# Object distance and image relationship

state the relation between object distance image distance and focal length of a spherical mirror fu5dfy0cc -Physics - teenbooks.info object size in image = Object size * focal length / object distance from camera Hands-on rule: Use the inverse relationship if angular size is. Equation 1 defines the relationship between the object distance (o), the focal length (f), and the image distance (i). The image distance is simply.

So d0 corresponds to this. They're both opposite this pink angle. They're both opposite that pink angle. So the ratio of d0 to d let me write this over here. So the ratio of d0. Let me write this a little bit neater.

The ratio of d0 to d1. So this is the ratio of corresponding sides-- is going to be the same thing. And let me make some labels here. That's going to be the same thing as the ratio of this side right over here. This side right over here, I'll call that A. It's opposite this magenta angle right over here.

### Object image height and distance relationship (video) | Khan Academy

That's going to be the same thing as the ratio of that side to this side over here, to side B. And once again, we can keep track of it because side B is opposite the magenta angle on this bottom triangle. So that's how we know that this side, it's corresponding side in the other similar triangle is that one. They're both opposite the magenta angles. We've been able to relate these two things to these kind of two arbitrarily lengths.

But we need to somehow connect those to the focal length.

And to connect them to a focal length, what we might want to do is relate A and B. A sits on the same triangle as the focal length right over here. So let's look at this triangle right over here.

Let me put in a better color.

### Converging Lenses - Object-Image Relations

So let's look at this triangle right over here that I'm highlighting in green. This triangle in green. And let's look at that in comparison to this triangle that I'm also highlighting. This triangle that I'm also highlighting in green.

## Converging Lenses - Object-Image Relations

Now, the first thing I want to show you is that these are also similar triangles. This angle right over here and this angle are going to be the same.

They are opposite angles of intersecting lines. And then, we can make a similar argument-- alternate interior angles. Well, there's a couple arguments we could make.

One, you can see that this is a right angle right over here.

This is a right angle. If two angles of two triangles are the same, the third angle also has to be the same. So we could also say that this thing-- let me do this in another color because I don't want to be repetitive too much with the colors.

We can say that this thing is going to be the same thing as this thing. Or another way you could have said it, is you could have said, well, this line over here, which is kind of represented by the lens, or the lens-- the line that is parallel to the lens or right along the lens is parallel to kind of the object right over there.

And then you could make the same alternate interior argument there. But the other thing is just, look. I have two triangles. Two of the angles in those two triangles are the same, so the third angle has to be the same. Now, since all three angles are the same, these are also both similar triangles. So we can do a similar thing. We can say A is to B.

Remember, both A and B are opposite the degree side. They're both the hypotenuse of the similar triangle. So A is to B as-- we could say this base length right here.

And it got overwritten a little bit. But this base length right over here is f. That's our focal length.

As f in this triangle is related to this length on this triangle. They are both opposite that white angle. So as f is to this length right over here.

Now, what is this length? So this whole distance is di, all the way over here. But this length is that whole distance minus the focal length. So this is di minus the focal length. If the object is a six-foot tall person, then the image is less than six feet tall.

Earlier in Unit 13, the term magnification was introduced; the magnification is the ratio of the height of the object to the height of the image.

In this case, the magnification is a number with an absolute value less than 1. Finally, the image is a real image. Light rays actually converge at the image location. If a sheet of paper were placed at the image location, the actual replica or likeness of the object would appear projected upon the sheet of paper.

The object is located at 2F When the object is located at the 2F point, the image will also be located at the 2F point on the other side of the lens. In this case, the image will be inverted i. The image dimensions are equal to the object dimensions.

**object-image-height-and-distance-relationship**

A six-foot tall person would have an image that is six feet tall; the absolute value of the magnification is exactly 1. As such, the image of the object could be projected upon a sheet of paper. The object is located between 2F and F When the object is located in front of the 2F point, the image will be located beyond the 2F point on the other side of the lens.

Regardless of exactly where the object is located between 2F and F, the image will be located in the specified region. The image dimensions are larger than the object dimensions.

A six-foot tall person would have an image that is larger than six feet tall. The absolute value of the magnification is greater than 1. The object is located at F When the object is located at the focal point, no image is formed. As discussed earlier in Lesson 5the refracted rays neither converge nor diverge. And we figured out in the last video that this triangle over here is similar to this triangle over here.

And since these two are similar, we could say that A is to B-- we did this over here. A is to B as-- and both of those are the sides opposite the right angles of these two similar triangles.

So that's going to be the same thing as the ratio of the sides opposite this yellow angle right over here. So in this triangle over here, since we started with A first, it's this height right over here. Now what is this height right over here? This is the height of the object.