Imagine two perfectly level beams mounted on two spirit levels and aimed at each other across a surface separation "s". Here, “level” means tangent to their local gravity field. On a curved Earth, the two local horizontals are not parallel — they differ by the central angle α = s/R′ — so the rays cross above the midpoint. On an flat earth, perfectly level beams would remain parallel and would not cross; any deviation would be due to refraction or misalignment and very small. Refraction is modeled with an effective radius R′ = R/(1 − k).
Notes: Distances are along the surface (arc length). For vacuum, set k = 0. A common near‑ground standard is k ≈ 0.13 (R′ ≈ 1.149R). The surveying “7/6 Earth” model corresponds to k ≈ 1/7.
Formulas: α = s/R′; h(exact) = R′(sec(α/2) − 1); small‑angle approx: h ≈ s²/(8R′); drop(d) ≈ d²/(2R′).