Focal ratio has no effect on image brightness.

Aperture does. An image in a 6" f/5 and a 6" f/10 standing side by side at 50x will be the same, all conditions being equal.

6" is 6", 20" is 20" no matter what the focal length. Though you would have to use different focal length eyepieces to achieve 50x magnification.

The major difference is Width of field. Shorter focal length scopes of a given aperture will have a larger field of view than a longer focal length of the same aperture, which is what you may have tried to say.

>>You wrote,
>>On extended objects, the smaller the f ratio, >>the brighter the image.

Its more like: "On ALL objects, the smaller the f ratio the LARGER THE FIELD OF VIEW".

>>you wrote,
>>On point objects, the larger the aperture, the >>brighter the image.

Where it should be: "On ALL objects, the larger the aperture, the brighter the image".

You are correct in saying that the chances of a poorer figure on an optic are increased as the focal ratio lowers. It`s easier to produce a good F/8 mirror than a good f/5. But good f/5 mirrors are out there.

Jim