Focal length of a rotating liquid mirror
= Focal length of a rotating liquid mirror
A liquid in steady rigid rotation has a free surface $z-z_0=\Omega^2r^2/(2g)$. Comparing with a paraboloid $z-z_0=r^2/(4f)$ gives $f=g/(2\Omega^2)$. The result follows from <hydrostatic equilibrium> in the rotating frame and is independent of <density>.