{
  "status": "new illustrative analytical study; no experimental measurements",
  "parameters": {
    "interfacial_tension_N_per_m": 0.03,
    "refractive_index_incident": 1.33,
    "refractive_index_transmitted": 1.5,
    "absolute_density_contrast_kg_per_m3": 200.0,
    "gravity_m_per_s2": 9.80665,
    "curvature_sweep_aperture_radius_m": 5e-05
  },
  "sign_convention": "Light travels left to right from medium 1 to medium 2. R is positive when the centre of curvature is to the right of the vertex. Pressure difference is p2-p1.",
  "equations": {
    "pressure": "2*gamma/R",
    "interface_power": "(n2-n1)/R",
    "bond": "abs(rho2-rho1)*g*a^2/gamma"
  },
  "limits": [
    "One spherical interface, not a complete lens or its focal length.",
    "Indices, density contrast and tension are hypothetical; no real liquid pair or wavelength is specified.",
    "Curvature sweep uses a/R<=0.05 and Bo=0.00016344416666666665; paraxial, nearly spherical illustrative regime.",
    "Bond curve is a scaling diagnostic, not a solved gravity-distorted surface. Bo much less than 1 supports capillary dominance but does not guarantee spherical shape; boundaries and wetting matter.",
    "The interface needs containment and pressure control. No unsupported liquid or weight cancellation is implied."
  ],
  "sources": [
    {
      "url": "https://openstax.org/books/university-physics-volume-3/pages/2-3-images-formed-by-refraction",
      "supports": "Paraxial refraction at a spherical interface"
    },
    {
      "url": "https://web.mit.edu/2.25/www/225_sect_11.html",
      "supports": "Young-Laplace spherical pressure jump and Bond number"
    },
    {
      "url": "https://ocw.mit.edu/courses/18-357-interfacial-phenomena-fall-2010/pages/lecture-notes/",
      "supports": "Surface tension and gravity scaling"
    }
  ],
  "checked_date": "2026-09-27"
}