William, you can’t assume you can use any lens designed for APS-C coverage on the full sensor of the BMPCC4K. You need to know the image circle of the specific lens.
When lens manufacturers refer to the suitability of their lenses for a stills camera, they often only consider the typical sensor size of three cameras:
A) 135 film or ‘full frame’ lenses which usually have an image circle greater than 43.3mm, ‘crop factor’ 1.0; such as Canon EF ir Nikon FX
B) APS-C Canon or Nikon DX, crops 1.6x or 1.53x
C) mFT, horizontal crop 2.08x; BMPCC4K 1.9x (or 2.02x for UHD).
These broad generalizations of lenses designed for these three options make sense when you think about the traditionally limited choices available for stills photography—now there are more sensor choices smaller than mFT.
But they’re not helpful when considering cinematography which has used different traditional ‘sensors’ such as Super 35 or Academy 35 and Super 16. There are about a hundred different sensor sizes for cinema cameras going back well over a hundred years of shooting film with some modern cinema cameras shooting with much larger sensors than these three.
The BMPCC was quite a small sensor in a cinema camera when introduced in 2013. With a horizontal crop of 2.88x. The Metabones SpeedBooster for BMPCC had a focal reducer factor of 0.58x and was designed to use APS-C lenses. 0.58x2.88x = 1.67x.
So APS-C lenses could work with the Pocket and SpeedBooster as long as the rest of the lens didn’t project into the glass of the SpeedBooster (which eliminates some lenses but others were fine with a small modification to the rear housing). At least it was a simple solution and you didn’t have to think about the actual image circle of the APS-C lens.
Similarly, the 0.64x SpeedBooster for BMCC could use Super 35 lenses. 0.64x2.28x = 1.46x and that’s a bit smaller than Super 35 so all good. Some APS-C stills lenses actually had image circled large enough to cover Super 35 so it was possible to use them with the SpeedBooster; an example is the very good Rokinon 16mm. Both the 16mm and 10mm are sold as APS-C lenses. But the image circle of the 16mm just covers Super 35 whereas the 10mm image circle is truly limited for use on APS-C sensors only.
Now getting to the BMPCC4K with its non-traditional width of 18.96mm versus the standard mFT 17.3mm, the math is potentially trickier. But the active sensor area of the BMPCC4K only has a height of 10mm so the diagonal of the sensor is very close to a traditional mFT diagonal. To be safe, I still figure with the crop factor of the sensor as 1.9x but calling it 2x is fine too as all lenses designed for mFT cameras will cover the BMPCC4K.
Now when you want to add a SpeedBooster, your options are harder to predict. On paper the 0.64x SpeedBooster XL excludes all APS-C lenses. 0.64x1.9x = 1.22x. Most lenses designed for Super 35 will vignette badly. So XL requires you use ‘full frame’ 135 film lenses on the BMPCC4K.
The SpeedBooster Ultra 0.71x may or may not work subject to the actual image circle of the lens. 0.71x1.9x = 1.35x. 0.71x2x = 1.42x. I expect all Super 35 lenses may cover this. APS-H stills lenses will too. But APS-C lens will not work. All ‘full frame’ lenses will work.
A long post, but I thought you might want a broader understanding. Hopefully Denny with chime in with the short answer!