# Focal length from thin lens to object distance

• mikey_d
In summary, the problem with using a lens to magnify an object is that both the original object and the magnified image may be diminished. The required focal length can be found by solving the thin lens equation using the given information.
mikey_d
Hello,

I've come across an problem that requires the lens to be at least about 350 mm away from the object.

Object to be examined is 80 mm tall and imaging plane is either 11 mm or 25 mm tall. I've tried to calculate required focal length, but have not succeeded. Distance from lens to imaging plane is not known.

See attached picture for clarification.

#### Attachments

• pf1.JPG
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I'd expect one image to be magnified (if object placed between f and 2f) and the other image to be diminished (if object placed between 2f and infinity). Don't understand how both possible images can be diminished. I take it that both are real. Have you checked the data?

Philip Wood said:
I'd expect one image to be magnified (if object placed between f and 2f) and the other image to be diminished (if object placed between 2f and infinity). Don't understand how both possible images can be diminished. I take it that both are real. Have you checked the data?

Only the image at P´ is diminished, original object at P is 80 mm tall.

What, then, do you mean when you say that the imaging plane is either 11 mm or 25 mm tall? I assumed you meant that these were the heights of two possible images.

Philip Wood said:
What, then, do you mean when you say that the imaging plane is either 11 mm or 25 mm tall? I assumed you meant that these were the heights of two possible images.

It means that there are two different focal lenghts to be figured for the same setup.

Focal length is a characteristic property of a lens. You mean that there are two different lenses to be considered? Just checking that I understand.

Philip Wood said:
Focal length is a characteristic property of a lens. You mean that there are two different lenses to be considered? Just checking that I understand.
Yes, there should be two different lenses.

From similar triangles it's easy to show that, disregarding signs, $$\frac{v}{u}=\frac{height\ of\ image}{height\ of\ object}$$
in which u is distance of object from lens and v is distance of image from lens. So you can get the ratios $\frac{v}{u}$ in the two cases.
But you also have $$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$$
(if you're using the real-is-positive sign convention).

If you assume that u = 350 mm you have enough information to find f in each case. If you know only that u is at least 330 mm, you don't have enough information.

mikey_d
Philip Wood said:
From similar triangles --

That was the clue I was missing, thank you!

(For a while I tried to play around by myself with the thin lens equation and was banging my head to the wall as I didn't have any value for s' and for some reason I didn't notice this similarity of triangles. Which should be QUITE obvious when looking at the picture I attached... :s )

Now I can calculate the required focal lengths with given information and following formula (symbols according to the original picture):
$$f=\frac{sy'}{y+y'}$$

## What is the definition of focal length?

Focal length is the distance between the center of a thin lens and its focal point. It is a measure of how strongly the lens converges or diverges light.

## How is the focal length of a thin lens calculated?

The focal length of a thin lens can be calculated using the thin lens equation: 1/f = 1/o + 1/i, where f is the focal length, o is the object distance, and i is the image distance.

## What is the relationship between focal length and object distance?

The relationship between focal length and object distance is inversely proportional. This means that as the object distance increases, the focal length decreases, and vice versa.

## Can the focal length of a thin lens be negative?

Yes, the focal length of a thin lens can be negative. A negative focal length indicates that the lens is diverging light, rather than converging it.

## How does changing the object distance affect the image formed by a thin lens?

Changing the object distance affects the size and position of the image formed by a thin lens. If the object distance is increased, the image will appear smaller and closer to the lens. If the object distance is decreased, the image will appear larger and farther away from the lens.

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