Are telescopes with a concave lens (instead of convex ones) ever useful for astronomy?
And if so, where are they used? Do they ever affect resolving power?
[Physics] Are telescopes with a concave lens useful for astronothe
astronomyopticstelescopes
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If one wants to be rigorous then the lens in the first picture should be called double convex or bi-convex since it is convex on both sides.
For camera lenses and magnifying glasses you mostly want to enlarge the picture and use convex lenses.
For the glasses you have to distinguish if the person is far- or nearsighted. For farsighted people you would take convex lenses, for nearsighted people you would take concave lenses. This is related to the length of the eyeballs and less to magnifying the picture.
Edit: In the first picture of your question the rays on the left side of the biconvex lens seem to run parallel to each other. This representation is often misleading since in reality the rays would converge and focus at one point (even if the point is far away.) For example look at this plan-convex lens:
In a plan-convex lens the rays on the left are coming parallel and may focus only at infinity. You can always construct such pictures yourself just remembering that the angles of rays with respect to the normal are larger in the medium with lower density (air). See for example the red ray in the picture above. By drawing the same picture for a bi-convex lens you would see that the rays would not remain parallel on the left side after leaving the lens, they would converge and focus in a single point similar to the right side of the lens.
In reality this is what you want to achieve for your farsighted glasses, magnifying glasses and so on. So you would use bi-convex lenses although the bending on both sides might be different. For nearsighted glasses you would rather use bi-concave lenses. Of course there are applications where plan-convex lenses would be preferred, e. g. to reduce unwanted optical effects (in telescopes and so on... see this question here).
If the concave lens was not there and the object was at a distance greater that its focal length the convex lens would form a real image.
Introducing a concave lens results in the incoming rays from the convex lens being refracted as shown in the diagram above.
The refracted rays are still convergent and so form an image $I$ at a distance $q_2$, your $d_v$, from the the concave lens.
After passing through the convex lens where the rays would have met is at a distance $p_2$, your $d_R$, from the concave lens and that can be thought of as a virtual object for the concave lens.
Best Answer
If you only have concave lenses, you won't be able to focus. If you remember your elementary optics, a concave lense has a negative focal length.
They can be utilized as part of a series of lenses. A concave eyepiece can avoid image inversion, which many people find irritating. A concave lense mounted just inside of a normal eyepiece can be used to increase magnification. These are called Barlow lenses.