Maximal resolution based on dawes limit/rayleigh...?

Question

I've read on different sites how atmospheric conditions limit telescopes' maximal performance/magnification based on Rayleigh criterion.
In telescopes' manuals are given 2 resolutions based on both standards.
They are given in arc seconds.So my question is:
If I know the Dawes limit ot the other can I calculate the maximal magnification based on it?I have resolution based on aperture and magnification based on aperture but such a "max reasonable magnification" is no good to me because that "reasonable" is relative.I want magnification based on resolution(arc seconds).How to calculate?

Answer 1

While it is subjective, magnifying the image so that the smallest resolvable details are about 3.5 to 4 arcminutes large is about the best you can hope for.

So, for an 8" scope, the dawes resolution limit is 4.56 / 8 = 0.57 arc seconds. 4 arcminutes is 240 arcseconds, so 240 / 0.57 = about 420x.

Answer 2

The Rayleigh and Dawes criteria are based on diffraction limits of the optics, which depends on the aperture. These resolution limits are most directly applicable to splitting identical double stars. Maximum useful magnification is a subjective limit, and depends in part on the acuity of your eye. The assumption, based on empirical evidence, is that once the image is magnified to the point that its blur radius is 4 arc-minutes, the eye will not benefit from further magnification. You can calculate the maximum useful magnification based on this criterion by dividing the resolution in arc-seconds into 240 (240" = 4').

In practice, only certain high-resolution targets (e.g. double stars, the moon, Saturn) will withstand the maximum theoretical magnification; most other objects will do best at lower magnifications depending on their size and contrast. You just have to try different eyepieces to see what works best.

Atmospheric conditions are a separate issue. Generally, larger apertures are relatively more sensitive to bad seeing because there is more variation over a larger radius. As a result, maximum magnification is often limited to 300x, and sometimes less, regardless of aperture.

Poorer optical quality will also suffer more as they put more light in the diffraction rings, which are smeared by bad seeing.

Answer 3

Very Good question!!
The final usable magnification is actually determined by the human eye. The human eye's resolution limit for detection of a bright object is about one arcminute.
The size of the image of a point source is determined by the formula " a = 5.45 / D"
where a is the size of the star's disc in arc-seconds and D is the objective's diameter in inches. For example, in a 3" Telescope, the central disc of the star image is nearly 2 arcseconds wide. So, only about 30X magnification is needed to make it clearly visible to the eye.
But it is a whole different story for very dim objects such as are common in observing deep space objects. Now, the eyes resolution is only 1800 arcseconds when the object is very dim.
The magnification limit is found by dividing the eye resolution by the Telescope resolution ( from the formula above).The absolute limit is 330X per inch of objective diameter. In other words, there really is no upper limit.
The practical limit is set by the atmosphere.
Normal seeing conditions for 99% of us are in the region of 2 to 3 arcseconds ON A GOOD DAY!!!. Most of the time it is 3 t0 5 arcseconds. The figures of 50X or 60X per inch are good rules of thumb. But on exceptional nights they are easily exceeded, especiallly in a refractor which has no central obstruction to reduce contrast.
On those nights my 6" Refractor will blow the pants off my 10" Reflector when looking at minute planetary detail. I have had this Refractor as high as 125X per inch. But those nights come along maybe a handfull of times a year.
The larger the objective diameter, the more the atmosphere will determine your maximum magnification. For practical purposes, 600X is the upper limit, regardless of the size of the Telescope.
If you read some of the books about the old observers like Herschel etc., these guys used magnifications of 1000X and more routinely. With their terrible optics that must have been nothing but a large blur. I have tried it with modern optics and the images are absolutely horrible.
I hope this helped a little.
BTW, there are slight differences of opinion amongst the optical experts as to the exact constant to use. Some of these debates are funny to read with these guys stopping barely short of calling each other names.
They can't even reach a consensus on the size of the fully dialated human pupil, which determines the faintest stars visible to the naked eye.

Adolph