Hey guys, read what I wrote. I said f1.8 on crop is brighter than f2.8 on full frame when both have the same shutter speed and ISO, then you start telling me that I'm wrong to say FF is brighter when they're both at f1.8 and the same shutter speed and ISO. I didn't say that, so what gives? I went to great lengths to explain that at the same aperture, shutter speed and ISO, they both expose the same due to the different light gathering of the format being compensated for by the amplifiers being set different. If you can look past that same exposure settings between formats and start to use the higher ISO's with lower noise levels this lower amplification of FF rewards you with, you'll find the true nature of the light gathering of FF lenses on FF sensors.
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80mm 1.0x [FF] @ f/2 aperture = 40mm diam pupil
50mm 1.6x [APSC] @ f/2 aperture = 25mm diam pupil
He is not.
In optics, the f-number (sometimes called focal ratio, f-ratio, f-stop, or relative aperture[1]) of an optical system is the ratio of the lens's focal length to the diameter of the entrance pupil.
You can't compare different focal lenghts. A 50mm is a 50mm both on crop and FF. However, being the former smaller, you crop the edges to a degree which would be equivalent to the angle of view of a 80mm on FF. This is a quick way to grasp the concept, but it's not exact in a way that you can make calculations.
Thanks indigo9, nice explanation. Albi86 - a 1.6x crop camera crops the FoV, so to get the same framing, you have to use a different focal length. This 18-35 crop lens is a rival to a 24-70 on FF, not a 16-35. 80mm on FF does frame the same as 50mm on crop - and if they both have the same aperture, the 80mm lens has to have a bigger entrance pupil.
And using indigo9's simple (yet still misunderstood) explanation, to compare the 18-35/1.8 to the 24-70/2.8 on FF we'd need to set them both to a focal length to give an equal field of view. So for the sake of this example, lets use the long end of the Sigma's zoom - set the 18-35/1.8 to 35mm, which is equivalent of 56mm on the 24-70. We get the following:
56mm 1.0x [FF] @ f/2.8 aperture = 20mm diam pupil
35mm 1.6x [APSC] @ f/1.8 aperture = 19.4mm diam pupil
So, vaguely less light gathering from the new Sigma lens, as well as a vaguely wider DoF.
Neuro - do you want to chime in at this point? People respect your opinion

And as I said before though, this is a very interesting lens, and its a great option for crop sensor users - while it lets in slightly less light and has a narrower zoom range than the 24-70/2.8, its a great alternative to moving to a more expensive body, and the internal zoom is a great feature for a normal lens.