Does 50/1.4 DOF = 100/2.8 DOF?

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Forgive me if this is a dumb question. But I was just shooting this week with a 100/2.8 SLR lens. And wide open, its depth of field seemed identical to what I would get if I were shooting wide open with a 50/1.4, but standing closer to my subjects. What's the physics at work here?
 
Hard to believe for those Noctilux owners, but pretty much

50/1.0 DOF = 100/2.8 DOF

At the same distance.

If the distance is not constant, all bets are open. For example:

50/1.4 DOF (1m) = 100/2.8 DOF (1.4m).

Roland.
 
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From a given camera position it's a function of lens (aperture) diameter, not f/stop.

A 50mm f/1 lens has a diameter of 50mm. That same diameter would give you f/2 on a 100mm lens, f/4 on a 200 lens, etc.
 
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