>>3461491>So would you have to use a faster shutter speed in order to get the same image wide open as on a full frame camera?Yes. With a one-stop speedbooster, the lens' maximum aperture will pretty much legitimately be one stop faster. So f/2 instead of f/2.8.
>>3461492>And to answer your question about depth of field; It remains unchanged since it is only dependent on the ratio of the diameter of the aperture to focal length and a speed booster does not change that at all.Kiiiiinda. There's a way to read your statement that's technically correct, but the way you're saying it is misleading so I think you might be wrong about it.
Effectively, what a speed booster does is that it keeps your entrance pupil size the same (i.e., the actual physical aperture opening) while shrinking your focal length. So the f/ in the f/stop calculation gets smaller, entrance pupil stays the same, and so you legitimately have a wider-aperture lens system on your camera.
Another way to look at it is, the lens is projecting a certain image. The speed booster takes the output of the lens and reduces it a bit but doesn't fundamentally change the image that was coming out of the native lens groups, so the depth of field that was happening in the light that came out of there is happening the same when the light goes through the speedbooster.
The end result being that a 50/1.4 on a full frame camera and a 50/1.4 on a crop-sensor camera with a speed booster will give you the same depth of field, just as if you were using a 35mm f/1.0 on the crop camera. Because, effectively, you ARE using a 35mm f/1.0 on the crop camera.
Now, there are a lot of little caveats in there (e.g., crop factor usually isn't a perfect sqrt(2), speed boosters usually aren't a perfect one stop, the circle of confusion is a little different when blowing up an image from a smaller sensor onto a larger one, etc), but MORE OR LESS, a speed booster gives you the same depth of field as the lens on the larger format.