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I'm reading a chapter on convex lenses and it has this diagram: enter image description here

The chapter explains that triangles ABC and ADE are similar. Thus, ratio of CB to DE is equal to the ratio of BA to AD. Does this mean that

  • if I look at the moon in the telescope that is 1 m long,
  • and the moon appears to be (I will make up a number) 1 cm in diameter,
  • knowing that the distance between moon and Earth is 384,000 km,

I can conclude that the moon is 3,840,000 m in diameter?

This is coming from 384,000 km / 1 m = X / 1 cm or, when converted to meters, 384,000,000 / 1 = X / 0.01

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  • $\begingroup$ Great question, and in this case you can replace the lens concept with a pinhole camera model and obtain the exact same result. As far as I can tell your thinking is correct, but my coffee hasn't kicked in so let's see what others say. Welcome to Astronomy! $\endgroup$
    – uhoh
    Mar 8, 2021 at 1:35
  • $\begingroup$ Okay, you said the moon is 3 840 000 m in diameter, or 3 840 km. It's off by ~400 km. Not bad. $\endgroup$
    – slowerthanstopped
    Mar 8, 2021 at 3:29

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A telescope wouldn't have a single lens, I'm sure you know. If you were to use the setup in your diagram, focusing the image of the moon on a flat surface, you could find its diameter with the method provided. The distances f in the diagram are the focal length of the lens, where a very distant object will be in sharp focus, and that's where you'd end up placing the flat surface.

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