Hi. It’s Mr. Andersen and this AP Physics
essentials video 120. It is on the refraction of light or the bending of light. And you
can see in this picture here there is a lot of bent light going on. And so what really
happens? If we look at a laser light, as it moves through the air you can see there is
no refraction of light or bending of light. But once it hits this glass surface there
is a bending of the light. Now there is a little bit of reflection off of the surface
but there is a lot of refraction or bent transmitted light like this. And the reason it is bending
is because we are changing the speed at which it is moving through the medium. And I will
give you an analogy that is going to help you in a little bit. What would happen if
we go straight into the medium? It is just going to go straight through. And so if you
look on the glass to the left the light that is coming straight through the middle where
the surface is flat, it is not being refracted at all. It is only on that bent surface where
we see that major refraction. And so when light moves from one medium to another, it
can be reflected, absorbed or transmitted. Now in this video we are dealing with light
that is transmitted into that other medium. Now in this example however the light came
in at a straight angle. And so we do not see that refraction. But what happens if it comes
in at an angle that is not along the normal, or not along the perpendicular? And so these
are the two mediums, this is the one on the left and the one on the right. This would
be the boundary between the two and then this is the normal line right here. And so what
happens if it comes in from one medium, enters another medium where it is going the same
exact speed? There is going to be no change in the angle. It is just going to go straight
through. Just like light goes straight in air, because the medium is never changing.
What happens however if it goes from one medium to another and that second medium, it actually
travels slower? As it does that it will actually bend towards the normal or it is going to
bend towards that dotted line or the perpendicular line. I will give you an analogy that will
help you to remember that. What happens if it comes in and it is moving into a faster
medium? It will actually bend away from that normal. So it is going to bend like like that.
Now that is called refraction. We see the bending of the light and we can actually quantify
that using something called Snell’s Law. Snell’s Law, to quantify it, we have to
add a couple of different variables. We first of all have to define this as the angle of
incidence and this as the angle of refraction. Again, we are always measuring the angle between
the normal and the light ray itself. And then we have n1 and n2. So this is what the formula
for Snell’s Law looks like. And so the index of refraction, we call that n1, on one side,
times the sign of the angle equals the index of refraction on the other side times the
sine of the angle of refraction on the other side. And so we can actually figure out what
angle it is going to bend at if we know a little bit about the speed at which it is
going through. And we also, if we see the bend, we could figure out the speed at which
it is going through as well. Because the index or the refraction is equal to the speed of
light divided by the velocity. Now if we take that angle and we start to increase it, increase
the angle of incidence, we eventually can reach what is called a critical angle. And
instead of being refracted it will not be refracted. It will just go straight along
the margin. And if we increase it above the critical angle then it is going to be reflected
into that first medium. And so what happens is eventually if you get the angle right you
will have to have total internal reflection. None of it is being refracted or transmitted
through that boundary. And so let’s get to that analogy I was talking about a second
ago. And so imagine we have a marching band that is all walking together. And so we are
looking at the marching band, the trumpet players, and we are looking at them from above.
And as they are marching they are trying to keep the space between them the same. So to
the person to your left or the person to your right we want to keep that exactly the same.
And so imagine that they are marching down a road. You can see that they are going to
keep the that spacing between them the same. But let’s say that there is a bunch of sand
in the road. And so what is going to happen to their speed as they enter into the sand?
Well the ones that enter into the sand first are going to slow down. But since they have
kept that distance between them the same you can see that the angle at which we came in
equals the angle at which we came out. So we do not see that refraction going on. But
now let’s set it up so they are marching in at an angle like this. And so they are
marching across let’s say a parking lot and they are going to hit some sand as well.
So what happens is as they come in, which one is going to start to slow down first?
Well it is going to be this one right here. They are still going to keep this distance
between all of them the same. And so watch what happens as they enter into the sand.
You can see they are bending like that. And so we are going from a medium where it is
faster to one where it is slower. So if I put in that normal right here, what happened?
This is our angle of incidence, so it is big. What happens to our angle of refraction? It
is going to be small. In other words it is approaching that normal. And so you always,
when you are looking at problems with refraction, you want to imagine that marching band in
your head and figure out which way it is going to go. So let’s try that again. We have
a marching band now going through sand and they are going to come out into an area where
they go faster. So they are all going slow, but they are going in a straight line. Now
which one is going to start to go faster first? Well it is going to be this one right here.
They are keeping the distance between them all the same and so watch what happens now.
So it is bending like that. And so if we put in that normal again, our angle is actually
increasing. Our angle of refraction is going to be bigger. Let’s try to apply that with
a prism. Let’s say that we have a light ray coming into a prism like this and inside
the prism the light goes slower. So in the glass it is going to go at a slower rate.
And so what is going to happen as the marching band approaches? Try to figure this out in
your head. I can see that the right side is going to start to slow down first. And so
if that does not work, you could just memorize putting in the normal and then figure out
what happens to our angle of incidence and angle of refraction. But it is going to bend
to the right like that. What happens if we go to the next one? So which side of the marching
band is going to start to accelerate first as we move out? It is going to be the left
side. If that does not work, again you could put in the normal and we could say that we
are going to see an increase in that angle of refraction or it is going to bend like
that. Now we could even make sure that that is right. So this is a PHET simulation. You
can shoot a laser at different prisms. So if I turn the laser light on you can see that
refraction occurring. And once you figure out this analogy, it works really well. So
in other words, what is going to happen if we shine a light right at a sphere and we
are going to try to hit it right along the normal? So it is hitting it flat. What should
happen to the refraction? Let’s try it. You can see that it is not lined up perfectly,
but it is going to go straight through. Let’s try another one. What is going to happen here
if we hit it at an angle like this. Where is going to be the bend? And so which one
is going to start to slow down first? I would say the marching band, you know, put yourself
in that position, but the marching band on the right side is going to slow up first.
What is going to happen as we bend, as we come out here? Try to figure it out in your
head? But this is what it would look like. So we are going to get refraction that looks
like that. And so you can see the more I get that bend, the more refraction. Or I could
go in the other direction. That is why we could hold this sphere up and if we look at
it the light coming from the other side is getting inverted. It is turning upside down
due to the refraction of the light coming through. Now let’s quantify a little bit.
So we are going to use Snell’s Law in a PHET simulation. Remember the index of refraction
times sine of the angle of incidence, it is how it comes in, equals the index of refraction
on the other side. And so index of refraction, remember is related to the velocity. And so
the index of refraction goes up as the velocity decreases. So let’s take a look at this.
So we have a laser light bouncing off the surface. And so you can see there is a lot
of reflection going on. But a lot of that light is also going to be refracted on the
surface. And so in this problem if you know the angle at which it comes in, could you
figure out the angle of refraction? You need Snell’s Law to do that. So I would write
it out like this. And then let me look at what information I have. So I have the angle
at which it is coming in. So that is a given. I also know in air the index of refraction
is 1. I am also given the index of refraction of the surface down here, the glass is 1.5.
And so what am I really trying to solve for? I want to figure out that angle of refraction,
how it comes out. So that is going to be my theta 2. So I plug in what I know. So this
is index of refraction of the light, the angle coming in, index refraction of the glass and
this is the angle coming out. So I solve for that. Now I have sine of theta 2 equals 0.577.
So I have to take the inverse sine to figure out what that angle is going to be. And so
I get around 35 degrees. And so you may want to pause the video and make sure that you
get an answer that is similar to that. And now we could remove the question mark and
you can see that that angle is going to be at 35 degrees. Also you can see that it is
less. And the reason it is less is we are going from an area where it is faster to an
area where it is going to be slower. Now you could also have the problem presented like
this. So in this problem, what am I giving you? I am giving you the actual refraction.
So it is coming in at an angle of 60 degrees. You could see that the angle of refraction
is going to be 20 degrees. And so could you figure out the index of refraction? Same thing.
We are going to use Snell’s Law and now you just have that one known, or those three
knowns and the one unknown that we do not have is going to be n2. Now what is interesting
is if we look at material moving from an area of slow to fast, it would look like this.
As we turn the angle, you can see that we are getting more refraction. But as we keep
turning the angle more and more and more you can see that less of that light is being refracted
or making its way through. And eventually what we approach is something called the critical
angle. Once we reach the critical angle then we do not get light be transmitted into that
next surface. And so what eventually happens is it is reflected back into this original
medium. Now when all of it gets returned back into the medium we call that total internal
reflection. And so if we look at this sea turtle right here the reason you are seeing
its reflection up here on the surface is that light is not moving out. It is being reflected
to you because of the angle at which you are looking at that turtle. And so did you describe
models of light traveling from one boundary into another when the speed of propagation
changes? Could you find the relationship using Snell’s Law? And then finally, could you
make predictions? The go to analogy is that marching band analogy. Remember they are going
to keep the distance between them the same. But depending on which one starts to speed
up or slow down first, we are going to get that refraction. And I hope that was helpful.