The task is to design and build a 10X telescope. We don't want to spend a lot of money so we will buy singlet surplus lenses from Surplus Shed. I'll assume that you can find PVC pipe with the right diameter and figure out a way to mount the lenses.
The design that follows is an attempt to bridge the chasm between simple paraxial lens approximations and an OSLO simulation. The basic idea is to reach a plausible (paraxial) solution for two telescope designs and then to explore the limitations of each. Of course, before we begin, we need to know the actual numbers that characterize the lenses that we'll be using. This will take a bit of effort.
We know that the magnification $M$ is given by $$M={f_0 \over f_e},$$ where $f_o$ is the focal length of the objective and $f_e$ is the focal length of the eyepiece. Thus $M=10$ means that $$f_o=10 f_e$$ and, if both are positive then the distance $d$ between them should be $$d=f_o+f_e = 11 f_e.$$ Then if we are hoping for a telescope that is about a foot or 250mm long, then $f_e\approx$24mm and $f_o\approx$240mm. (A quick visit to Surplus Shed indicates that there are a handful of lenses that might suit our purpose. In fact, now we need to choose between an achromat (ACH), a double convex (DCX), a plano-convex (PCX), or a positive meniscus (PMN) shape.
Let's ignore the achromats and meniscus lenses for now. These are surplus lenses, we can't calculate the curvature of the surfaces.
If I rummage around on the Surplus Shed website then I might end up selecting the following lenses for the telescope. I opted for lenses with similar diameters to simplify mounting, even though the objective lens of a telescope usually has a larger diameter.
| Objective | Eyepiece | |||
|---|---|---|---|---|
| Focal Length | Diameter | Focal Length | Diameter | |
| Telescope | mm | mm | mm | mm |
| DCX | 235 | 20 | 23 | 20 |
| PCX | 222 | 15.9 | 22 | 16 |