One person took experiment from Montenegro and with distance 201 km he saw clearly montains that are 1521 meters high. He was on 189 meters above the sea level. Official calculator says you cannot see less than 1811 meters from that distance. My question is: Why he saw the mountain? Is there any reference that can help me understand that. I'm a mathematician and I calculated that the radius of the Earth should be 7260 km for that to be possible. I need to understand which physical laws are related to this problem and please give me a reference.
These are selective quotes from the link:
The atmosphere of earth consists of different layers of air. Out of these some air layers are hot which have low densities, while the others are cold which have high densities. The hot layers of air behave as optically rarer medium for light rays, whereas the cold layers of air behave as optically denser medium for light rays. So, when an object emits light rays in the atmosphere, these light rays pass through the atmosphere having different air layers of different densities and get refracted by atmosphere. So, the refraction of light caused by the atmosphere of earth is called atmospheric refraction.
Looming is also an optical illusion which occurs usually in very cold regions. In looming, a distant object such as a ship moving in polar areas appears to be hanging in midair due to atmospheric refraction and the total internal reflection of light rays.
In Polar Regions the layers of air near the surface of earth are very cold and hence behave as optically denser medium. Whereas, the upper layers of air are comparatively warm and hence behave as optically rarer medium. Now, a ray of light coming from point S of ship goes from denser to rarer medium along the path SB and bends away from the normal, at every layer due to atmospheric refraction. But, at a particular layer, when the angle of incidence becomes greater than the critical angle, the total internal reflection occurs, and the totally reflected ray travels along the path BE and reaches the observer. As we have already discussed that we can see the light only in straight line path, so the reflected ray BE appears to be coming from the point S’ to the observer. Due to this, the observer sees a virtual and erect image of the ship at position S’, which is much above the actual position of the ship in the sea.
Per @John Forkosh, the refraction phenomena is called "looming":