Measure index without knowing the fringe order

A normal-incidence thickness scan under 640 nm light shows successive reflected maxima separated by 200 nm in film thickness. The interface phase offset stays fixed.

What film refractive index follows from the spacing?

Organize the givens & assumptions

λ₀ = 640 nm
Adjacent-maximum thickness spacing = 200 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 $2.00$
B $1.60$
C $3.20$
D $0.80$

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