How to calculate achievable flashlight beam divergence

Assuming a typical white-light flashlight with a parabolic reflector,
how do I calculate the achievable beam divergence?

I know it involves the source size, reflector size and focal ratio
but I can't find the formula.

Also, if you focus the light so the beam is initially convergent,
how do I calculate the achievable distance limit for a given beam
spot size, and how does that vary with different reflector sizes, f/ratios
and source sizes?

E.g, a common question is why can't a given flashlight create a
convergent beam that makes a small spot at a great distance.
Any formula to calculate this is appreciated.

-- Joe D.



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