Overpowering Your Telescope.

We've all seen the advertisements for cheap toy telescopes advertising 400x Power! 700x! 10,000x POWER! And if you do a little reading you'll probably have found out these claims are hogwash. Yes, you can technically enlarge an image in a telescope by whatever factor you want if you have barlow lenses and short-focus eyepieces. But a telescope's maximum magnification is related to its aperture, and you can't do much better than 50x per inch or 2x per millimeter of aperture. So a 50mm toy telescope can't really get much better than 100x.

Now you and I both know that this is only a rule of thumb. I had to do some digging around to get to the bottom of the problem, of where "2x per mm" etc comes from, why that's the limit, and why some people claim to get 3x per millimeter or better when discussing very fine telescopes.

According to my research the problem is this.

There is no optical law for maximum magnification.

The way maximum magnification works is you're finding the magnification where objects at the resolution limit of your telescope are separated by the much more strict resolution limit of the human eye. By what I can only assume is a handy coincidence, this happens, for objects of 100% contrast, at about 1x per millimeter of aperture. (Of course it can never be exactly that, for different eyes have different resolutions) You might expect, then, that to go above that you'd be getting empty magnification. But this isn't so.

Above 1x per millimeter is also when the surface brightness of the image goes down enough that eyeball floaters become disturbingly noticeable, and it gets worse the higher power you go.

The human eye has a higher resolution for bright, contrasty objects than for dim, dull objects. When there is low contrast, there is lower resolution. So when viewing subtle differences in the brightness of cloud belts on Jupiter or ring gaps around Saturn or albedo features on Mars, it can be helpful to make the image larger, even as the true resolution remains the same. This is where 2x per mm comes from--at about that point, subtle details on planets cease to get any better resolved.

People claiming 3x per mm probably get there from a combination of having a refractor with no central obstruction and apochromatic performance, sharp optics throughout the light path, and differences in their own eye.

Above 200x, a different mechanism becomes important--atmospheric seeing conditions, or thermals and turbulent air which causes an image of a planet to blur, wobble, and boil, or a star to twinkle. On excellent nights, you can get past 400x fine, on average nights, 200x is near the limit, and on terrible nights, 100x might be difficult. This also means that, dependent on seeing, the resolution of a telescope does not go up linearly with aperture anymore.

Essentially, 50x per inch or 2x per millimeter is a good place to start, and when choosing a high power eyepiece, 1x to 1.5x is a safe place to start, working up to 2x per mm if you're satisfied. But going over 2x is not always useless.

For my part, on a night of exceptional seeing, Mars was still very nice and clear at 400x in a 6" dob, though there were definitely diminishing returns compared to 200x to 300x. I almost always observe at no more than 200x.

Splitting double stars which are close to the limit of resolution  can still reward overpowering, to get the apparent star disks ("airy disks") larger and easier to see.

One other point--if your mount shakes and wobbles at the lightest touch, and using your focuser sends you scope into seconds long shakes, getting to maximum power practically may be impossible. Since the toy refractors advertising 10 quadrillion million billion power tend to have the worst mounts, that makes their googolplex * tree(graham's number) magnifications all the more unlikely. (can you tell that I'm a little salty about this form of advertising?)