Nota Bene

As stated in the first paragraph of our web page titled, Refraction Overview:

The purpose of the REFRACTION section is to (a) present to the reader, the underlying rationale for (spheroidal earth) geodesists using (alleged) tropo[spheric] refraction to explain (in many cases) the visibilty of subjects of observation that should otherwise be below the horizon (i.e., below and normal to the observer’s horizon line of sight), and (b) give the benefit of the doubt to the fallacious spheroidal earth paradigm by allowing readers to assume the impact of maximum tropo[spheric] refraction on their field observation calculations (see Introduction to the (Allegedly Spheroidal) Earth Calculators).

Such calculations are of paramount importance in REVEALING THE PLANAR LARGE-SCALE STRUCTURE OF THE EARTH’S SURFACE.

The decreasing density of the air with altitude in the lowest part of the atmo[sphere]¹ known as the tropo[sphere],^2,3 causes both optical and radar refraction. In this case, light is not propagating from a rarer, uniform medium to a denser, uniform medium, but is propagating through a non-uniform medium of increasing density in the direction of the earth’s surface. The following diagram illustrates the phenomenon:

Figure 1. Tropo[spheric] refraction and (so-called) sunrise on the (allegedly) spheroidal earth. (Note: Object sizes and distances—especially the Tropo[sphere]—have been scaled or exaggerated for illustrative purposes.)

In Figure 1, the Observer is located at a position on the (Allegedly) spheroidal earth having the Tropo[sphere] consisting of a non-uniform medium with a refractive index \(n(ρ)\), i.e., \(n\) is proportional to the air density \(ρ\), and hence, proportional to the height or altitude above mean sea level. The Horizon line is tangent to the observer’s position on the (alleged) spheroid. In this (currently accepted) model of the large-scale structure of the earth’s surface, the Apparent position of the sun during the period of Sunrise will be above the horizon while the Real position of the sun is still below the horizon. This is because (in said model) a light ray from the sun upon entering the tropo[sphere] curves toward the earth as it traverses the density gradient of the tropo[sphere]. As Figure 1 illustrates, the ray tangent to that curve at the observer’s position depicts the direction of the Apparent position of the sun.

— FINIS —

The historically established limits of optical refraction in the tropo[sphere] are discussed and summarized on our web page titled, Optical Refraction Curvature in the Tropo[Sphere]: The Optical Coefficient of Refraction (\(k\)).