Maximum Magnification of Microscope

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SUMMARY

The maximum magnification of a compound microscope with an objective lens focal length of 0.70 cm and an eyepiece lens focal length of 5.0 cm, mounted 18 cm apart, is calculated to be 130. The formula used for overall angular magnification is M = (25/f_e) * ((l - f_e)/d_o). The magnification is dependent on the object distance (d_o), and while theoretically, it approaches infinity as d_o decreases, practical constraints establish the maximum at 130 due to the physical setup of the microscope.

PREREQUISITES
  • Understanding of lens optics and focal lengths
  • Familiarity with the formula for angular magnification
  • Knowledge of the relationship between object distance and magnification
  • Basic principles of compound microscope construction
NEXT STEPS
  • Study the derivation of the magnification formula for compound microscopes
  • Explore the effects of varying object distance (d_o) on magnification
  • Learn about the limitations of microscope design and practical applications
  • Investigate the role of lens quality and alignment in achieving maximum magnification
USEFUL FOR

Students in optics, physics enthusiasts, and anyone involved in designing or using microscopes for scientific research.

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Homework Statement


You are building a compound microscope with an objective lens of focal length 0.70 cm and an eyepiece lens of focal length 5.0 cm. You mount the lenses 18 cm apart. What is the maximum magnification of your microscope?


Homework Equations


M=\left(\frac{25}{f_e}\right)\left(\frac{l-f_e}{d_o}\right)

The Attempt at a Solution


I tried using the above formula for overall angular magnification and got $\frac{65}{d_o}$ and so the magnification depends on $d_o$, and the smaller $d_o$ gets the larger the magnification. However it looks like the largest magnification is \infty, but the answer is 130. How do you do this problem?
 
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Does anybody know how to approach this problem?
 
I feel like there is no maximum magnification unless there is a minimum distance the object can be placed to the objective lens.
 

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