Help me calculate/understand the physics of aperture, DOF and BG blur -

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Help me calculate/understand the physics of aperture, DOF and BG blur -
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So for anybody offended by "equivalence", or technical discussion of photography physics, this is your warning before you jump in. As for the thread subject, im looking to calculate aperture (entrance pupil) after a few factors are included. So i will start off with a few defining points.

First off, as i understand it, for any particular lens, the maximum BG blur is defined by the entrance pupil diameter (physical aperture), so a 25mm f/1 will have less BG blur than a 100mm f/2, simply because it only has 25mm of aperture vs 50mm. Given BG distance is far enough to achieve maximum blur, the larger the entrance pupil, the more blur you get.

F stop on the other hand, dictates that per given framing, the DOF will go from sharp to blurry faster with the smaller ratio. So that 25mm f/1 may not blur as much at it's max, but it will go from sharp to blurry faster at the focal plane due to the faster F ratio. Ok so pretty simple so far right?

Now what if i add a speed booster to that 100mm f/2 for example. By the math of the more common boosters, it turns into (equivalently) a 71mm f/1.4 within the new image circle. If im trying to calculate the entrance pupil, do i still use the physical lens numbers, or do i use the boosted numbers?

There shouldn't be much difference but there will be some. So a 100mm f/2 is a simple 50mm of aperture, but a 71mm f/1.4 is 50.7. It's a small difference but which one is the legitimate entrance pupil? I can see a case for each but im gonna guess it's #2, since the entrance pupil is technically how big the aperture "looks" through the elements, and adding a booster will change that optical quality.

Anybody know the actual physics behind this?

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