Kin hit it on the nose, but to summarize:
That Tokina lens is an EF mount, not an EF-S. The confusion is that its an EF mount (which we associate with FF incorrectly) that produces an aps-c sized image circle.
Its not a metabones speedbooster, so I dont get electronics, but I use the Tokina 11-16mm 2.8, Sigma 18-35mm f1.8 on my GH4 every day to great success.
Joe, it is helpful, but it seems this Dpreview article and the wikipedia page on Depth of field disagree with you that:
"Those same two lenses will also have the exact same depth of field at the same f stop. Depth of field does not change based on sensor size."
Same focal length for both formats:
Many small-format digital SLR camera systems allow using many of the same lenses on both full-frame and “cropped format” cameras. If, for the same focal length setting, the subject distance is adjusted to provide the same field of view at the subject, at the same f-number and final-image size, the smaller format has greater DOF, as with the “same picture” comparison above. If pictures are taken from the same distance using the same f-number, same focal length, and the final images are the same size, the smaller format has less DOF. If pictures taken from the same subject distance using the same focal length, are given the same enlargement, both final images will have the same DOF. The pictures from the two formats will differ because of the different angles of view. If the larger format is cropped to the captured area of the smaller format, the final images will have the same angle of view, have been given the same enlargement, and have the same DOF.
The blur disc size b is approximately equal to (please refer to the DoF Wikipedia article):
b = f ·ms / N = (f ·w2) / (N ·w1),
f is the focal length (the actual focal length, not the 35mm equivalent),
N is the aperture or f-number,
*******w2 is the sensor width,*******
w1 is the subject height in portrait orientation or picture width in landscape orientation and
ms = w2/w1 is the subject magnification of the lens.
Please note, that the equation above is only valid, if the background is sufficiently distant from the subject.
The absolute value of b does not tell much by itself, when comparing cameras with different sensor sizes. If we however compare b to the sensor size w2 we can estimate how big the blur disc size is compared to the total picture height (please refer to the photo above) and thus come to a definition of the strength of the background blur B:
B = b / w2
As per the above quote, these lenses are say, 10mm f4.
To match the depth of field/f stop on a 10mm f4 on a GH4 I would need to set the 6D to 22mm and f10.76.
This is confusing, the article (scroll down to Depth of Field) is where I did my research, and the question originally rose from switching from my trusty but soft Canon 6D to my new GH4 and hearing "f2 on the gh4 is more like f5.6 on the 6D in terms of depth of field"
When I use the included calculator, the result is skewed because I DO NOT mean that I adjust my focal length to give each camera the same Angle of View in this test, I'm proposing a Canon 6D and GH4 side by side with the same manual lens set to the same settings (aside from camera settings). However the result is the calculation I provided abov, that if I wanted the equivelant depth of field on both camers (as if I was matching A cam to B cam) I would need to set the 6D to f3.2 and the GH4 to f1.4 (I used T1.5 above, sorry).
"As an example calculation, if one wanted to reproduce the same perspective and depth of field on a full frame sensor as that attained using a 10 mm lens at f/11 on a camera with a 1.6X crop factor, one would need to use a 16 mm lens and an aperture of roughly f/18. Alternatively, if one used a 50 mm f/1.4 lens on a full frame sensor, this would produce a depth of field so shallow it would require an aperture of 0.9 on a camera with a 1.6X crop factor — not possible with consumer lenses!"
Also, you're right - focal lengths are expressed independently, the term I should have used is:
Are these expressed in 35mm equivalent "Angle of View" or 16mm equivalent "Angle of View."
Again, as per my other comment, everyone knows a 10mm on a 2.2x crop will "look" like (or have the equivalent "Angle of View") of a 22mm on a FF camera taking the same shot.
So again I ask, what's the "Angle of View" on this 10mm Kish when applied to a D16 camera? its certainly not 10mm FF equivalent, and I bet it'ss be a 26.9mm equivalent - which would mean my other comment that the depth of field will vastly increase is true as well once the crop factor is applied to the depth of field (f4 x 2.69).
You're right, Aperture values don't change on frame size, but my current Rokinon lenses at T1.5 are completely different depths of field on a 5d and on my GH4. So I'm asking if the same lens then put on a D16 is going to have an even WIDER depth of field?
i.e. the same lens at T1.5 on a 5D is X depth of field, which looks like "T1.5" to me, as I began on a FF. That lens on a GH4 (in 4k: 2.2x) has the equivalent depth of field of "T3.3" if matched on a FF, and then again on a D16 (2.69x) would have the equivalent depth of field of around an T4 setting on a FF.
So same question as before, but I understand the aperture size is a ratio of focal length to aperture diameter now. What I should have asked is this:
Is f4 on a D16 equivalent depth of field to f10.76 on a FF camera?
How would one ever use a D16 camera to achieve the shallow depth of field of even an f2.8 on a FF?