Could you say where does it diverge?

Yes, have a look at:

The "chart and equation", are however, an excellent approximation to the drop of the surface of the

below the local horizon.

Have a look at Walter Bislin's **Eight Inches per Miles squared Formula Derivation** which shows that the formula is within 0.1% up to almost 500 miles!

This formula is an approximation: until 550 km or 342 mi the error stays within ∓0.032%. Until 800 km or 497 mi the error is less than 0.1%.

It is a very good approximation to the

*geometric drop* right out to 500 miles.

The 8"/mile squared is not, however, a good estimate of the

*hidden height* of a distant object unless allowance is made for both the

*height of the observer* and

*refraction*.

*Refraction* is sometimes a severe effect. See these two photos from the same location and the same claimed height above sea-level:

The difference is simply from atmospheric effects - looming and towering.

Observations like this, close to the surface of water or ice, often give excess refraction but not too often this severe.