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.