Posted 12 September 2015 - 03:10 PM
I will use some simpler numbers for demonstration.
Some basics that you know or can easily figure out:
One my LX 70 8 inch reflector, it has a 1000 mm focal length and a diameter of 200 mm. The focal length of the eyepiece I want to use is 5 mm, then the magnification is 1000 divided by 5 or 200X.
The magnification is 200 and my diameter of the telescope is 200 mm, therefore the ratio of magnification to diameter is 1.0. If I stick a 2X Barlow in this system, then the magnification is doubled to 400X. 400x divided by the 200 mm is 2.0.
For 200X magnification on this scope, the size of the image as it goes through the pupil of my eye is decreased from the size of the primary mirror by whatever the magnification is. Therefore 200 divided by 200 is 1.0 mm.
Now for some other items:
Rod Mollise, in his book on Urban Astronomy, talks about a pupil diameter that seems to be the best for contrast with light pollution as being about 1.25. For larger scopes, I have found his number to be a reasonable guide for seeing things like nebula. For my scope, a pupil diameter of 1.25 translates into 200 mm mirror diameter divided by the 1.25 mm pupil diameter or 160X. To translate that into something I can apply to a different sized scope, I normally think of magnification divided by the mirror diameter. Therefore, the number I can carry to another scope is 160X divided by the 200 mm of my LX 70 8R or 0.8.
If I wanted to take that to my Polaris 130 to see what magnification would be best for contrast from my back yard, then I can multiply the 130 mm diameter of the Polaris by 0.8, which gives me a magnification of 0.8 times 130 or 104X. If I want to know what eyepiece to use to get that, I divide the focal length of the Polaris 130, which is 650, by the magnification, 104X, which give me 6.25 mm for the eyepiece focal length.
For observing most things from my back yard, there seems to be a practical atmospheric limit at my elevation for my LX 70 8R of about 400X. Divide that number by the 200 mm diameter and I get a ratio of 2.0. I know many people that use that same 400X limit as about as high as one can go with just about any scope, unless you go to high elevations. Smaller scopes may not be able to reach 400X, but larger ones seem to be limited more by atmospheric disturbance than small or medium sized ones, like my 8 inch reflector. The larger ones have more light gathering power, which allows them to see dimmer objects, but the magnification seems to be limited more for them.
For double star work, the 400X limit on my 8 inch scopes seems to apply to some extent, but I find I can go beyond that if the scope is perfectly collimated and either weather conditions are perfect or I am willing to be patient and look for those momentary glimpses when a good image shows up out of the chaotic wiggles. Even though I have gone higher than 600X with the 8 inch reflector to see what happened and I was able to see things as high as 888X, I really do not see anything more or better than I do at 600X, which is 600X divided by 200 mm diameter of the scope or a ratio of 3.0.
Another way to think about that is how big is the image as it passes through the lens of your eye. With my LX 70 8R, that 1.0 ratio we talked about is 1 mm, the 0.8 ratio I talked about is 1.25 mm. I have heard some people state that the optimum diameter that our eyes are designed for is a pupil diameter someplace between 1 and 2 mm, but I have no confirmation of that from an authoritative source. It probably depends on the individual a lot. The 2.0 ratio that I talked about as a reasonable limit for most things, like planets, has a pupil diameter going through my eye lens of 0.5 mm and the 3.0 ratio as a practical top limit for double star work has a pupil diamter of one-third of a mm. If you think about it, just about any imperfection in your eye that is located in the wrong place could affect an image that is only a third of a mm across.
Well, that is probably enough rambling. Please pick out the parts that mean something.
Sky Hunters' Haven Observatory,
Broken Arrow, Oklahoma