Remove an unknown central gap from a ring measurement

A spherical glass surface forms a thin air gap above a plane. The central separation is unknown. At 600 nm, squared diameters of reflected dark rings three orders apart differ by 7.2 mm².

What is the spherical curvature radius?

Organize the givens & assumptions

ΔD² = 7.2 mm²
Order separation p = 3
λ₀ = 600 nm

Coherent monochromatic light, lossless ordinary dielectric interfaces, normal or explicitly stated incidence, and the two principal reflected beams. Higher reflections are neglected unless stated; phase extrema do not imply exact zero reflectance.

A $4.0\ \mathrm m$
B $0.25\ \mathrm m$
C $3.0\ \mathrm m$
D $1.0\ \mathrm m$

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