Anyone taking this seriously needs to go back and do physics at...

Anyone taking this seriously needs to go back and do physics at high school.

Its called atmospheric refraction. The earths atmosphere bends the light due to temperature, pressure and moisture variations.

Terrestrial refraction, sometimes called geodetic refraction, deals with the apparent angular position and measured distance of terrestrial bodies. It is of special concern for the production of precise maps and surveys.^[24][25] Since the line of sight in terrestrial refraction passes near the earth's surface, the magnitude of refraction depends chiefly on the temperature gradient near the ground, which varies widely at different times of day, seasons of the year, the nature of the terrain, the state of the weather, and other factors.^[26]

As a common approximation, terrestrial refraction is considered as a constant bending of the ray of light or line of sight, in which the ray can be considered as describing a circular path. A common measure of refraction is the coefficient of refraction. Unfortunately there are two different definitions of this coefficient. One is the ratio of the radius of the Earth to the radius of the line of sight,^[27] the other is the ratio of the angle that the line of sight subtends at the center of the Earth to the angle of refraction measured at the observer.^[28] Since the latter definition only measures the bending of the ray at one end of the line of sight, it is one half the value of the former definition.

The coefficient of refraction is directly related to the local vertical temperature gradient and the atmospheric temperature and pressure. The larger version of the coefficient k, measuring the ratio of the radius of the Earth to the radius of the line of sight, is given by:^[27]

{\displaystyle k=503{\frac {P}{T^{2}}}\left(0.0343+{\frac {dT}{dh}}\right),}

where temperature T is given in kelvins, pressure P in millibars, and height h in meters. The angle of refraction increases with the coefficient of refraction and with the length of the line of sight.

Although the straight line from your eye to a distant mountain might be blocked by a closer hill, the ray may curve enough to make the distant peak visible. A convenient method to analyze the effect of refraction on visibility is to consider an increased effective radius of the Earth R_eff, given by^[11]

{\displaystyle R_{\text{eff}}={\frac {R}{1-k}},}

where R is the radius of the Earth and k is the coefficient of refraction. Under this model the ray can be considered a straight line on an Earth of increased radius.

The curvature of the refracted ray in arc seconds per meter can be computed using the relationship^[29]

{\displaystyle {\frac {1}{\sigma }}=16.3{\frac {P}{T^{2}}}\left(0.0342+{\frac {dT}{dh}}\right)\cos \beta }

where 1/σ is the curvature of the ray in arcsec per meter, P is the pressure in millibars, T is the temperature in kelvins, and β is the angle of the ray to the horizontal. Multiplying half the curvature by the length of the ray path gives the angle of refraction at the observer. For a line of sight near the horizon cos β differs little from unity and can be ignored. This yields

{\displaystyle \Omega =8.15{\frac {LP}{T^{2}}}\left(0.0342+{\frac {dT}{dh}}\right),}

where L is the length of the line of sight in meters and Ω is the refraction at the observer measured in arc seconds.