Object distance and magnifiation

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Homework Help Overview

The discussion revolves around a problem involving a microscope objective with a specified focal length and diameter, where the goal is to determine the object distance required to achieve a specific lateral magnification. The subject area is optics, specifically related to lens equations and magnification concepts.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between object distance, focal length, and magnification, with one participant attempting to apply a formula for magnification. Questions arise regarding the validity of using adapted formulas and the implications of the lens diameter on the calculations.

Discussion Status

The discussion is active, with participants sharing various equations and interpretations. Some guidance has been offered regarding the use of the Gaussian lens formula, and there is an exploration of different approaches to the problem. However, there is no explicit consensus on the correct method or final answer.

Contextual Notes

Participants note potential confusion regarding the relationship between the object distance and the focal length, as well as the implications of the lens diameter on the calculations. There is an acknowledgment that the object distance should be close to the focal length, which contrasts with initial calculations.

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Homework Statement



A 6mm diameter microscope objective has focal length 9mm.

What object distance is required to achieve a lateral magnification of -40?

Homework Equations



mobj=-L/fobj

The Attempt at a Solution



-40x=-L/9mm

L=360mm

Why isn't the answer 360mm? I think it might have something to do with the diameter of the lens, but I'm not completely sure. Can someone explain? Thanks!
 
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Well, the formula I included is basically an approximation derived from the Gaussian lens formula...at least, that's how my book put it.

Basically, with a microscope, the object is very very close to the focal point, so s[tex]\approx[/tex]f. Similarly, the focal length of the objective is much less than the length of the microscope tube, so s'[tex]\approx[/tex]L

Is it wrong to use these adapted formulas from the book?
 
Yes, the object distance will be close to f=9mm. So your answer of 360mm is way way off.
 
Hmmm, after some thinking I got:

[tex]1/f=1/s+1/s'[/tex]
[tex]1/9mm=1/x+1/40x[/tex]
[tex]x=9.225mm[/tex]

And it was right! Thanks for the suggestion to use the Gaussian optics formulas :)
 

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