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A magnitude 8 star is about 2.5 times as bright as a magnitude 9 star, a magnitude 9 star is about 2.5 times as bright as a magnitude 10 star etc.
So if your telescope aperture increases in area by 2.5 you will see a magnitude fainter. The following list compares aperture size and the estimated limiting magnitude in an outer-urban area affected by skyglow.
2.4 inch, Vmag 10
4 inch, Vmag 11
6 inch, Vmag 12
10 inch, Vmag 13
16 inch, Vmag 14
In each case the aperture size has increased in area by roughly 2.5.
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