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I plan to buy a 12" or 14" dobson, the choice depending on my final budget and on the total weight of the instrument. I have several options for the primary mirror. I tried to find a formula that would give the acceptable range for mirror thickness depending on the diameter, maybe also on the material (BK7, pyrex, ....). Is there such a formula, or a back-of-the-enveloppe calculation, which could help me? If not, what do people go with usually (for these diameters, I mean)?

Thank you for your help.

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If you're buying the instrument, as opposed to making it from scratch, my advice is to worry about the overall quality, as opposed to a single parameter such as mirror thickness. It boils down to whether you trust the vendor or not.

In any case, there is no simple formula. You could run the PLOP simulator and try a few different scenarios, and see what the overall RMS error is in each case. But the values will vary very significantly. The main factors are:

  • the diameter / thickness ratio
  • the number of support points in the mirror cell
  • the relative positions of the support points

All of the above assumes a traditional mirror with a flat back, and a classic mirror cell with multiple-of-three support points. But the analysis gets even more complex if it's a cell mirror (the back is not flat), or a honeycomb structure (the back is flat but there are empty spaces in the volume of the mirror). And then there are conical mirrors, etc.

It's difficult to second-guess the vendor, especially if you've never built an instrument. Just read the reviews, ask other owners, try and gauge the overall build quality.

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Since you're just buiding a Dobsonian, you're not going for aspherics and in fact not going for particularly high-quality surface figure at all. In particular, there's no need to worry about orientation-dependent sag (not that this is a significant factor for such a small diameter in the first place).
It's not clear whether you are buying or fabbing the primary. If the latter, just choose a blank such that the center thickness, which is the thinnest spot on the mirror, is at least maybe 5 mm. You also haven't specified the focal length of your primary, which certainly figures into the thickness and mass calculations.

If you just like having fun :-) , buy the blank as thick as you like and use an end mill to lightweight it by removing most of the material from behind, leaving a "web" to support the figured surface.

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    $\begingroup$ As a Dobsonian user, I expect a high-quality paraboloid and would not trust a 30cm primary thinner than 15mm. $\endgroup$
    – Mike G
    Commented Apr 17, 2018 at 22:21
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    $\begingroup$ "Since you're just buiding a Dobsonian, you're not going for aspherics and in fact not going for particularly high-quality surface figure at all" - your idea of a dobsonian is a very peculiar one. Let me reassure you that some of the highest quality optics I've ever seen were installed in dobsonian telescopes. The best parabolic mirror I've made so far, at approx lambda/24 error, powers one of my telescopes, a dobsonian. You're probably thinking of cheap, mass produced toy dobsonians - but then every industry has its rock bottom. $\endgroup$
    – Florin Andrei
    Commented Apr 17, 2018 at 23:21
  • $\begingroup$ @FlorinAndrei Dobson himself was opposed to home-builders going nutso over primary figure. I fear his fundamental intent has been co-opted. $\endgroup$
    – Carl Witthoft
    Commented Apr 18, 2018 at 12:00
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    $\begingroup$ No need for fear. If you want dobs with bad optics, there's plenty of that stuff out there. Poor quality is always an option. We should celebrate the fact that high quality optics are now available with simple architectures such as dobs - it's the design with the highest performance / price ratio when done right. Also, John Dobson had his own share of strange ideas - he unfortunately believed in a lot of pseudo-science as related to cosmology. Finally, using a parabolic mirror in a large dob is not "going nutso" - spherical mirrors don't pass minimal performance criteria below f/8. $\endgroup$
    – Florin Andrei
    Commented Apr 18, 2018 at 20:56

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