I'm confused on this, even after researching:
Given 2 cameras- one full frame with 50mm lens, one Micro Four Thirds (2x crop factor) with 25mm lens, let's pretend the cameras are beside each other, ISO is set the same:
If both lenses are f2.8 for instance, does the MFT require double the exposure time to achieve the same exposure?
No. You can imagine the micro4/3 to simply cut out the middle of the image. If you had a 25mm lens on a full frame camera and exposed it properly, the middle part of the frame is part of what's exposed properly.
The definition of f-stop factors out the lens length so only f-stop and shutter speed determine the EV (exposure value). Let me make this clear: for calculating exposure, the f/stop means the same thing on any lens and format. That's what it is for: calculating the exposure. (Other effects vary with the physical aperture size and image size.)
A 50mm lens or a 25mm lens makes no difference to the EV, determined by f-stop and shutter speed. So the 25mm lens on the full frame would be the same exposure as the 50. So do that, and then crop out the center.
There are differences, but this is not among them,
Yes and No, if exposure is the same, smaller sensors give more image noise, if you crop factor ISO and changes exposure accordingly to compensate, then you will get the same picture but different exposure.
More detailed explanation in this video: