# A Is it possible to magnify with a focal length of zero?

1. Sep 30, 2016

### ksam

Is it possible to magnify an object if the magnifier is sitting directly on top of the object (a focal length of zero)? How can this be accomplished if it is not possible with a traditional magnifier?

2. Sep 30, 2016

### Jonathan Scott

A focal length of zero is not physically meaningful.

Focal length is normally measured from the effective average position of a lens, so for a thin lens it is assumed to be from the middle of the lens, rather than the surface which is closest to the object.

For a thicker lens, it is necessary to use a more complex calculation, involving the shapes of both faces.

It is possible for example to have a thick lens where the base is flat and the top is curved in such a way that the plane of the base is in focus when viewed from a suitable distance above the lens.

3. Sep 30, 2016

### pixel

Last edited by a moderator: May 8, 2017
4. Sep 30, 2016

### Andy Resnick

Do you mean an object distance of zero?

5. Sep 30, 2016

### CWatters

With atomic force magnification the object is very close to the magnifier..

https://en.m.wikipedia.org/wiki/Atomic-force_microscopy

6. Sep 30, 2016

### ksam

Ok, let me simplify. How can I accomplish magnifying an image on a piece of paper with the magnifier sitting directly on top of the image, with no distance between the magnifier and the piece of paper. I have tried this with a magnifier sheet but if I sit the magnifier sheet directly on the paper, I get no magnification. I have to pull the magnifier back off the paper to get magnification. Thanks for your help.

7. Oct 1, 2016

### CWatters

I don't think that's possible because it implies an object distance that puts it on the lens.

I'm a bit rusty but I think you can start getting internal reflection instead of refraction. The change in refractive index is no longer Rair/Rlens but Robject/Rlens.

8. Oct 1, 2016

### sophiecentaur

The magnifier in question would be 'Plano convex', I guess?? With the flat face on the paper.
What happens when there is a small but finite space underneath? (Say you support it on matchsticks or drinking straws). An easy experiment to try, which would avoid actual contact.
It's a good idea to dip into the Maths for this.
The only formula I know is for a thin bi convex lens. That tells you
m= f/(f-o)
Where m is the angular magnification, o is the object distance and f is the focal length. For o=0, this becomes m=1, which is what you are seeing.
See the Wiki article on lens magnification.