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Hi Roger
Generally light increases by the ratio of surface areas, or vary simply by the square of the ratio of aperture size. An 8" scope then shows objects 4 times brighter than a 4" . The ratio of sky background brightness to object indeed stays the same - those are properties of the sky not the telescope. The situation with CCD detectors is somewhat more complex and involves pixel size and readout noise .
The f ratio of the telescope is completely irrelevant to the discussion on brightness of objects between different telescopes . Only the aperture and exit pupil used are relevant.
Perceived brightness of point sources may not be as consistent as large apertures will often have their light spread out into a larger disc by the seeing and therefore not show as intense a point source as they are capable of.
If you spread the light of star into a disc twice the size then it becomes somewhat fainter - the star image is usually some kind of Gaussian curve so its not that simple , but its been obvious to me many times that smaller high quality optics can reach a similar magnitude limit visually as poor quality larger ones, although the smaller scope may not have the same ability on extended objects.
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