Why does magnification work? I have read the question How do telescopes work as magnifiers? but it doesn't quite address, as far as I can tell, my question.
I'm trying to wrap my head around why magnification works rather than how it works. Based on my understanding of the functioning of lens-based magnification, the three objects all function, essentially, the same way:

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I'm intentionally ignoring reflective mirror-based telescopes for simplicity. Sets of curved lenses refract light, thus collecting more light, to specific focal points creating virtual images where more details can be perceived. Though I'm not deeply versed on the formulas that describe this phenomena, I understand the basics.
What I'm grappling with is that magnification happens at all. Assuming my understanding is correct, this would mean that, standing on a high mountain on a clear night and looking up at the stars with the naked eye, the "information" that's available to our eyes is that same as the information available to an observatory telescope nearby.
I imagine the explanation is simple but I can't "fill in the gap" that makes such a dramatic difference in perceptible (not accessible) information  between the naked eye and the sky seen through the telescope. Why does "more light", which is fairly diffuse and coming from an extremely distant origin (another planet, for example), produce so much extra perceptible information?
If someone has answer, that would be amazing but I would be just as happy as being pointed to a good discussion of what's really happening.
 A: The light carries the information just fine. But your eye can only distinguish and interpret this information down to certain resolution due to the size of the rods or photoreceptor cells in your retina.
Basically, if your visual sense is a screen then each pixel on this screen can only depict one colour. Showing an enormous image will thus requires trade-off's when several pieces of information is comes with the same pixel. The pixel can only show one and thus must choose a way to "blend" it together. Enlarging a smaller portion of the full picture, which is what a telescope does, spreads out the information bits our your visual "screen" allowing for the details to be spread out more, thus covering more pixels and thus becoming distinguishable.
A: It sounds like you’re looking for an intuitive answer.
Imagine looking into a night sky. You will see almost half of the sky. If you try to focus on a small area you will be unsuccessful. Even if you close one eye. Squinting might help a little but not much. You have an extremely wide field of view.
Now next to you is a telescope. Unlike your eyes it will only focus the parallel rays of light that fall onto its surface. Compared to your eyes it’s field of view is much smaller.
When the telescope’s focused light passes the focal point it begins to spread out. If a lens is place in the spreading light’s path the rays will be refracted to parallel once again.
When you look through this lens your entire pupil will be fill with this parallel light. It will look big because it will fill your entire field of view.
A: When using an optical device, the magnification is the angular size of the final virtual image divided by the angular size of the object as seen by an unaided eye.  To record a real image with film or a charge coupled device, an objective lens (or mirror) with a longer focal length gives a larger image (Consider a pinhole camera).  (A larger aperture gives a brighter and sharper image.)  With a “magnifying glass” (a convex lens), an object inside the focal length gives a larger virtual image at a distance where it can be in focus for the eye.
A: The simple and maybe unsatisfying answer is that given the laws of refraction (which one may derive from Maxwell's equations), magnification is bound to happen (with the expectation of special cases where the magnification is 1).
If your trace light rays from an object to its image which is formed by a lens (or any arbitrarily complex optical system), you find that rays that originate from two points on the object with some distance X between them will converge into two points on the image with a distance X` which is larger or smaller than X (with the exception of magnification being equal to 1).

A: The main thing about a telescope is not that the magnification has this value or that value, but that the aperture and the relevant optical components such as a mirror are large. This has two implications, and both are important:

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*in each second a lot more light enters a big telescope than enters your eye

*the diffraction owing to the finite size of the aperture is less in a telescope than in your eye

By choosing the placement of the optical components, you can get any finite value of magnification. This means that two rays entering the telescope with some small angle between them can leave the telescope with a much larger angle between them. That is what magnification means. But no more light is coming out than went in. Therefore the output light is being spread out, and is correspondingly dimmer. So really what magnification offers you is a trade-off: you can have small magnification and a bright image, or large magnification and a dim image. But what we want is large magnification and a bright image, so our best bet is to increase the size of the telescope aperture.
That is one major difference between the human eye and a telescope, and it should answer your intuition about information.
The other important consideration is resolution and diffraction (item 2 in my list above). Diffraction results in an angle blur of the order of $\lambda/D$ for light of wavelength $\lambda$ passing through an aperature of diameter $D$. If you set the magnification very large (and remember, any value is easily obtained just by adjusting the distances between optical components) then all you succeed in doing is blowing up the blurry diffraction effects. You won't see any more detail that way. The best policy is to pick the magnification so that diffraction blur is matched to the size of your light-detecting elements (pixels in a CCD camera; rods and cones in your eye). We can go sub-diffraction limit, to some extent, by deconvolving the data so there is value in blowing up the diffraction blur so that it spreads over, say, a radius of 10 pixels or so, but there is not much to be gained by increasing the magnification beyond that.
