I am trying to make home telescope, I have a convex lens of focal length 1000mm and eyepiece (plano-convex) with 25mm focal length. What is the ideal distance between objective and eyepiece to see objects more than one kilometre away.
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$\begingroup$ Hello and welcome. I tried to edit your question to make it more clear. Please rollback if what I wrote was not your intended meaning. $\endgroup$– usernumberJun 25, 2020 at 8:25
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tl;dr: 1025 +1/-3 mm
If you were to focus at infinity, then the primary focus is 1000 mm from the primary lens and you would put the eyepiece lens one of its focal lengths away from that point to make a new parallel beam. That's 1025 mm. If your eyes can not focus at infinity without glasses, then wear them so that you can see the parallel beam and image it on your retina.
If you don't have your glasses or would like to try without, then your eye needs a diverging beam which means the eyepiece should be a little less than its 25 mm focal length from the primary focus, i.e. a tiny bit closer to the objective, perhaps 1 or 2 mm.
Now you mentioned that objects are over 1 kilometer away from your telescope. If they were exactly 1 km (1,000,000 mm) then the primary focus would be farther from the objective by a little bit.
The thin lens equation 1, 2 is
$$\frac{1}{d_{img}} = \frac{1}{f} - \frac{1}{f_{obj}}$$
so your image distance would then be 1001 mm, and so you'd have to move your eyepiece away from the objective by 1 mm to correct for that.
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$\begingroup$ Thanks @uhoh, but I am getting inverted image, how to get upright image, do I need to change my eyepiece to concave lense, or Plano convex, or something else to get upright image, $\endgroup$– BinderJun 25, 2020 at 16:42
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$\begingroup$ @Binder - A concave lens can get you an erect image, but it will have a very small field of view at the same magnification. Telescopes for terrestrial use and binoculars have an erecting prism so they can show an erect image with (effectively) convex oculars. $\endgroup$ Jun 25, 2020 at 16:55
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$\begingroup$ @antlersoft. And which side erecting prism is used in binoculars, objective side or eyepiece? $\endgroup$– BinderJun 25, 2020 at 17:15
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$\begingroup$ The erecting prism is between the objective and the eyepiece, usually just before the eyepiece. $\endgroup$ Jun 25, 2020 at 17:22
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$\begingroup$ @antlersoft thanks, one last question, I made my telescope, but can see a very small field of view, do I need to big diameter lenses for more area capture, or something else, can you refer some documentation where I can read all information related to telescope and binoculars, ie.how lenses work, which lenses combination use for which purpose(terrestrial astronomical) and increase or decrease area and magnification. $\endgroup$– BinderJun 25, 2020 at 19:07