Presets
Playback
Mirror
A liquid in rigid rotation settles into a perfect paraboloid whose focal length depends only on the spin rate.
Compare
Model checks
The science
What is modelled
In the frame rotating at ω, each liquid element feels gravity and the centrifugal force, so the free surface is an equipotential z = ω² r² / (2 g): an exact paraboloid with focal length f = g / (2 ω²). At 1.25 rad/s this is 3.14 m, the 3D page's reference value. Rays are traced with the law of reflection on the true surface normal.
Equations
- Surface slope:
dz/dr = ω² r / g. - Spin-up: the liquid approaches the drive speed on the Ekman time
∼ H / √(ν ω)(3x for the plot). - Coma of a paraboloid:
∼ 3 θ / (16 N²)radians, N = f / D.
Checks run in the page
- Integrated surface slope against the closed form.
- Exact ray tracing finds the focus at g/(2ω²).
- The traced coma length matches 3θ/(16N²) for a slow mirror.
Meridian-plane tracing only; ripple, vibration and the mercury vapour hazard are not modelled.
What to try
- Press Compare with rigid sphere: the sphere of the same curvature blurs on-axis rays (spherical aberration), the liquid paraboloid does not.
- Raise the off-axis angle until the green spot grows a one-sided tail (coma).
- Reduce the depth of the liquid and watch the spin-up get faster.