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

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Discussion Overview

The discussion revolves around the possibility of magnifying an object when a magnifier is placed directly on top of it, effectively resulting in a focal length of zero. Participants explore the implications of this scenario, including the physical meaning of focal length and the conditions under which magnification might occur.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants argue that a focal length of zero is not physically meaningful, as focal length is typically measured from the effective average position of a lens.
  • Others suggest that a thicker lens could potentially allow for magnification under specific conditions, such as having a flat base and a curved top.
  • A participant questions whether the inquiry pertains to an object distance of zero rather than focal length.
  • One participant mentions atomic force microscopy as a method where objects are very close to the magnifier, implying a different context for magnification.
  • Another participant expresses skepticism about the possibility of magnification at zero object distance, suggesting that internal reflection may occur instead of refraction.
  • A suggestion is made to conduct an experiment with a small gap between the magnifier and the object to explore the effects on magnification.
  • Mathematical considerations are introduced, with a formula for angular magnification indicating that an object distance of zero results in a magnification of one, which aligns with the experiences shared by participants.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the possibility of magnification with a focal length of zero, with multiple competing views and uncertainties remaining regarding the physical implications and conditions necessary for magnification.

Contextual Notes

Discussions include limitations related to definitions of focal length, assumptions about lens types, and the mathematical implications of object distance on magnification outcomes.

ksam
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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?
 
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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.
 
ksam said:
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?

Do you mean an object distance of zero?
 
ksam said:
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?
With atomic force magnification the object is very close to the magnifier..

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

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