Understanding the Magnification of a Telescope: Why is M = f_o / f_e?

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Discussion Overview

The discussion focuses on the magnification of a two converging lens telescope, specifically examining the relationship expressed by the formula M = f_o / f_e, where f_o is the focal length of the objective lens and f_e is the focal length of the eyepiece. Participants explore the concepts of angular versus linear magnification and the implications of viewing distant objects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the formula M = f_o / f_e, suggesting confusion over why magnification exists when both object and image distances approach infinity.
  • Another participant clarifies that M = f_o / f_e refers to angular magnification, while M = image distance / object distance refers to linear magnification, indicating they represent different concepts.
  • A participant notes the angular magnification formula M = tan E / tan E_0 and seeks to understand how it relates to M = f_o / f_e, questioning the equivalence of the two formulas.
  • Another response asserts that the two formulas for angular magnification are inherently equivalent, emphasizing that both are ratios, though they represent different aspects (spatial dimensions versus angles).

Areas of Agreement / Disagreement

Participants express differing views on the relationship between angular and linear magnification, with some confusion remaining about the equivalence of the formulas. No consensus is reached on the clarity of these relationships.

Contextual Notes

Participants highlight the need for careful consideration of definitions and the context in which magnification is discussed, particularly regarding the assumptions made about distances and angles.

Who May Find This Useful

This discussion may be useful for students and enthusiasts of optics, particularly those interested in the principles of telescopes and magnification concepts.

quietrain
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hi, i don't understand why the 2 converging lens telescope's magnification is given by M = f_o / f_e

where f_o = focal length of objective, and f_e = focal length of eyepiece...

issn't M = image distance / object distance...

in the case of a infinity object, the image is also infinity for the eye to view it without straining.

so why is there still a magnification ? infinity over infinity?

need help thanks a lot!
 
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quietrain said:
the 2 converging lens telescope's magnification is given by M = f_o / f_e

This is angular magnification.

issn't M = image distance / object distance...

This is linear magnification.

They're different things.
 
oh. i see.

i look up the angular magnification and the formula was

M = tan E / tan E_0 (wikipedia)

where E_0 = the angle subtended by the object at the front focal point of the objective and E =the angle subtended by the image at the rear focal point of the eyepiece.

so how does this become the formula

M = f_o / f_e ?

even with small angle approximation the formula M = tan E / tan E_0 is still not M = f_o / f_e ?
 
The two formulas for angular magnificaion are equivalent by their very nature and you don't need to prove equality by making arithmetic substitutions
They are both ratios (the focal length equation is simply a ratio of spatial dimensions, where as the angle equations is a ratio of the angles subtended by the magnitude of these dimensions)
Both ratios are in direct proportion.
 

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