Optics - Diameter of moon viewed through telescope

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SUMMARY

The problem involves calculating the diameter of the moon's image as viewed through a terrestrial telescope, given the angle subtended by the moon at the objective lens and the focal lengths of the lenses. The objective lens has a focal length of 20 cm, while the ocular lens has a focal length of 5 cm. The magnification formula M = -fo/fe is applied, resulting in a magnification of 1.25. To find the diameter of the moon's image at the near point of 25 cm, further calculations based on this magnification are necessary.

PREREQUISITES
  • Understanding of basic optics principles, specifically magnification.
  • Familiarity with focal lengths of lenses in telescopes.
  • Knowledge of angular measurements in degrees.
  • Ability to apply geometric optics equations.
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  • Calculate the actual diameter of the moon's image using the magnification result.
  • Review the principles of angular size and its relation to image size in optics.
  • Explore the effects of different focal lengths on image quality in telescopes.
  • Investigate additional optical formulas relevant to telescope design and function.
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Homework Statement



I've been stuck on this problem for a while now, and have tried it several different ways, but with no results. I'm sure I'm missing something obvious or simply approaching it from the wrong direction.

The moon subtends an angle of 0.5 degrees at the objective lens of a terrestrial telescope. The focal lengths of the objective and ocular lenses are 20 cm and 5 cm, respectively. Find the diameter of the image of the moon viewed through the telescope at near point of 25 cm.


Homework Equations



M = - fo/fe where fo = focal point of objective and fe = focal point of eyepiece
 
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The Attempt at a Solution I've tried to work this problem multiple times, and so far I have come up with the following equation, but I'm not sure if it's correct: M = (20/5) * (25/20) = 1.25 From here, I'm not sure what to do. Any help would be greatly appreciated.
 

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