.890 --> 00:05:20.690
behind the image.

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Our brain just uses
these diverging lights

00:05:23.310 --> 00:05:27.470
and creates a model
inside of our brain

00:05:27.470 --> 00:05:29.470
to say, OK, that
book exists there,

00:05:29.470 --> 00:05:31.769
even though the source of
the light is over here.

00:05:31.769 --> 00:05:33.560
Now I'm just going to
draw another diagram,

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and you normally won't
have the diagrams that

00:05:36.190 --> 00:05:38.250
have this type of
perspective, but just

00:05:38.250 --> 00:05:40.337
to give you a sense
of the same thing.

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And just to get you familiar
with some of these diagrams

00:05:42.670 --> 00:05:46.540
that we're going to do when
we study mirrors and lenses,

00:05:46.540 --> 00:05:50.850
is we could imagine
that this is the ground,

00:05:50.850 --> 00:05:53.040
let's say that this is a mirror.

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And let's say that
this is actually

00:05:55.360 --> 00:05:58.290
could be somebody standing
in front of a mirror.

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Although usually people
will draw an arrow here

00:06:00.310 --> 00:06:01.643
to just say an arbitrary object,

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Well, let's just say we have an
arrow in front of the mirror,

00:06:04.690 --> 00:06:06.360
just so you get used
to this notation.

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This is actually a physical
arrow, this is not a light ray.

00:06:09.620 --> 00:06:12.220
Now let's think about what
the image of this arrow--

00:06:12.220 --> 00:06:14.700
let's say this arrow had eyes,
so it's actually a person.

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So this arrow had eyes,
what would this arrow see?

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Well, let's just pick an
arbitrary point of this arrow.

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You could do it with any
point-- this object--

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because every point will be
reflecting light diffusely.

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So I'm going to take
one point that's

00:06:27.840 --> 00:06:30.850
coming straight out of the
mirror-- one light ray that

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goes straight to the mirror--
so just parallel to the ground,

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straight to the mirror.

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Well, it's just going to reflect
straight off and then come back

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to the source of that light.

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Maybe that arrow's eye, if
you view it as a person.

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And let's just do another
point, another ray

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coming from that point.

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So another ray coming from that
point might come out like that.

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Incident angle is equal
to reflected angle,

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so then it would
come back like that.

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Now, maybe this whole
thing is an eye.

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Maybe that'll simplify things.

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So let's say this
whole thing is you're

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looking really
close at a mirror.

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This whole thing is an eye.

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Now what would the eye see?

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Well, it's looking--
this ray looks

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like it's coming
from back over here.

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And then this ray
looks like it's

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coming from back over here.

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This is where they
converge, so the eye

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would see this point
of the eye over there.

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So it will actually see itself.

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And in general, these
type of diagrams

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are used to think about what
would the real or virtual image

00:07:37.410 --> 00:07:41.630
be of an object once the
light from that object

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either is reflected
off of a mirror,

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or goes through
some type of lens.

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And we'll be doing this a
lot more in future videos.

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But anyway, hopefully that
gets you a little bit familiar

00:07:50.485 --> 00:07:52.970
with the things we'll
be dealing with.


Total internal reflection

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:02.320
We know from the last few videos

00:00:02.320 --> 00:00:11.460
we have light exiting a slow medium. Let's say I have light ray exiting a slow medium there

00:00:11.600 --> 00:00:17.090
Let me draw. This is its incident angle right over there

00:00:17.400 --> 00:00:26.540
Though it's not the true mechanics of light, you can imagine a car was coming from

00:00:26.710 --> 00:00:33.210
a slow medium to a fast medium; it was going from the mud to the road

00:00:33.490 --> 00:00:38.400
If the car was moving in the direction of this ray, the left tires would get out of the mud

00:00:38.400 --> 00:00:41.330
before the right tires and they are going to be able to travel faster

00:00:41.460 --> 00:00:44.590
So this will move the direction of the car to the right

00:00:44.590 --> 00:00:48.490
So the car will travel in this direction, like that

00:00:48.510 --> 00:00:55.350
where this angle right over here is the angle of refraction

00:00:55.350 --> 00:00:58.750
This is a slower medium than that. This is a fast medium over here

00:00:59.060 --> 00:01:04.440
We get theta 2 is going to be greater than theta 1

00:01:04.680 --> 00:01:10.740
What I want to figure out in this video is

00:01:10.740 --> 00:01:15.720
is there some angle depending on the two substances that the light travels in

00:01:15.870 --> 00:01:19.860
where if this angle is big enough--because we know that this angle is always

00:01:19.860 --> 00:01:21.490
is always larger than this angle

00:01:21.490 --> 00:01:24.400
that the refraction angle is always bigger than the incident angle

00:01:24.420 --> 00:01:26.840
moving from a slow to a fast medium

00:01:26.850 --> 00:01:30.580
Is there some angle--if I approach it right over here

00:01:30.580 --> 00:01:35.900
Let's call this angle theta 3

00:01:35.900 --> 00:01:38.210
Is there some angle theta 3

00:01:38.210 --> 00:01:43.550
where that is large enough that the refracted angle is going to be 90 degrees

00:01:43.550 --> 00:01:47.470
if that light is actually never going to escape into the fast medium?

00:01:47.470 --> 00:01:55.340
And if I had a incident angle larger than theta 3, like that

00:01:56.090 --> 00:02:02.210
So whatever that is, the light won't actually even travel along the surface

00:02:02.210 --> 00:02:06.980
it definitely won't escape. It won't even travel on surface. It will actually reflect back

00:02:07.000 --> 00:02:11.190
So you actually have something called total internal reflection

00:02:11.340 --> 00:02:16.990
To figure that out, we need to figure out at what angle theta three

00:02:16.990 --> 00:02:25.020
do we have a refraction angle of 90 degrees?

00:02:25.040 --> 00:02:29.020
That incident angle is going to be called our critical angle

00:02:29.020 --> 00:02:32.790
Anything larger than that will actually have no refraction

00:02:32.790 --> 00:02:35.180
It's actually not going to escape the slow medium

00:02:35.280 --> 00:02:39.280
It's just going to reflect at the boundary back into the slow medium

00:02:39.300 --> 00:02:43.070
Let's try to figure that out and I'll do it with an actual example

00:02:43.080 --> 00:02:48.720
So let's say I have water. This is water

00:02:50.030 --> 00:02:54.310
It has an index of refraction of 1.33

00:02:54.580 --> 00:02:56.580
And let's say I have air up here

00:02:56.580 --> 00:02:59.560
And air is pretty darn close to a vacuum

00:02:59.710 --> 00:03:03.970
And we saw this index of refraction 1.00029 or whatever

00:03:03.970 --> 00:03:11.260
Let's just for sake of simplicity say its index of refraction 1.00

00:03:11.270 --> 00:03:21.530
For light that's coming out of the water

00:03:21.790 --> 00:03:29.120
I want to find some critical angle. I'll call it theta critical

00:03:42.480 --> 00:03:47.950
and so if I have any incident angle less than this critical angle, I'll escape

00:03:48.220 --> 00:03:51.600
At that critical angle, I just kind of travel at the surface

00:03:51.600 --> 00:03:59.280
Anything larger than that critical angle, I'll actually have total internal reflection

00:03:59.280 --> 00:04:02.700
Let's think about what this theta, this critical angle could be

00:04:03.050 --> 00:04:05.410
So I'll break out Snell's Law again

00:04:06.100 --> 00:04:08.990
We have the index of refraction of the water

00:04:09.210 --> 00:04:16.720
1.33 times the sine of our critical angle

00:04:16.730 --> 00:04:21.670
is going to be equal to the index of refraction of the air which is just one

00:04:22.440 --> 00:04:30.470
times the sine of this refraction angle, which is 90 degrees

00:04:30.660 --> 00:04:34.350
Now what is the sine of 90 degrees? To figure that out, you need to think about the unit circle

00:04:34.350 --> 00:04:36.130
You can't just do the soh-cah-toa

00:04:36.330 --> 00:04:38.990
This is why the unit circle definition is useful

00:04:39.460 --> 00:04:41.610
Think of the unit circle

00:04:42.110 --> 00:04:45.820
You go 90 degrees. We are now here on the unit circle

00:04:45.820 --> 00:04:51.490
And the sine is the y coordinate. On a unit circle, that is 1

00:04:51.510 --> 00:04:57.240
So the y coordinate is 1. So this right over here is going to be 1

00:04:57.550 --> 00:05:02.520
So to figure this out, we can divide both sides by 1.33

00:05:02.520 --> 00:05:16.170
So we get the sine of our critical angle is going to be equal to be 1 over 1.33

00:05:16.360 --> 00:05:20.390
If you want to generalize it, this is going to be the index of refraction--

00:05:20.540 --> 00:05:24.530
this right here is the index of refraction of the faster medium

00:05:24.530 --> 00:05:28.750
That right there we can call that index of refraction of the faster medium

00:05:29.410 --> 00:05:35.600
This right here is the index of refraction of the slower medium. So it's ns

00:05:35.660 --> 00:05:39.530
Because the sine of 90 degrees is always going to simplify to 1

00:05:39.530 --> 00:05:41.680
when you're finding that critical angle

00:05:42.090 --> 00:05:44.840
So I'll just keep solving before we get our calculator out

00:05:44.840 --> 00:05:46.880
We take the inverse sine of both sides

00:05:46.920 --> 00:05:57.580
And we get our critical angle. It's going to be the inverse sine 1 / 1.33

00:05:57.600 --> 00:06:04.110
Let's get our handy TI-85 out again

00:06:04.490 --> 00:06:11.960
We just want to find the inverse sign of 1 / 1.33

00:06:12.640 --> 00:06:18.980
And we get 48.8 degrees.

00:06:18.980 --> 00:06:29.380
So this right here, so our critical angle
is 48.8 degrees

00:06:29.420 --> 00:06:32.940
So this right here is 48.8 degrees

00:06:33.200 --> 00:06:43.220
which tells us if we have light leaving water at an incident angle of more than 48.8 degrees

00:06:43.250 --> 00:06:47.280
it actually won't even be able to refract; it won't be able to escape into the air

00:06:47.280 --> 00:06:52.410
It's actually going to reflect at that boundary

00:06:52.680 --> 00:06:56.980
If you have angles less than 48.8 degrees, it will refract

00:06:56.980 --> 00:06:58.810
So if you have an angle right over there

00:06:58.830 --> 00:07:01.250
it will be able to escape and refract a little bit

00:07:01.250 --> 00:07:06.330
And then right at 48.8, right at that critical angle

00:07:06.330 --> 00:07:09.710
you're gonna have refraction angle of 90 degrees

00:07:09.710 --> 00:07:12.130
or really just travel at the surface of water

00:07:12.130 --> 00:07:16.910
And this is actually how fiber-optic cables work. Fiber-optic cables are just--

00:07:17.520 --> 00:07:21.580
You can view them as glass pipes

00:07:21.720 --> 00:07:29.600
And the light is traveling and the incident angles are so large here

00:07:29.600 --> 00:07:34.250
that the light would just keep reflecting within the fiber-optic

00:07:34.250 --> 00:07:35.580
So this is the light ray

00:07:35.580 --> 00:07:38.090
If they travel at larger than the critical angle

00:07:38.420 --> 00:07:42.640
so instead of escaping into the surrounding air or whatever

00:07:42.720 --> 00:07:47.610
it'll keep reflecting within the glass tube

00:07:47.630 --> 00:07:50.150
allowing that light information to actual travel

00:07:50.170 --> 00:07:53.331
Anyway, hopefully you found that reasonably interesting

00:07:53.331 --> 00:07:55.000
Subtitles by Isaac@RwmOne : youtube.com/RwmOne


Snell's law example 2

WEBVTT
Kind: captions
Language: en

00:00:00.560 --> 00:00:04.140
Let's do a slightly more
involved Snell's law example.

00:00:04.140 --> 00:00:06.240
So I have this person
over here, sitting

00:00:06.240 --> 00:00:08.510
at the edge of this pool.

00:00:08.510 --> 00:00:11.380
And they have a little
laser pointer in their hand

00:00:11.380 --> 00:00:13.202
and they shine
their laser pointer.

00:00:13.202 --> 00:00:14.660
So in their hand,
where they shine,

00:00:14.660 --> 00:00:18.970
it's 1.7 meters above
the surface of the pool.

00:00:18.970 --> 00:00:21.980
And they shine it so
it travels 8.1 meters

00:00:21.980 --> 00:00:24.600
to touch the surface
of the water.

00:00:24.600 --> 00:00:27.660
And then the light
gets refracted inward.

00:00:27.660 --> 00:00:28.950
It's going to a slower medium.

00:00:28.950 --> 00:00:30.680
If you think about
the car analogy,

00:00:30.680 --> 00:00:33.560
the outside tires get to stay
outside a little bit longer,

00:00:33.560 --> 00:00:34.480
so they move faster.

00:00:34.480 --> 00:00:35.900
So it gets refracted inward.

00:00:35.900 --> 00:00:38.290
And then it hits the
bottom of the pool

00:00:38.290 --> 00:00:40.220
at some point right over here.

00:00:40.220 --> 00:00:42.950
And the pool, they tell
us, is three meters deep.

00:00:42.950 --> 00:00:50.000
What I want to figure out is how
far away does this point hit.

00:00:50.000 --> 00:00:52.423
So what is this distance
right over here?

00:00:56.612 --> 00:00:58.070
And to figure that
out, I just need

00:00:58.070 --> 00:01:00.249
to figure out what
this distance is.

00:01:00.249 --> 00:01:02.790
I need to figure out what this
distance is-- so this distance

00:01:02.790 --> 00:01:04.005
right over here.

00:01:04.005 --> 00:01:06.130
And then figure out what
that distance is, and then

00:01:06.130 --> 00:01:06.870
add them up.

00:01:06.870 --> 00:01:09.980
So I can figure out
this part-- trying

00:01:09.980 --> 00:01:12.280
to do it in a different
color-- this part right

00:01:12.280 --> 00:01:13.860
until we hit the
surface of the water

00:01:13.860 --> 00:01:16.180
and then figure out this
incremental distance, just

00:01:16.180 --> 00:01:17.154
like that.

00:01:17.154 --> 00:01:18.820
And hopefully with a
little trigonometry

00:01:18.820 --> 00:01:21.310
and maybe a little
bit of Snell's law

00:01:21.310 --> 00:01:22.620
we'll be able to get there.

00:01:22.620 --> 00:01:24.760
So let's start on maybe
what's the simplest thing.

00:01:24.760 --> 00:01:26.610
Let's just figure
out this distance.

00:01:26.610 --> 00:01:29.360
And it looks like it will
pay off later on, as well.

00:01:29.360 --> 00:01:31.950
So let's figure out this
distance right over here.

00:01:31.950 --> 00:01:35.800
So just the distance along
the surface of the water,

00:01:35.800 --> 00:01:37.860
to where the laser
point actually

00:01:37.860 --> 00:01:39.810
starts touching the water.

00:01:39.810 --> 00:01:42.760
And this is just a straight up
Pythagorean theorem problem.

00:01:42.760 --> 00:01:44.870
This is a right angle.

00:01:44.870 --> 00:01:46.540
This is the
hypotenuse, over here.

00:01:46.540 --> 00:01:51.216
So this distance, let's
call this distance x.

00:01:51.216 --> 00:01:54.030
x squared plus
1.7 meters squared

00:01:54.030 --> 00:01:56.227
is going to be equal
to 8.1 squared-- just

00:01:56.227 --> 00:01:57.560
straight up Pythagorean theorem.

00:01:57.560 --> 00:02:01.620
So x squared plus
1.7 squared is going

00:02:01.620 --> 00:02:04.260
to be equal to 8.1 squared.

00:02:04.260 --> 00:02:07.140
Or we could subtract 1.7
squared from both sides.

00:02:07.140 --> 00:02:13.360
We get x squared is equal to
8.1 squared minus 1.7 squared.

00:02:13.360 --> 00:02:15.070
If we want to solve
for x, x is going

00:02:15.070 --> 00:02:16.730
to be the positive
square root of this,

00:02:16.730 --> 00:02:19.350
because we only care
about positive distances.

00:02:19.350 --> 00:02:24.570
x is going to be equal to the
principal root of 8.1 squared

00:02:24.570 --> 00:02:27.460
minus 1.7 squared.

00:02:27.460 --> 00:02:29.210
And let's get our
calculator out for that.

00:02:29.210 --> 00:02:38.190
So x is going to be equal to
the square root of 8.1 squared

00:02:38.190 --> 00:02:42.760
minus 1.7 squared.

00:02:42.760 --> 00:02:50.130
And I get 7.9-- looks about--
let me just round it, 7.92.

00:02:50.130 --> 00:02:53.900
So x is about 7.92, although we
could save that number there,

00:02:53.900 --> 00:02:55.510
so we can get a
more exact number.

00:02:55.510 --> 00:03:01.300
So this is equal to 7.92.

00:03:01.300 --> 00:03:02.440
That is x.

00:03:02.440 --> 00:03:05.160
Now, we just have to figure out
this incremental distance right

00:03:05.160 --> 00:03:07.860
over here, add that
to this x, and then we

00:03:07.860 --> 00:03:09.280
know this entire distance.

00:03:09.280 --> 00:03:11.210
So let's see how we
can think about it.

00:03:11.210 --> 00:03:15.700
So let's think about what
the incident angle is

00:03:15.700 --> 00:03:17.820
and then the angle
of refraction is.

00:03:17.820 --> 00:03:20.560
So I've dropped a
perpendicular to the interface,

00:03:20.560 --> 00:03:22.950
or to the surface.

00:03:22.950 --> 00:03:27.970
So our incident angle is
this angle right over here.

00:03:27.970 --> 00:03:30.750
That is our incident angle.

00:03:30.750 --> 00:03:32.830
And remember,
Snell's law-- we care

00:03:32.830 --> 00:03:34.220
about the sine of this angle.

00:03:34.220 --> 00:03:36.720
Actually, let me just write
down what we want to care about.

00:03:36.720 --> 00:03:40.140
So we know this is
our incident angle.

00:03:40.140 --> 00:03:43.540
This is our angle of refraction.

00:03:43.540 --> 00:03:46.000
We know that the
index of refraction

00:03:46.000 --> 00:03:47.510
for this medium
out here-- and this

00:03:47.510 --> 00:03:51.690
is air, so it's going to be the
index of refraction for air--

00:03:51.690 --> 00:03:57.790
times the sine of theta 1--
this is just Snell's law,

00:03:57.790 --> 00:04:00.200
so times our incident
angle, right here--

00:04:00.200 --> 00:04:03.350
is going to be equal to
the index of refraction

00:04:03.350 --> 00:04:06.910
for the water-- and
we'll put the values

00:04:06.910 --> 00:04:11.970
in the next step-- times
the sine of theta 2-- times

00:04:11.970 --> 00:04:16.890
the sine of our refraction
angle, sine of theta 2.

00:04:16.890 --> 00:04:20.100
Now, we know-- we can
figure out these ends

00:04:20.100 --> 00:04:21.579
from this table right over here.

00:04:21.579 --> 00:04:24.220
I actually got this problem
from ck12.org's flex book

00:04:24.220 --> 00:04:27.300
as well or at least the
image for the problem.

00:04:27.300 --> 00:04:29.810
And so if we want to
solve for theta 2--

00:04:29.810 --> 00:04:32.174
or if we know theta 2, we
could then solve for this.

00:04:32.174 --> 00:04:34.340
And we'll do that with a
little bit of trigonometry.

00:04:34.340 --> 00:04:37.350
Actually we won't even have to--
if we know the sine of theta 2,

00:04:37.350 --> 00:04:40.370
we'll be able to solve for this.

00:04:40.370 --> 00:04:42.270
All right, we'll think
about it either way.

00:04:42.270 --> 00:04:44.840
Actually, we'll just
solve for this angle,

00:04:44.840 --> 00:04:47.200
and then if we know
this angle, then we'll

00:04:47.200 --> 00:04:49.810
be able to use a little
trigonometry to figure out

00:04:49.810 --> 00:04:51.352
this distance over here.

00:04:51.352 --> 00:04:53.560
So to solve for that angle,
we can look up these two.

00:04:53.560 --> 00:04:55.380
And so we just have to
figure out what this is.

00:04:55.380 --> 00:04:57.590
We need to figure out what
the sine of theta 1 is.

00:04:57.590 --> 00:05:00.820
So let's put in
all of the values.

00:05:00.820 --> 00:05:04.160
Our index of refraction
of air is 1.00029.

00:05:04.160 --> 00:05:05.770
So let me put that in there.

00:05:05.770 --> 00:05:08.140
So that's this.

00:05:08.140 --> 00:05:13.144
So 1.00029 times
the sine of theta.

00:05:13.144 --> 00:05:15.310
And you say, oh, how do we
figure out sine of theta?

00:05:15.310 --> 00:05:17.170
We don't even know
what that angle is.

00:05:17.170 --> 00:05:19.510
But remember, this is
basic trigonometry.

00:05:19.510 --> 00:05:23.480
Remember "soh cah toa."

00:05:23.480 --> 00:05:25.257
Sine is opposite
over hypotenuse.

00:05:25.257 --> 00:05:26.840
So if you have this
angle here-- let's

00:05:26.840 --> 00:05:30.920
make it a part of
a right triangle.

00:05:30.920 --> 00:05:33.550
So if you make that as part
of a right triangle, opposite

00:05:33.550 --> 00:05:35.950
over hypotenuse-- it's
the ratio of this side,

00:05:35.950 --> 00:05:39.827
it's the ratio of that
distance to the hypotenuse.

00:05:39.827 --> 00:05:41.660
This distance over here
we just figured out,

00:05:41.660 --> 00:05:43.368
it's the same as this
distance down here.

00:05:43.368 --> 00:05:44.060
It's x.

00:05:44.060 --> 00:05:47.130
So this is 7.92.

00:05:47.130 --> 00:05:49.330
So the sine of theta
1 is going to be

00:05:49.330 --> 00:05:53.050
the opposite of the angle,
opposite over the hypotenuse.

00:05:53.050 --> 00:05:55.920
That just comes from
the definition of sine.

00:05:55.920 --> 00:05:59.380
So it's going to be times-- so
this part right over here, sine

00:05:59.380 --> 00:06:01.930
of theta 1-- we don't have
to know what theta 1 is.

00:06:01.930 --> 00:06:13.960
It's going to be 7.92 over 8.1.

00:06:13.960 --> 00:06:16.810
And that's going to be equal
to the index of refraction

00:06:16.810 --> 00:06:18.100
of water.

00:06:18.100 --> 00:06:21.307
So that's index of
water is 1.33-- so let

00:06:21.307 --> 00:06:22.640
me do that in a different color.

00:06:22.640 --> 00:06:26.060
So that's going to be-- no, I
wanted to do a different color.

00:06:26.060 --> 00:06:29.900
So that's going to be-- let
me do it in this dark blue.

00:06:29.900 --> 00:06:35.851
So that's going to be 1.33
times sine of theta 2.

00:06:35.851 --> 00:06:37.850
And so, if we want to
solve for sine of theta 2,

00:06:37.850 --> 00:06:41.900
you just divide both sides
of this equation by 1.33.

00:06:41.900 --> 00:06:42.650
So let's do that.

00:06:42.650 --> 00:06:43.650
So I'll do it over here.

00:06:43.650 --> 00:06:46.420
So if you divide
both sides by 1.33,

00:06:46.420 --> 00:06:58.280
we get 1.00029
times 7.92 over 8.1,

00:06:58.280 --> 00:07:00.880
and we're also going
to divide by 1.33.

00:07:00.880 --> 00:07:06.120
So we're also dividing by 1.33.

00:07:06.120 --> 00:07:08.940
That is going to be equal
to this sine of theta 2.

00:07:12.920 --> 00:07:15.050
So let's figure what that is.

00:07:15.050 --> 00:07:16.210
So let's do that.

00:07:16.210 --> 00:07:19.650
Get the calculator out.

00:07:19.650 --> 00:07:26.174
So we have 1.00029 times 7.92.

00:07:26.174 --> 00:07:28.340
Well, actually I could even
say times second answer,

00:07:28.340 --> 00:07:30.250
if we want this exact value.

00:07:30.250 --> 00:07:32.750
That was the last-- so I'm going
to do that-- second answer.

00:07:32.750 --> 00:07:35.570
So that's the actual
precise, not even rounding.

00:07:35.570 --> 00:07:40.030
And then we want to divide by
1.33, that's this right here.

00:07:40.030 --> 00:07:45.460
And then we want to divide
by 8.1, and we get that.

00:07:45.460 --> 00:07:48.890
And that's going to be equal
to the sine of theta 2.

00:07:48.890 --> 00:07:51.997
So that's going to be equal
to the sine of theta 2.

00:07:51.997 --> 00:07:53.080
So let me write this down.

00:07:53.080 --> 00:08:00.752
So we have 0.735 is equal
to the sine of theta 2.

00:08:00.752 --> 00:08:02.210
Now, we could take
the inverse sine

00:08:02.210 --> 00:08:04.540
of both sides of this
equation to solve for theta 2.

00:08:04.540 --> 00:08:07.470
So we get theta 2 is
equal to-- let's just take

00:08:07.470 --> 00:08:10.340
the inverse sine of this value.

00:08:10.340 --> 00:08:14.080
So I take the inverse sine of
the value that we just had,

00:08:14.080 --> 00:08:16.510
so answer is just
our last answer.

00:08:16.510 --> 00:08:19.570
And we have theta 2
being 47.3-- let's

00:08:19.570 --> 00:08:22.550
say rounded-- 47.34 degrees.

00:08:22.550 --> 00:08:29.200
So this is 47.34 degrees.

00:08:29.200 --> 00:08:34.299
So we were able to figure out
what theta 2 is, 47.34 degrees.

00:08:34.299 --> 00:08:36.590
So now we just have to use
a little bit of trigonometry

00:08:36.590 --> 00:08:41.059
to actually figure out
this distance over here.

00:08:41.059 --> 00:08:44.490
Now what trig ratio involves--
so we know this angle.

00:08:44.490 --> 00:08:49.540
We want to figure out its
opposite side, to that angle.

00:08:49.540 --> 00:08:51.420
And we know the
adjacent side-- we

00:08:51.420 --> 00:08:52.900
know that this right here is 3.

00:08:52.900 --> 00:08:56.030
So what trig identity deals
with opposite and adjacent?

00:08:56.030 --> 00:08:57.900
Well, tangent-- toa.

00:08:57.900 --> 00:09:00.740
Tangent is opposite
over adjacent.

00:09:00.740 --> 00:09:05.230
So we know that the tangent
of this angle right over here

00:09:05.230 --> 00:09:11.130
of 47.34 degrees is going to
be equal to this opposite side

00:09:11.130 --> 00:09:15.110
over here-- so I'll
call that y-- is going

00:09:15.110 --> 00:09:18.750
to equal y over
our adjacent side.

00:09:18.750 --> 00:09:20.400
And that's just 3 meters.

00:09:20.400 --> 00:09:24.340
Or if we want to solve
for y, we multiply

00:09:24.340 --> 00:09:26.330
both sides of this
equation by 3.

00:09:26.330 --> 00:09:34.840
You get 3 times the tangent of
47.34 degrees is equal to y.

00:09:34.840 --> 00:09:36.890
So let's just get
the calculator out.

00:09:36.890 --> 00:09:41.430
So 3 times the tangent
of that 47.34 degrees--

00:09:41.430 --> 00:09:45.170
I'll use the exact answer--
3 times the tangent of that

00:09:45.170 --> 00:09:48.470
is 3.255.

00:09:48.470 --> 00:09:51.610
So this distance right here, y.

00:09:51.610 --> 00:09:52.990
And we're at the home stretch.

00:09:52.990 --> 00:09:58.660
y is equal to 3.255 meters.

00:09:58.660 --> 00:10:02.280
Now, our question was, what
is this total distance?

00:10:02.280 --> 00:10:04.900
So it's going to be
this distance, x,

00:10:04.900 --> 00:10:07.130
plus y, plus the 3.25.

00:10:07.130 --> 00:10:09.830
So x was 7.92.

00:10:09.830 --> 00:10:11.540
And I'll round here.

00:10:11.540 --> 00:10:16.090
So it's literally just going
to be 7.92 plus our answer

00:10:16.090 --> 00:10:16.650
just now.

00:10:19.270 --> 00:10:21.652
So we get about 11.18.

00:10:21.652 --> 00:10:24.110
Or maybe if we want to really
round, or get the same number

00:10:24.110 --> 00:10:26.350
significant digits,
maybe 11.2 meters.

00:10:26.350 --> 00:10:29.550
I'll just say 11.18 meters.

00:10:29.550 --> 00:10:34.820
So this right here, the distance
that we wanted to figure out

00:10:34.820 --> 00:10:40.300
is the point on the bottom of
the pool where the actual laser

00:10:40.300 --> 00:10:43.280
pointer actually hits
the surface of the pool

00:10:43.280 --> 00:10:49.950
will be 11.18--
approximately, I'm

00:10:49.950 --> 00:10:54.320
rounding a little bit-- meters
from this edge of the pool

00:10:54.320 --> 00:10:54.880
right there.

00:10:54.880 --> 00:10:55.990
Anyway, hopefully you
found that useful.

00:10:55.990 --> 00:10:58.531
It's a little bit more involved
than the Snell's law problem.

00:10:58.531 --> 00:11:00.790
But really the hard part was
just in the trigonometry,

00:11:00.790 --> 00:11:03.080
recognizing that you didn't
have to know this angle,

00:11:03.080 --> 00:11:04.590
because you have
all the information

00:11:04.590 --> 00:11:05.726
for the sine of that angle.

00:11:05.726 --> 00:11:07.600
You could actually figure
out that angle now.

00:11:07.600 --> 00:11:09.430
Now that you know its
sine, you could figure out

00:11:09.430 --> 00:11:10.340
the inverse sine of that.

00:11:10.340 --> 00:11:11.589
But that's not even necessary.

00:11:11.589 --> 00:11:15.010
We know the sine of the angle
using basic trigonometry.

00:11:15.010 --> 00:11:17.250
We can use that and
Snell's law to figure out

00:11:17.250 --> 00:11:18.534
this angle right here.

00:11:18.534 --> 00:11:19.950
And then once you
know this angle,

00:11:19.950 --> 00:11:21.420
use a little bit
more trigonometry

00:11:21.420 --> 00:11:24.255
to figure out this
incremental distance.


Snell's law example 1

WEBVTT
Kind: captions
Language: en

00:00:00.630 --> 00:00:05.400
As promised, let's do a couple
of simple Snell's law examples.

00:00:05.400 --> 00:00:12.530
So let's say, that
I have two media-- I

00:00:12.530 --> 00:00:14.180
guess the plural of mediums.

00:00:14.180 --> 00:00:17.620
So let's say I have
air right here.

00:00:17.620 --> 00:00:21.219
And then right here
is the surface.

00:00:21.219 --> 00:00:23.010
Let me do that in a
more appropriate color.

00:00:23.010 --> 00:00:25.455
That is the surface
of the water.

00:00:31.140 --> 00:00:38.040
And I know that I have a light
ray, coming in with an incident

00:00:38.040 --> 00:00:49.640
angle of-- so relative to the
perpendicular-- 35 degrees.

00:00:49.640 --> 00:00:53.580
And what I want to know is
what the angle of refraction

00:00:53.580 --> 00:00:54.560
will be.

00:00:54.560 --> 00:00:56.780
So it will refract a little bit.

00:00:56.780 --> 00:00:58.280
It will bend inwards
a little bit,

00:00:58.280 --> 00:01:00.780
since this outside's going to
be in the air a little longer,

00:01:00.780 --> 00:01:04.410
if you buy into my car
travelling into the mud

00:01:04.410 --> 00:01:05.080
analogy.

00:01:05.080 --> 00:01:07.840
So it will then
bend a little bit.

00:01:07.840 --> 00:01:10.140
And I want to figure out
what this new angle will be.

00:01:10.140 --> 00:01:12.830
I want to figure out
the angle of refraction.

00:01:12.830 --> 00:01:14.460
I'll call that theta 2.

00:01:14.460 --> 00:01:17.060
What is this?

00:01:17.060 --> 00:01:19.950
This is just straight
up applying Snell's law.

00:01:19.950 --> 00:01:23.500
And I'm going to use the
version using the refraction

00:01:23.500 --> 00:01:25.420
indices, since we
have a table here

00:01:25.420 --> 00:01:29.510
from the ck12.org FlexBook
on the refraction indices--

00:01:29.510 --> 00:01:31.850
and you can go get it
for free if you like.

00:01:31.850 --> 00:01:35.010
And that just tells
us that the refraction

00:01:35.010 --> 00:01:38.250
index for the
first medium-- that

00:01:38.250 --> 00:01:44.250
is air-- times the sine of the
incident angle, in this case

00:01:44.250 --> 00:01:48.280
is 35 degrees, is going to
be equal to the refraction

00:01:48.280 --> 00:01:56.310
index for water, times the
sine of this angle right

00:01:56.310 --> 00:02:00.750
over here-- times
the sine of theta 2.

00:02:00.750 --> 00:02:04.700
And we know what the refraction
index for air and for water is,

00:02:04.700 --> 00:02:06.650
and then we just have
to solve for theta 2.

00:02:06.650 --> 00:02:07.640
So let's just do that.

00:02:07.640 --> 00:02:11.770
The refraction index for
air is this number right

00:02:11.770 --> 00:02:15.100
over here, 1.00029.

00:02:15.100 --> 00:02:23.010
So it's going to be, there's
three 0's, 1.00029 times

00:02:23.010 --> 00:02:27.830
the sine of 35 degrees, is going
to be equal to the refraction

00:02:27.830 --> 00:02:31.400
index for water, which is 1.33.

00:02:31.400 --> 00:02:37.540
So it's 1.33 times
sine of theta 2.

00:02:37.540 --> 00:02:46.000
Now we can divide both sides
of this equation by 1.33.

00:02:46.000 --> 00:02:48.750
On this side, we're just left
with the sine of theta 2.

00:02:48.750 --> 00:02:52.190
On the left-hand side, let's
get our calculator out for this.

00:02:52.190 --> 00:02:55.810
So let me get the
handy calculator.

00:02:55.810 --> 00:02:58.230
And so we want to
calculate-- and I made sure

00:02:58.230 --> 00:03:05.300
my calculator is in degree
mode-- 1.00029 times

00:03:05.300 --> 00:03:08.390
the sine of 35
degrees, so that's

00:03:08.390 --> 00:03:10.320
the numerator of
this expression right

00:03:10.320 --> 00:03:16.280
here-- the green part--
that's 0.5737 divided by 1.33.

00:03:16.280 --> 00:03:18.160
I'm just dividing by
the numerator here.

00:03:18.160 --> 00:03:19.647
When you just
divide this answer,

00:03:19.647 --> 00:03:20.730
it means your last answer.

00:03:20.730 --> 00:03:24.180
That's the numerator up here
divided by that denominator.

00:03:24.180 --> 00:03:26.890
And so I get 0.4314.

00:03:26.890 --> 00:03:28.970
I'll just round a little bit.

00:03:28.970 --> 00:03:32.760
So I'll get-- I'll
switch colors--

00:03:32.760 --> 00:03:39.300
0.4314 is equal to
sine of theta 2.

00:03:39.300 --> 00:03:41.760
And now to solve
for theta, you just

00:03:41.760 --> 00:03:44.410
have to take the inverse
sine of both sides of this.

00:03:47.442 --> 00:03:49.150
This doesn't mean sine
to the negative 1.

00:03:49.150 --> 00:03:50.940
You could also use the arcsine.

00:03:50.940 --> 00:03:55.180
The sine inverse
of 0.4314 is going

00:03:55.180 --> 00:03:58.610
to be equal to-- the inverse
sine of sine is just the angle

00:03:58.610 --> 00:04:00.630
itself or, I guess
when we're dealing

00:04:00.630 --> 00:04:04.240
with angles in a
normal range, it's

00:04:04.240 --> 00:04:05.520
going to be the angle itself.

00:04:05.520 --> 00:04:07.950
And that's going to be the
case with this right over here.

00:04:07.950 --> 00:04:10.340
And if any of that
is confusing you

00:04:10.340 --> 00:04:13.652
might want to review the
videos on the inverse sine

00:04:13.652 --> 00:04:15.110
and the inverse
cosine, and they're

00:04:15.110 --> 00:04:16.550
in the Trigonometry playlist.

00:04:16.550 --> 00:04:18.160
But we can very
easily figure out

00:04:18.160 --> 00:04:20.579
the inverse sine for
this right over here.

00:04:20.579 --> 00:04:23.250
You literally, you
have sine here,

00:04:23.250 --> 00:04:25.720
when you press Second
you get the inverse sine.

00:04:25.720 --> 00:04:27.430
So it's the inverse
sine, or the arcsine

00:04:27.430 --> 00:04:29.047
of that number right over there.

00:04:29.047 --> 00:04:30.630
And instead of
retyping it, I can just

00:04:30.630 --> 00:04:32.984
put Second, and then Answer.

00:04:32.984 --> 00:04:34.900
So I'm taking the inverse
sine of that number.

00:04:37.864 --> 00:04:39.155
And that will give me an angle.

00:04:41.730 --> 00:04:48.660
And I get 25.55, or I'll
round it, 25.6 degrees.

00:04:48.660 --> 00:04:56.900
So this theta 2,
is equal to 25.6,

00:04:56.900 --> 00:05:00.840
or I'll say approximately
equal to some 25.6 degrees.

00:05:00.840 --> 00:05:03.780
So Snell's law goes
with our little car

00:05:03.780 --> 00:05:05.396
driving in to the mud analogy.

00:05:05.396 --> 00:05:06.770
It's going to be
a narrow degree.

00:05:06.770 --> 00:05:09.450
It's going to come inwards a
little bit closer to vertical.

00:05:09.450 --> 00:05:15.110
And theta 2 is equal
to 25.6 degrees.

00:05:15.110 --> 00:05:16.910
And you could do the other way.

00:05:16.910 --> 00:05:20.330
Let's do another example.

00:05:20.330 --> 00:05:26.470
Let's say that we have,
just to make things simpler,

00:05:26.470 --> 00:05:28.660
that I have some
surface right over here.

00:05:28.660 --> 00:05:31.180
So this is some
unknown material.

00:05:31.180 --> 00:05:33.620
And we're traveling in space,
we're on the space shuttle,

00:05:33.620 --> 00:05:34.965
and so this is a vacuum.

00:05:38.650 --> 00:05:40.520
Or pretty darn
close to a vacuum.

00:05:40.520 --> 00:05:46.910
And I have light coming in at
some angle, just like that.

00:05:46.910 --> 00:05:49.570
Let me drop a vertical.

00:05:49.570 --> 00:05:52.349
So it's coming in at some angle.

00:05:52.349 --> 00:05:53.890
Actually, let me
make it interesting.

00:05:53.890 --> 00:05:55.590
Let me make the light go
from the slower medium

00:05:55.590 --> 00:05:57.755
to the faster medium, just
because the last time we

00:05:57.755 --> 00:05:59.470
went from the faster
to the slower.

00:05:59.470 --> 00:06:00.610
So it's in a vacuum.

00:06:00.610 --> 00:06:06.690
So let's say I have some
light traveling like this.

00:06:06.690 --> 00:06:10.460
And once again, just to get
the "get" of whether it's

00:06:10.460 --> 00:06:12.020
going to bend inward
or bend outward,

00:06:12.020 --> 00:06:13.940
the left side is going
to get out first,

00:06:13.940 --> 00:06:17.890
so is going to
travel faster first.

00:06:17.890 --> 00:06:20.970
So it will bend inwards when it
goes into the faster material.

00:06:20.970 --> 00:06:22.550
So this is some unknown.

00:06:22.550 --> 00:06:26.130
This is some unknown material,
where light travels slower.

00:06:26.130 --> 00:06:32.560
And let's say we were able
to measure, the angles.

00:06:32.560 --> 00:06:34.430
So let me drop a
vertical right here.

00:06:38.050 --> 00:06:44.840
And so let's say that this
right here, is 30 degrees.

00:06:44.840 --> 00:06:46.360
And let's say we're
able to measure

00:06:46.360 --> 00:06:47.690
the angle of refraction.

00:06:47.690 --> 00:06:49.940
And the angle of
refraction over here

00:06:49.940 --> 00:06:53.880
is, let's say that
this is 40 degrees.

00:06:53.880 --> 00:06:55.880
So given that we're able
to measure the incident

00:06:55.880 --> 00:06:58.030
angle, and the
angle of refraction,

00:06:58.030 --> 00:07:01.714
can we figure out the refraction
index for this material?

00:07:01.714 --> 00:07:03.880
Or even better, can we
figure out the speed of light

00:07:03.880 --> 00:07:04.660
in that material?

00:07:04.660 --> 00:07:06.618
So let's figure out the
refraction index first.

00:07:09.270 --> 00:07:12.810
So we know the refraction index
for this questionable material

00:07:12.810 --> 00:07:17.440
times the sine of
30 degrees is going

00:07:17.440 --> 00:07:20.364
to be equal to the refraction
index for a vacuum.

00:07:20.364 --> 00:07:22.030
Well, that's just the
ratio of the speed

00:07:22.030 --> 00:07:24.488
of light in the vacuum to the
speed of light in the vacuum.

00:07:24.488 --> 00:07:26.755
So that's just going to be 1.

00:07:26.755 --> 00:07:30.500
This is the same thing
as n for a vacuum--

00:07:30.500 --> 00:07:33.270
and I'll just write a 1 there--
times the sine of 40 degrees.

00:07:36.060 --> 00:07:39.020
Or If we wanted to solve for
this unknown refraction index,

00:07:39.020 --> 00:07:42.270
we just divide both sides of
the equation by sine of 30.

00:07:42.270 --> 00:07:44.392
So our unknown
refraction index is

00:07:44.392 --> 00:07:46.100
going to be-- this is
just the sine of 40

00:07:46.100 --> 00:07:52.005
degrees-- over this-- over
the sine of 30 degrees.

00:07:54.710 --> 00:07:57.320
So we can get our
handy calculator out.

00:07:57.320 --> 00:08:05.280
And so we have the
sine of 40 divided

00:08:05.280 --> 00:08:10.320
by the sine of 30 degrees.

00:08:10.320 --> 00:08:12.390
Make sure you're in degree
mode, if you try this.

00:08:12.390 --> 00:08:16.420
And you get, let's
just round it, 1.29.

00:08:16.420 --> 00:08:20.720
So this is approximately equal
to-- so our unknown refraction

00:08:20.720 --> 00:08:24.830
index for our material
is equal to 1.29.

00:08:24.830 --> 00:08:28.710
So we were able to figure out
the unknown refraction index.

00:08:28.710 --> 00:08:30.460
And we can actually
use this to figure out

00:08:30.460 --> 00:08:33.100
the velocity of light
in this material.

00:08:33.100 --> 00:08:36.990
Because remember, this
unknown refraction index

00:08:36.990 --> 00:08:39.220
is equal to the
velocity of light

00:08:39.220 --> 00:08:43.360
in a vacuum, which is 300
million meters per second,

00:08:43.360 --> 00:08:47.780
divided by the velocity in this
material, the unknown material.

00:08:47.780 --> 00:08:51.780
So we know that 1.29 is equal
to the velocity of light

00:08:51.780 --> 00:08:52.480
in a vacuum.

00:08:52.480 --> 00:08:58.360
So we could write
300 million meters

00:08:58.360 --> 00:09:01.780
per second, divided by
the unknown velocity

00:09:01.780 --> 00:09:02.680
in this material.

00:09:02.680 --> 00:09:04.380
I'll put a question mark.

00:09:04.380 --> 00:09:06.040
And so we can
multiply both sides

00:09:06.040 --> 00:09:07.502
times our unknown velocity.

00:09:07.502 --> 00:09:08.960
I'm running out of
space over here,

00:09:08.960 --> 00:09:10.840
I have other stuff
written over here.

00:09:10.840 --> 00:09:12.990
So I could multiply
both sides by this v

00:09:12.990 --> 00:09:18.720
and I'll get 1.29 times
this v with a question mark,

00:09:18.720 --> 00:09:24.560
is going to be equal to 300
million meters per second.

00:09:24.560 --> 00:09:27.360
And then I could divide
both sides by 1.29.

00:09:27.360 --> 00:09:33.920
v question mark is going to be
this whole thing, 300 million

00:09:33.920 --> 00:09:37.380
divided by 1.29.

00:09:37.380 --> 00:09:38.910
Or another way to
think of it is,

00:09:38.910 --> 00:09:41.830
light travels 1.29
times faster in a vacuum

00:09:41.830 --> 00:09:43.750
than it does in this
material right over here.

00:09:43.750 --> 00:09:45.790
But let's figure
out it's velocity.

00:09:45.790 --> 00:09:49.420
So in this material,
light will travel a slow--

00:09:49.420 --> 00:09:56.840
so the 300 million
divided by 1.29.

00:09:56.840 --> 00:10:03.370
Light will travel a super slow
232 million meters per second.

00:10:03.370 --> 00:10:08.850
So this is approximately,
just to round off,

00:10:08.850 --> 00:10:16.485
232 million meters per second.

00:10:16.485 --> 00:10:18.360
And if we had to guess
what this material is,

00:10:18.360 --> 00:10:20.200
let's see-- I just
made up these numbers--

00:10:20.200 --> 00:10:22.533
but let's see if there's
something that has a refraction

00:10:22.533 --> 00:10:23.950
index close to 1.29.

00:10:23.950 --> 00:10:25.920
So that's pretty
close to 1.29 here.

00:10:25.920 --> 00:10:27.610
So maybe this is some
type of interface

00:10:27.610 --> 00:10:29.640
with water in a vacuum,
where the water somehow

00:10:29.640 --> 00:10:31.070
isn't actually
evaporating because

00:10:31.070 --> 00:10:32.070
of the lack of pressure.

00:10:32.070 --> 00:10:33.486
Or maybe it's some
other material.

00:10:33.486 --> 00:10:35.600
Let's keep it that
way, maybe it's

00:10:35.600 --> 00:10:36.794
some type of solid material.

00:10:36.794 --> 00:10:38.210
But anyway, those
were, hopefully,

00:10:38.210 --> 00:10:40.690
two fairly straightforward
Snell's law problems.

00:10:40.690 --> 00:10:43.930
In the next video, I'll do a
slightly more involved one.


Refraction in water

WEBVTT
Kind: captions
Language: en

00:00:00.660 --> 00:00:03.520
Before doing more examples with
Snell's Law, which essentially

00:00:03.520 --> 00:00:05.820
amount to some math
problems, what I want to do

00:00:05.820 --> 00:00:07.880
is get an intuitive
understanding

00:00:07.880 --> 00:00:11.440
for why this straw looks bent
in this picture right over here.

00:00:11.440 --> 00:00:13.270
To do that, let me
just draw a simplified

00:00:13.270 --> 00:00:14.910
version of that picture.

00:00:14.910 --> 00:00:18.880
So let's draw, this is
the cup right over here.

00:00:18.880 --> 00:00:21.080
We'll do a side
profile of the cup.

00:00:21.080 --> 00:00:27.710
So this is a side profile of
this glass right over here.

00:00:27.710 --> 00:00:29.410
It's the best that
I can draw it.

00:00:29.410 --> 00:00:31.580
And then let me draw
the actual straw.

00:00:31.580 --> 00:00:35.400
So I'm going to first draw the
straw where it actually is.

00:00:35.400 --> 00:00:37.720
So it's coming in off
the side of the cup,

00:00:37.720 --> 00:00:40.080
and the straw is
actually not bending,

00:00:40.080 --> 00:00:43.350
and it goes to the bottom
of the cup just like that.

00:00:43.350 --> 00:00:46.380
And then it goes up
like that, and then it

00:00:46.380 --> 00:00:47.360
goes slightly above it.

00:00:47.360 --> 00:00:49.810
And then it actually does
bend up here, up here, right

00:00:49.810 --> 00:00:51.851
over here, and then the
straw actually does bend.

00:00:51.851 --> 00:00:54.112
But that is irrelevant to
what we want to talk about.

00:00:54.112 --> 00:00:56.570
What I want to do in this video
is talk about why-- when we

00:00:56.570 --> 00:01:02.150
look over here, why does it
look like the straw got bent?

00:01:02.150 --> 00:01:04.780
And it all comes out
of the refraction

00:01:04.780 --> 00:01:09.820
of the light as the light from
the straw down here changes,

00:01:09.820 --> 00:01:11.500
as it goes from one
medium to another.

00:01:11.500 --> 00:01:13.370
Now, we know from
refraction indices,

00:01:13.370 --> 00:01:16.910
or just in general, that
light moves slower in water

00:01:16.910 --> 00:01:17.930
than it does in air.

00:01:17.930 --> 00:01:22.410
So it's slower in water
and faster in air.

00:01:25.200 --> 00:01:28.250
So let's think about
what's going to happen.

00:01:28.250 --> 00:01:32.260
Let me draw two
rays that are coming

00:01:32.260 --> 00:01:34.790
from this point on the
straw right over here.

00:01:34.790 --> 00:01:38.810
So if I draw one
ray right over here,

00:01:38.810 --> 00:01:41.630
so I'm just going to pick
an arbitrary direction.

00:01:41.630 --> 00:01:45.230
So if I pick one
ray just like that.

00:01:45.230 --> 00:01:47.800
Now, when it goes from the
slower medium to the faster

00:01:47.800 --> 00:01:49.620
medium, what's going
to happen to it?

00:01:49.620 --> 00:01:52.540
And it's at a slight angle here,
so the left side of the ray

00:01:52.540 --> 00:01:55.160
is going to end up in the
air before the right side.

00:01:55.160 --> 00:01:58.177
And I'm just using this
as a way of the-- I'm

00:01:58.177 --> 00:01:59.760
using the car example
to kind of think

00:01:59.760 --> 00:02:01.650
about which way this
light's going to bend.

00:02:01.650 --> 00:02:03.566
So if you visualize it
as a car-- or sometimes

00:02:03.566 --> 00:02:05.150
people visualize as
a marching band--

00:02:05.150 --> 00:02:06.661
the left side of
the marching band

00:02:06.661 --> 00:02:08.410
is going to get out
before the right side.

00:02:08.410 --> 00:02:10.020
And it's going to
start moving faster.

00:02:10.020 --> 00:02:11.603
So this is going to
turn to the right.

00:02:15.500 --> 00:02:18.290
Now, let me do another ray.

00:02:18.290 --> 00:02:21.600
So let me do another ray that's
going from that same point.

00:02:21.600 --> 00:02:24.020
I don't want it to go
right along the straw,

00:02:24.020 --> 00:02:25.720
so another ray just like that.

00:02:25.720 --> 00:02:28.040
It will also turn to the right.

00:02:28.040 --> 00:02:30.930
So it is also going
to turn to the right.

00:02:30.930 --> 00:02:37.080
Now, if someone's eye is right
over here, so that's your eye.

00:02:37.080 --> 00:02:38.360
That's the eyelashes.

00:02:38.360 --> 00:02:39.240
That someone's eye.

00:02:39.240 --> 00:02:42.160
You can draw their
nose and all the rest.

00:02:42.160 --> 00:02:44.010
If they're looking
down, where does it

00:02:44.010 --> 00:02:45.730
look like these two
light rays-- let's

00:02:45.730 --> 00:02:48.396
say their eye is big enough that
it captured both of these rays.

00:02:48.396 --> 00:02:51.480
Where does it look like these
two rays are coming from?

00:02:51.480 --> 00:02:53.010
So if you trace
both of these rays

00:02:53.010 --> 00:02:55.476
back, if you just assume
that there was a line here,

00:02:55.476 --> 00:02:57.100
that's what our eyes
and our brains do.

00:02:57.100 --> 00:03:00.120
If you assume that whatever
direction this ray is currently

00:03:00.120 --> 00:03:02.660
going is the direction
it came from,

00:03:02.660 --> 00:03:07.700
and same thing for this
magenta ray, just like that,

00:03:07.700 --> 00:03:10.610
it would look to this observer
that this point on the straw

00:03:10.610 --> 00:03:12.682
is actually right over there.

00:03:12.682 --> 00:03:14.140
And it would look--
and if you kept

00:03:14.140 --> 00:03:16.320
doing that for a bunch
of points on the straw,

00:03:16.320 --> 00:03:18.070
it would look like
this point on the straw

00:03:18.070 --> 00:03:19.650
is actually right over here.

00:03:19.650 --> 00:03:22.440
It would look like we could do
it for this point on the straw.

00:03:22.440 --> 00:03:24.190
It would look like
that point on the straw

00:03:24.190 --> 00:03:25.940
is actually right over here.

00:03:25.940 --> 00:03:30.440
So to this observer, the
straw would look like this.

00:03:30.440 --> 00:03:39.240
It would look like
something like that.

00:03:39.240 --> 00:03:40.610
It would look bent.

00:03:40.610 --> 00:03:43.520
This part would-- even
though the light from here

00:03:43.520 --> 00:03:46.390
is going up and then up
and then it moves out,

00:03:46.390 --> 00:03:48.390
because it gets bent,
when you converge it back,

00:03:48.390 --> 00:03:49.850
it would converge to
this, just like we

00:03:49.850 --> 00:03:50.970
saw with that first point.

00:03:50.970 --> 00:03:53.570
The light from this point,
when it goes out and gets bent,

00:03:53.570 --> 00:03:55.960
if you were to just
extrapolate backwards

00:03:55.960 --> 00:03:58.280
from their new directions,
you'd get to that point.

00:03:58.280 --> 00:04:01.170
So to this observer,
this point on the straw

00:04:01.170 --> 00:04:04.140
will look to be right over
here, even though the light was

00:04:04.140 --> 00:04:05.430
emitted down here.

00:04:05.430 --> 00:04:10.720
And that's why the straw
actually looks bent.

00:04:10.720 --> 00:04:12.770
So this is all really just
because of refraction,

00:04:12.770 --> 00:04:15.423
from going from a slow or
medium to a faster one.

00:04:15.423 --> 00:04:17.589
So hopefully you find that
a little bit interesting.

00:04:17.589 --> 00:04:19.677
In the next video, we'll
actually do some examples

00:04:19.677 --> 00:04:21.260
with Snell's Law
just to get ourselves

00:04:21.260 --> 00:04:23.440
comfortable with
the mathematics.