A lighthouse's range is two numbers braided together. How far the light is bright enough to be seen (its luminous range, set by the lamp and the weather), and how far the curve of the earth even lets you see it (its geographic range, set by heights — including yours). The smaller one wins. Change where you stand and watch which one that is.
Geographic range uses the standard horizon formula with atmospheric refraction, d(km) ≈ 3.86·(√Hlight + √Heye) for heights in metres, then converted to nautical miles. Luminous range uses Allard's law with Koschmieder's 0.05 contrast threshold, calibrated so each light reaches exactly its charted nominal range at the standard 10 nm visibility. Lighthouse figures are from the infobox of each light's Wikipedia entry (focal height, nominal range). It is a teaching model, not a navigation tool.