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That's not the issue
the issue is the diameter of the front lens element.
I have a 135mm f2.8 camera lens with a 50mm front element hence its light gathering ability is limited by its front lens element.
I also have a 100mm front lens element zoom that has a focal length of 120-300mm f2.8 So If I zoom to 135mm with the zoom, all things equal the zoom with the larger front lens element will extract more light then the 135 with the smaller front lens element.
so the light gathering is determined not so much by focal length but rather it's lens aperture size.
Focal length determines magnification.
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