Mig see my website for my guide setup.
I'm not a mathematician, so I'm not going to try and explain the maths.

I wouldn't even know where to start.
But it's all to do with image scale.
Take an 80mm scope at f/5 into a 100x100 pixel 10um chip...
Image FOV will be 8.6' x 8.6'
That same chip at f/10 will be 4.3' x 4.3' It's all to do with image scale. Now it's a little more complicated than that as often imaging scopes are different aperture from guiding scopes. The 1.5x f/ratio is simply a guideline..
But let's look at my setup with our fictitious 100x100pixel 10um chip..
Guidescope 80mm @ f/5 : Image size = 8.6' x 8.6'
Imagescope 200mm @ f/10 : Image size = 1.7' x 1.7'
So actually to get pixel for pixel correction I really need my guiding scope to be f/25 or 2.5x that of the imaging scope.
Right that's probably lost everyone... or put them to sleep

Including me! I was probably a little optimistic in my previous post. My setup is worse than I thought!! I'd just never worked it out before!.. But as I siad, I don't care much for rules..
Cheers