jack44556677 - Whatever you want to call it, there is a huge group of people doing what they call "science" most of which is "settled" (f=ma, periodic table, RE, etc). The same ideas, equations, experiments all consistent with each other, all over the world in schools, engineering labs, etc. It works, chemistry, physics, etc produces working gadgets, airplanes, computers, internet, including google earth and nav equipment and gps. All matches, all works, all based on RE. There is a part of this which is blurry or controversial at the edge of what is known (string theory, quantum, big bang, etc). But that is not what we are talking about here, the science of refraction is well known and not controversial, the are many refraction calculators available.
Then there is Bob Knodel, seeing 15 degrees per hour on his ring laser gyroscope and refusing to accept RE, attributing it to "unknown forces". In FE, some say gravity does not exist, in the FAQ it says light bends (due to unknown forces with unknown equations) to explain the problem that the north star angle above the horizon matches latitude, but if the earth is a flat disk, the angles don't meet in the same place, see the diagram in the FAQ.
I call the collection of settled proven consistent science believed by consensus RE science. I use the phrase FE science to describe whatever changes, exceptions, misunderstandings, etc used to explain the gap between observed reality (north star/sextant/latitude) and the mismatch to FE geometry.
You got me on temperature, it is density, but the point is the same, both contribute, lessen with altitude, and both bend the light down. Search astral navigation refraction and you will find warnings that if you shoot a star near the horizon it will appear higher than it really is. This makes no sense, as the mountain appeared to sink into the water.
Let's get to the heart of the OP. Here is a diagram of where I was with the earth surface flat:
/\
/ \
/ \ _o__
/ \_________________________\ /
Here is what I saw:
/ \ _o__
/ \ ________________\ /
Per your explanation, the real position of the mountain would be, minus the part I didn't see:
/\
/ \
_o__
________________\ /
Please draw the light rays to show how they travel. Bear in mind that your ray is just one of many, there are rays going lower and higher, all directions, some crash into the ocean and some reach the eye if no object blocks it. In RE what blocks it is the crest of the curved surface of the ocean. In what I call FE science, the light bends however it needs to and disappears entirely without equation, explanation, or experiment.