Like we did with parabolic mirrors, what I really want to do in this video
is just for put objects at different distances relative to this convex lens
and just think about what its image will look like
And the whole point of doing that is going through all the different situations but
more is getting practice of how to think about it
So let's first put an object out here
That's more than two focal lengths away from the lens
I'll put the object right here
We'll do our classic arrow
Actually I'll make a point here. When we dealt with parabolic mirrors
we talked about the distance of two focal lengths being our center of curvature
Over here we're just gonna call it 2 focal length, because it's really not
the center of curvature--
or this distance really isn't the radius of curvature of
each of these curves. So we're just gonna call it 2 focal lengths
So with that said, let's actually try to figure out what the image of this thing would look like
as the light from it gets refracted through this lens
So like always, it's useful to draw one ray
Every point of this object is emitting rays in every direction
because it's diffusely reflecting light
So we can just pick rays that are convenient
So we can go from the tip of the arrow
and go parallel to our principal axis just like that
I'm not gonna show all the internal refraction within this lens right here
But we know that if we enter the lens, parallel to the principal axis
when we get refracted, we will go through the focal point on the other side of the lens
And on the left side of the lens
we'll do another ray that goes through the focal point on the left side
and then comes out parallel
The incident ray goes through the left focal point
and when it gets refracted, it will now be parallel
And so the light that came from that point of the object will reconverge right over here
So if you did this for every point of this object
if you did a point in the middle right over here, it would reconverge right over here
If you did this point right over here, it would reconverge right over there
So the image of this object is going to look like this
So it's going to be a real image. The rays actually converge here. So it's a real inverted image
It was pointing up before. Now it's pointing that down
And in this situation, it's actually going to be smaller than the original
So, real, smaller, inverted image
Let's do a couple of other scenarios
Let me copy and paste this before starting this video to save on time
Let's do a situation now where the object is at the 2 focal distances. I guess we can call that
Let's put the object right over here
We can do the exact same thing
You might want to do it on paper on your own to get some practice doing it
We'll do one ray that's parallel
When it gets refracted, it will go through the focal point on the other side
And then we'll do another ray that goes through the focal point on the left side
and then it will become parallel
And they can reconverge or they converge right over there
So you can see that this is actually a parallelogram
This distance right there is going to be the same thing as that distance over here
It is actually--I don't want to say symmetry. You can't flip it over
But this is a--and this distance right over here is going to be the same
thing as this distance over here. I won't go into all the geometry
Anyway, this would be an inverted image of exactly the same size at the exact same distance
Actually I didn't talk about distance in this one over here
Over here, it's a real image; it's smaller and it's also going to be closer in
than this one was. It's gonna be closer to lens
But here the image is going to be the same size as the original object
It's going to be inverted, but it's going to be at the same distance from the lens
just on the other side. Once again this is a real image
Let's do another one
Copy and paste
So let's stick something between one focal length and two focal lengths
So what's put my object right over there
So once again, let's go parallel
then we will refract through the focus on the other side
And then let's go through the focus on the left side
And then we will refract and go parallel
So here, we will have--remember, I could use any point. Here I just used the tip
because I know the base will converge over there
If I took 2 points, it would go converge right back there
And then if I did with a point right here
and I did that same exercise, it would go right over there
And so the whole image would show up over here
So here, it's real; it's inverted; and it's larger
and it is now further away from the lens than the object on the other side
This is really kind of the reverse of the first example
The first example, the object was larger and more than two focal lengths away
and the image was in this range
Now the object is here and now the image's on the other side. So they're kind of--
that's really just the other side of that first examples
Let's do a couple more
So let's put the object at the focal point and see what would happen
And sometimes people memorize this type of things for physics exams
You don't need to. All you have to do is remember just think about 2 rays
usually from the tip of the arrow that gives you a sense what the image will look like
and you do one parallel and one that goes through the focal point
Well, with that said
we're gonna do something slightly different when something is sitting at the focal point
When something is sitting at the focal point
one is we can do the parallel
It will be refracted through the focal point on the other side
And then instead of doing a ray that goes through the focal point on this side
because actually you can't. You're sitting on the focal point right there
Let's do a ray that does not get refracted. We did a similar thing with the parabolic mirrors
What I want do is a ray that'll go right to the center of the lens
where it won't get refracted
It's just go straight through the center of the lens
So what you have here is, both of these rays that were diverging from this point from this tip
they don't reconverge anywhere
And they don't even look like they're diverging from another point
if someone's eyeball is right over here
They're just going to see these as 2 parallel rays of light
So no image will form. Not a real image or virtual image
So we can say no image is going to form
Now the last case is, let's put the object less than one focal distance away
Let's put the object right over here. And think about what happens
Once again, the light ray from this tip
where to go parallel. It will be refracted through the focal point on the other side
And then let's do another light ray, going
in a direction as if it were coming the direction of the focal point on this side
So it comes from that direction
The light ray would go like that
And then it would come out on the other side parallel
So clearly, these two light rays are not converging
So no real image's going to form
But they do look like they're diverging from some point
Continue these lines. They both look like they're coming from a point right over there
So what's going to happen? If someone's eyes are processing these light rays
they're gonna see the tip of this arrow all the way up here
They're gonna see the base of this arrow down here
And essentially, they're going to see a magnified virtual image of the actual arrow
Anyway, hopefully you found that interesting