Expectation:

Simulation I found:

Equation I used:

Now, the simulation isn't completely accurate. I can't change the grid size so I've multiplied all measurements by 10 and the lens is only 26 scaled mm instead of 27, but the difference is quite drastic between the formula and raytracing.

At least I'm correct in thinking that if there is a F-4mm lens 26mm away from a F30 lens (in other words, 4mm away from the F30's focal point, the light will be parallel:

However, I'm getting what looks to be F33 for what should be closer to 51!

I think... I think what's gone wrong is this assumption:

In terms of a physical fresnel lens, yeah sure maybe it's thin, but the fresnel is essentially approximating a lens that looks like this:

So what if I trace it backwards from the double concave lenses?

Okay... alright...

The beam is too large for the 32mm lens but let's not worry about that for now.

Well that failed. Oh right, the distance between lenses moved. Ok, what if I calculate a few permutations?

Ok now the two values match up after around 5 iterations... and the simulation still doesn't.

Okay... the focal point is about -6mm at a distance of 6mm... hmmm.

And the equation for thick lenses isn't even that different:

So I'm quite lost as to where the issue could be.

Well if I move the lenses so that I do get a parallel beam, I get approx F40 when the first lens is at 24mm from the fresnel. And the calculation I've got is about twice that. Coincidence? Yeah probably:

Effective focal length is only 48mm and 2*48 does not equal 120.