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Is it possible to create a telescope with only one convex lens?

Specifically, is the image I drew below possible?
(This was supposed to be rotated 90 degrees counterclockwise.)

Picture of my hypothesis(?)

In this picture, the object (smaller thing) is supposed to be infinitely far away. The lens focuses the light rays on to the eye (top in picture). Then the eyes "sees" as if it is enlarged to be the bigger image (bigger thing).

Some of my friends argue that humans can only see light rays which are parallel to each other. My counter argument is the picture below:

Picture of eye seeing at infinity and nearer than infinity.

So if anybody could explain to me why or why not could I create a telescope out of a single convex lens. Thank you!

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The term "focusing" means something else than the OP suggests. It means that the different light rays coming that a single, specific point $P$ of the object emits to different directions re-converge back and reach the same place of the retina.

If the object, and/or its point $P$, is infinitely (very) far, then the light rays coming from $P$ are (nearly) parallel near the eye. But even if they're divergent, not parallel, the eye is able to refocus them so that they reach the same pixel of the retina.

So the single convex lens don't magnify anything. At most, they do exactly what the lens in the eyes do and what is needed for focusing – to redirect the nearly parallel light rays so that they intersect against less than an inch from the eye's surface, on the retina, again.

The diagram posted above is misleading because it suggests that the two parallel rays that are supposed to converge to the same point of the retina come from different ends of the objects we observe, $P_1$ and $P_2$. But that's not the case at all. If the diagram is fixed so that it makes sense, we see just one point $P$ and both (nearly parallel) light rays originate from the same $P$.

If we want to consider two points $P_1$, $P_2$ of the object, as the bottom part of the picture clearly wants, they must create two distinct dots $Q_1,Q_2$ on the retina, i.e. two different intersections of pairs of light rays!

So again, a single convex lens doesn't magnify anything. It just does what the eye has to do to focus, anyway: to make the light rays converge. To calculate whether an arrangement of lens (and yes, at least two lens or lens+mirrors are needed) are able to magnify, one has to consider the size of the image on the retina, i.e. different intersections of the light rays on the retina, separated from each other. To approximate the eye by a single dot isn't good enough to calculate the magnification!

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  • $\begingroup$ "single convex lens don't magnify anything" not true, because experiment beats theory. Get a single convex lens ~100mm fl, hold it against your eye, then move it away. You'll see the image become blurry and larger, then "infinitely large," then inverted and larger, then inverted and small. Single convex lens most assuredly do produce magnification, but with severe blurring (at least for normal eyes.) the magnification is identical to that employed by telescopes. Also, the first diagram is correct for telescopes: the rays do not focus on the retina, instead the eye is a camera obscura. $\endgroup$ – wbeaty Apr 26 '17 at 6:37
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Telescope is an Optical device which capture more light & gives you more clear, sharper & deeper view of the object under observation. So It is possible to make an Telescope with single lens (You may call it a telescope), but It will not justify properly the use & its efficiency for which it is used! Also the eye piece (the lens nearer to your eyes) is used so that you are able to observe it in your viewing limits, or else directly viewing it from a bigger lens or mirror won't be a very good Image to watch or observe at. So It is better to use at least use two lenses (One the Objective having larger aperture & larger focal length, 2nd the Eyepiece having small aperture & focal length; more lenses are also used to adjust the final Image Produced). Telescopes(along with the 2 lenses) produce a brighter & sharper Image of the distant object(s), which is seen through our eyes.

You are right about the fact that Human Eye can also perceive Intersecting & non-parallel Rays.

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It is possible to build a basic telescope with one long focal length convex lens and a pinhole (very small aperture).

I used tinfoil with a pinhole in it next to my eye just inside the focal length of the convex lens.

It does work without the pinhole but the image is out of focus. On a positive not the image produced is upright.

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Yes, a single convex lens is a telescope, as your diagrams show, but only if the lens is held away from your eye, and the image in the lens appears inverted. Notice: the focal length of the lens must be significantly smaller than the length of your arm!! Find a lens with a fairly long fl, but not too long.

To produce telescopic magnification, move the lens away from your face until the image seen in the lens becomes extremely large and uselessly blurred ...then move the lens even farther. The image now should be upside-down, large and blurred. Next, cross your eyes, hard. While they're crossed, look at one of the pair of views, and find the lens. Everything in the lens will be clearer! Move the lens in and out until the image is sharp. It will have some low-power magnification.

By crossing your eyes, you also adjust them to focus on very nearby objects. The real-image produced by the convex lens is behaving as a nearby object. This real-image is close to your eyes, and hence larger. By crossing your eyes, your eyes remove the blur. They become the eyepiece of a Newtonian (inverting) telescope, and the image seen through the lens becomes sharp and clear.

If your eyes could focus on objects a few mm in front of your cornea, then even with no eyepiece used, any convex lens could behave as an inverting telescope of several-power magnification. (Also, you could use such an eye to examine insects in great detail without needing a hand lens!)

More: if you're an extreme myope, and can clearly see objects held very close to your eyes, then you can use a single convex lens as an inverting telescope, no need for crossed eyes, and no eyepiece. Your own eyes serve as the eyepiece.

And, if you're an extreme presbyope, far-sighted, then you can use a single convex lens as a Galilean or 'terrestrial' telescope. In that case look at a distant object, hold the lens close to your face, then move it away until the view becomes clear and sharp. The view will be magnified, but won't be upside-down as described earlier. Your eyes are acting as the concave eyepiece of a Galilean-type telescope.

Simplified explanation of telescopes: when viewing distant objects, the Objective lens produces a real image, a floating or "aerial image" positioned out at the focal plane of the lens. To produce large magnification, we place our eye very close to this aerial image, then add a "corrective lens" to our eye in the form of an eyepiece-lens to remove the blur. If the real-image had been placed just outside our eyeball, then the image will be inverted, the eyepiece lens must be be convex, and the resulting telescope type is the Newtonian. But if the real-image was placed inside our eyeball (closer than zero distance!) then a concave-type eyepiece is used, the image will be erect (not upside-down,) and the type of telescope formed is called Galilean. In general, the Newtonian type is superior because of field of view and abberation issues. So, most small telescopes and binoculars use this inverting type of 'scope, but then they add an "image erector" composed of a pair of 90deg prisms acting as four mirrors. Expensive binoculars may use a Newtonian with a Dove-prism or Roof-prism erector rather than two 90deg prisms. Very inexpensive binoculars or 'opera glasses' just use the inferior Galilean setup, with concave eyepiece and no prisms for erecting the inverted image.

The most inexpensive telescope of all uses a piece of aluminum foil with a tiny pinhole:

DIY telescope with foil-pinhole "eyepiece"

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