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What's the role of the focuser?
I've been playing with geometrical optics of two lens system, and it looks like the image is always formed, either true or false - except when the object to a lens is at its focal point.

Is it because of the eye, or because of other properties not described by geometrical optics?

And why should the focal lengths of the objective and eyepiece overlap (false image)?

Yes, image is formed by telescope objective in the focal plane. The role of EP is to magnify this image. Since EPs have different focal lengths you need focuser to converge the focal planes of EP and telescope objective. Any time you add additional elements to the optical train (observe eye, diagonal, barlow, etc.) you need to do further adjustments.

A single lens will form an image but with convergent rays towards the focal point and divergent from there on. In order for the human eye to see an image, the light rays must come in approximately parallel. That's why you need a second lens, the eyepiece. It will make the divergent rays parallel tuned by your hand turning the focuser.

I've read that the focal lengths have to overlap a bit. if the object of second lens is exactly in its focal point, there is no image, true or false. If the object is outside of the focal point, the image is true, an if it's inside of the focal point, the image is false. And since the image of the objective forms at its focal plane (its object in optical infinity)...

Also the angle that a lens "bends" the beam doesn't depend on the distance.

But I guess, it has to do with the eye: whether or not the image forms on the retina, in front of it, or behind it?
To get it, I should study 3 lens systems with true final images?

turboscrew wrote: ↑Tue Jan 12, 2021 4:56 am But I guess, it has to do with the eye: whether or not the image forms on the retina, in front of it, or behind it?

Yes.

turboscrew wrote: ↑Tue Jan 12, 2021 4:56 am To get it, I should study 3 lens systems with true final images?

No because the shape of the human eye leads to a nearly fixed focus lens. For comfortable viewing the rays must come in parallel. They may diverge a bit but then the eye's lens must work to focus. So just assume parallel. Then there's not that much to study really.

SkyHiker wrote: ↑Tue Jan 12, 2021 9:31 am

turboscrew wrote: ↑Tue Jan 12, 2021 4:56 am But I guess, it has to do with the eye: whether or not the image forms on the retina, in front of it, or behind it?

Yes.

turboscrew wrote: ↑Tue Jan 12, 2021 4:56 am To get it, I should study 3 lens systems with true final images?

No because the shape of the human eye leads to a nearly fixed focus lens. For comfortable viewing the rays must come in parallel. They may diverge a bit but then the eye's lens must work to focus. So just assume parallel. Then there's not that much to study really.

Re-reading it, what I meant to say is that a parallel light bundle (for instance from a star at infinity) must be processed by the optics into a parallel light bundle emerging from the eyepiece, for most comfortable viewing by the human eye. Of course the rays coming from different stars are not parallel but the rays contained in the light bundle of each individual star, are.

turboscrew wrote: ↑Sun Jan 10, 2021 1:02 pm What's the role of the focuser?

https://www.physicsforums.com/attachments/3-png.184389/

In the above image, the role of the focuser is to place the EP (actually the EP lens) at "fe" distance away from the focal plane of the primary which is fixed at distance "fo" from the primary.