Astronomical telescope: derivation - greatest magnification (detail) formula

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SUMMARY

The discussion focuses on deriving the formula for the greatest magnification of an astronomical telescope, expressed as M = fo/foe, where M represents magnification, fo is the focal length of the objective lens, and foe is the distance of the primary image from the eyepiece. Participants clarify the distinction between maximum magnification and maximum resolution, emphasizing that these concepts are fundamentally different. The conversation highlights the importance of understanding the ratio of image distances (di/do) in the context of telescope optics.

PREREQUISITES
  • Understanding of optical principles, specifically lens behavior.
  • Familiarity with the concepts of focal length and image distance.
  • Basic knowledge of geometric optics and magnification formulas.
  • Ability to differentiate between magnification and resolution in optical systems.
NEXT STEPS
  • Study the derivation of the lens maker's equation for better understanding of focal lengths.
  • Research the differences between maximum magnification and maximum resolution in telescopes.
  • Explore the impact of aperture size on telescope performance and resolution.
  • Learn about the role of eyepieces in determining the overall magnification of telescopes.
USEFUL FOR

Astronomy students, optical engineers, and amateur astronomers seeking to deepen their understanding of telescope optics and magnification principles.

jemerlia
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Homework Statement


I am seeking a derivation of the formula for greatest detail or maximum resolution of an astronomical telescope, which is:


Homework Equations



M = fo/foe where:

M: magnification
fo: focal length of objective lens
foe: distance of primary image from the eyepiece

N.B. Of course, the final image (seen through the eyepiece) is at the eye's near point

The Attempt at a Solution



Clearly the ratio di/do is important but I am uncertain about how to proceed from here. The formula is puzzling because it seems disjoint (related to two different lenses). Any help gratefully received. Sadly, geometric proofs are not my strongpoint! :)

Many thanks
 
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It is unclear what you want to obtain. Maximum magnification or maximum resolution? These are quite different.
 

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