Purpose

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.¹

Assuming \(K=1\) (meaning w/o tropo[spheric] refraction),² EQUATION A-1, EQUATION A-2, and EQUATION B definitively portray the basic visibility limitations of the currently accepted, geometrical model of the large-scale structure of the earth’s surface.³ In consideration of the existing heliocentric paradigm, the visibility impacts of phenomena otherwise within the realm of air mass and water vapour limit extreme, long-distance observations.⁴ On the other hand, the (so-called) atmo[sphere] refracts light, ostensibly enabling the observation of islands, promontories, and structures from distances in excess of what would otherwise be determined exclusively from geometry using (with \(K=1\)) EQUATION A-1, EQUATION A-2, and EQUATION B. Hence, the correct value for \(K>1\) must be determined for use with EQUATION A-1, EQUATION A-2, and EQUATION B. For the purposes of this website, the essential visibility issue in terms of the (so-called) tropo[sphere] is refraction. Water vapour or humidity is briefly considered only to the extent that it impacts refraction.⁵

Whereas the phenomenon of tropo[spheric] refraction (allegedly) extends the horizon of the (allegedly) spheroidal earth, thereby ostensibly reducing the (alleged) distance \(d_{n(K)}\)⁶ of a subject of observation (i.e., either (I) the highest elevation of the island, promontory, or mountain, or the top of the marine or shoreline structure, or marine vessel, or the top of the land structure at elevation, or (II) the aircraft or radio frequency transmitter) below the (alleged) spheroidal earth horizon—more specifically, (allegedly) below and normal to the observer’s or optical instrument’s (alleged) horizon line of sight, the REFRACTION section establishes reasonable upper limits for tropo[spheric] optical and radar (or radio frequency) refraction and analytically incorporates such upper limits in a manner that can be applied to all observations, thereby erring on the side of the currently accepted (spheroidal) model of the large-scale structure of the earth’s surface. This approach will serve to categorically preclude anyone from using the refraction argument to dismiss observations that are otherwise impossible on the (allegedly) spheroidal earth.

Summary

Basic and tropo[spheric] refraction are described in the Snell’s Law of Refraction and Tropo[spheric] Refraction subsections respectively. The Optical Refraction Curvature in the Tropo[sphere] subsection establishes the upper limit for tropo[spheric] optical refraction in terms of a fraction of the (alleged) curvature of the earth. The Radar (or RF) Refraction Curvature in the Trops[sphere] subsection provides a brief review of the effective earth radius model developed in respect of tropo[spheric] radar (or RF) refraction. Finally, the Effective Earth Radii for Radar (or RF) and Optical Refraction in the Tropo[sphere] subsection provides a literature review concerning limitations to the effective earth radius model (and the necessary incorporation of modifications thereto) as well as literature implying its conceptual adaptation to the optical range, concluding with the provision of effective earth radii for both radar (or RF) and optical refraction in the tropo[sphere], the corresponding \(K\) values being applied in the CALCULATORS section.

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To understand the basic principle of refraction, the reader is advised to proceed to our web page titled, Snell’s Law of Refraction.