Hi. It’s Mr. Andersen and this AP Physics essentials 122. And in this video I am going
to show you how to draw ray diagrams for both converging and diverging lenses. I have been
wearing lenses most of my life and the reason why is that I am near-sighted. In other words
the converging lens in my eye is focusing the image in front of my retina. And so everything
is out of focus. And so what you can do to solve that is you simply put a diverging lens
out here. What that does is move the rays apart so they are focusing in the proper location.
But you might be far-sighted. If you are far-sighted you are putting the image too far inside your
retina. And so how would we solve that problem? Just with another converging lens. So we can
focus it right at this point back here. And so when you are looking at where the image
is created, remember we are looking at the focusing of those rays. And so light, as it
moves from one medium to another, it can be bent. We call that refraction. And what is
doing the bending is going to be a lens. The ones that we will deal with in here are converging
and diverging lenses made of glass. And so as it does that it creates an image. Sometimes
that image is real and sometimes it is a virtual image. How do you tell the difference between
the two? If you put a piece of paper there the real image will show up and a virtual
image will not. When you are looking at a mirror for example there is a virtual image
of you on the other side but you can not put a piece of paper there. You simply cannot
get in. Two lenses we will deal with are going to be converging and diverging lenses. And
a way to figure out where that image actually is is to use a ray diagram. We will draw just
two or three rays at each of our drawings. So as the rays come in they will either be
converged or diverged. And figuring out where they go tells us where the image is going
to be. Before we get to that you should have a good gut feeling for how refraction occurs
and I use a marching band analogy for this. Imagine a marching band is going down through
a parking lot. They are keeping, we are looking at it from above, but each of the trumpet
players keep an equal distance between them and the person next to them. And so as they
are marching through the parking lot they eventually come up to some sand. And so what
is going to happen to that group in the front, well it is going to slow down compared to
the ones behind it. But since there is no angle here it is simply going to go at a slower
rate through it and there would be no bending or no refraction. But watch what happens if
we come in at an angle like this. As it comes in at an angle which of those trumpet players
are going to slow down first? It is going to be the one on the bottom. And so as the
one on the bottom slows down first, watch what happens to the other ones. They are bending
like that so we get refraction. And you can see that right here. As the light comes in,
as it hits the glass it is refracting in, because it is traveling at a slower rate.
So let’s get to a converging lens and figure out where that image is actually going to
be. Now there is a few things we want to define. We first have 2f and f. This stands for the
focal point and this is two times the focal point. For dealing with mirrors we sometimes
call this the center of curvature. So you could imagine if this is a circle over here
the radius would always be the same to 2f right here. So let’s draw how this works
with the lens. Again the light is going to go through this lens. This is glass and this
is going to be air out here. So to draw that you first start by taking the top of your
image or the object rather and you are going to draw a parallel line into the lens itself.
So we are going from parallel and then we are going to through the focal point. And
so we draw a line like that. And so that is going to bend or refract right here and it
goes right through the focal point like that. Now let’s turn that around and we are going
to start by drawing it through the focal point. So how do we do that? We draw a line like
that. So now we go through the focal point and now it is going to go parallel. And so
now we have converging, you can see the converging rays over here. And so since those rays are
converging we know that the image is going to be upside down here, since this was the
top over here. And we also know that it is going to be a real image, a true image. In
other words you could put a piece of paper right here and you would have that on the
other side, just like you have a true image on the inside of your eye. Now we can check
ourselves on this as well. So you can draw another ray that goes right through the center
of the lens. And so we know that this is going to be where that image is going to be. Now
let’s watch what happens as we move inside the focal point. It gets a little weird here.
And so what do we do? Again we draw from the top of this object here, we draw parallel.
And then we are going to go through the focal point. But now it is a little bit different.
Since we are inside the focal point, how do you draw it from the focal point? Well it
is going to look like that. And now it is going to be parallel like this. And so as
we look at this, these two rays on this side are diverging from each other. You can see
that they are not going to intersect at any point. And so we are not going to find an
image on the right side. We are going to have to play those backwards. Same thing with the
line through the center. All of these diverging. And so we have to play those lines backwards.
And so where is our image going to be? It is going to be on the same side as the object.
We now call this a virtual image. You could put a piece of paper there and it is simply
not going to show up. But that is where it is going to appear to show up. Now let’s
test this. So we are going to us a simbucket simulation. So we are going to be able to
drag the object on the left side. And you can see as we drag the object the image is
true and it is on the right side. But watch what happens as we approach the focal length.
Now the image is on the left side and it is going to be a virtual image. You can see that
through the dotted lines right here. And we can even measure the distances to figure out
where that image is going to be. A better way to do this is actually use lenses and
figure out where those objects are going to be found and the virtual or true images. Now
let’s go to a diverging lens. So how do we do this? Still have a focal point. Still
have 2f. I start by drawing that parallel. And then you want to draw through the focal
point. That is the tendency to draw right down in this direction. But remember a diverging
lens is not going to do that. That marching band is approaching, it is going to bend away
and then bend away like that. And so what focal point are we going to use? We are going
to use this focal point right here. So that is going to be where the ray moves out. And
now we could go through the focal point. So it goes like that. Where is our parallel line?
It is going to be like that. And so on the right side again we have all these diverging
lines back here. Even at the center line like that. And so where is the image going to be?
Well we have to go backwards and find where they intersect so we are going to have that
virtual image right here. It is going to be upright and it is also going to be smaller.
But it is a virtual image. So we could check that again. So if we take our object on the
left side you can see our virtual image right here. As we approach the focal length or the
focal point it is going to get bigger and bigger and bigger. But it is always upright
and virtual in nature. And so did you learn to use diagrams for both converging and diverging
lenses? Again the one thing, the caveat is once you move in the focal point on the converging
lens it gets a little tricky. And then finally could you plan data collection. Could you
use a simulation like the one I did or actual lenses to figure out where the images are?
I hope so. And I hope that was helpful.