Telescope resolution

We have the following common estimations of telescope resolution, the first one is called Dawes's Limit, which is probably the best known among amateur astronomer, it's more like an empirical formula:

Resolution in arc sec = 116 divided by aperture in mm

And the second one is Rayleigh Criterion, the formula is:

Resolution in arc sec = 140 divided by aperture in mm

Finally, we have another one called Sparrow limit:

Resolution in arc sec = 70 divided by aperture in mm

All the above is estimated with different assumptions, for example, they assume green light (~550nm) and they're for point light source. That said, the above probably couldn't be reached with atmosphere distortion like seeing and poor transparency - constrast will also affects the resolution. For example, you can resolve two dots with completely different color like red and yellow, but if they're both very similar in color, like both are red (zero contrast), you will not be able to resolve them at all.

Despite they're for point light source, they could be a nice approximation for extended objects. Okay, let's give an example again using the 33 arc min sun as our target. Yes, it's not point light source, but we just use the above as estimation. Suppose we use Dawes's limit, and we have a 40mm filter like my Solarmax 40:

Resolution in arc sec = 116/40 = 2.9 arc sec

The sun is 33 arc min in size, and we will want at least two pixels to cover any resolvable feature by sampling theory, so we have a sun of:

33 * 60 / 2.9 * 2 = 1365.5 pixels

And therefore, in order to get what a 40mm can deliver, we will want to create solar image with above size, by using a particular combination of CCD chip and telescope focal length.