With regard to DOF and teleconverters...

I was sitting here trying to calculate whether you'd get a shallower DOF using a telephoto (100-300 f/4, for argument's sake) at 300mm f/4 or with a 1.4x making it 420mm f/5.6... when I realised I'd been going about it all wrong. It's an effective f/5.6 - the darkening there is not a function of aperture at all, thus should have no impact on DOF in itself. Thus the teleconverter is always going to result in narrower DOF.

So my thinking now is that to calculate the correct DOF for a 300mm f/4 lens with a 1.4x teleconverter on is to use 420mm f/4 as your figures?

Sort of, yes, and no.
It's not just the "effective" f ratio, it's the real f ratio. f has changed as a result of using the TC.
Use of a TC will always result in a narrower DoF.
Use 420 mm and f/5.6 as your figures. These are the optical parameters of the compound lens produced by adding a TC.

P.S.
Or so I see it. I'm always happy to be proven wrong

Jim G,
That theory seems to work on Julian's Lens Calculator

Jim G wrote in post #6383969
I was sitting here trying to calculate whether you'd get a shallower DOF using a telephoto (100-300 f/4, for argument's sake) at 300mm f/4 or with a 1.4x making it 420mm f/5.6... when I realised I'd been going about it all wrong. It's an effective f/5.6 - the darkening there is not a function of aperture at all, thus should have no impact on DOF in itself. Thus the teleconverter is always going to result in narrower DOF.

It still is a function of aperture. Aperture is defined as (front) lens diameter in mm divided by focal length in mm. Adding a 1.4X converter means you are multiplying the total focal length of the lens by 1.4X, and hence decreasing the maximum aperture by 1.4X, IOW, a decrease by 1 f-stop. This is also why it gets darker in your viewfinder.

No. You need to use 420 F/5.6 in this example. See above.

HTH, kind regards, Wim