Astronomical telescope: derivation - greatest magnification (detail) formula

In summary, the conversation is about seeking a derivation for the formula of greatest detail or maximum resolution of an astronomical telescope. The formula is M = fo/foe, where M represents magnification, fo represents focal length of the objective lens, and foe represents the distance of the primary image from the eyepiece. The person is unsure about how to proceed from the ratio di/do and is seeking help, as geometric proofs are not their strong point.
  • #1
jemerlia
28
0

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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  • #2
It is unclear what you want to obtain. Maximum magnification or maximum resolution? These are quite different.
 

What is an astronomical telescope?

An astronomical telescope is a type of telescope used for observing objects in the night sky, such as stars, planets, and galaxies. It is designed to gather and focus light, making distant objects appear brighter and larger.

How is the greatest magnification formula derived for an astronomical telescope?

The greatest magnification formula for an astronomical telescope is derived using the simple magnification formula, M = focal length of objective lens/focal length of eyepiece. By rearranging this formula, we can calculate the maximum magnification for a telescope to be M = aperture of objective lens/aperture of eyepiece.

What is the significance of the greatest magnification formula for an astronomical telescope?

The greatest magnification formula for an astronomical telescope is important because it helps determine the maximum potential magnification for a telescope. This can be useful for astronomers in choosing the right telescope for their observations and understanding its capabilities.

What factors can affect the greatest magnification of an astronomical telescope?

The greatest magnification of an astronomical telescope can be affected by several factors, including the size and quality of the objective lens, the quality of the eyepiece, atmospheric conditions, and the observer's eyesight. A larger objective lens and higher quality eyepiece can result in a higher maximum magnification.

Is the greatest magnification formula the most important factor in choosing an astronomical telescope?

No, the greatest magnification formula is not the most important factor in choosing an astronomical telescope. Other factors, such as the aperture, focal length, and quality of the optics, also play a significant role in the performance and capabilities of a telescope. It is important to consider all of these factors when selecting a telescope for specific astronomical observations.

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