Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Early Posting Feature Issues

Below the horizon—the physics of extreme visual ranges

Michael Vollmer

Open Access Open Access

Abstract

Visual ranges of up to 440 km have recently been documented by photographs of ground-based observers. A report from 1948 claimed a record visual range from a plane of more than 530 km and a similar recent observation from 2017 was documented by a photo. Such extreme visual ranges can in principle be explained by the interplay of refraction and light scattering. However, they require optimal atmospheric conditions, and cleverly chosen locations and times.

© 2020 Optical Society of America

Full Article  |  PDF Article

Corrections

26 June 2020: Corrections were made to Figs. 8 and 9.

More Like This
Extended visual range during solar eclipses

Michael Vollmer and Joseph A. Shaw
Appl. Opt. 57(12) 3250-3259 (2018)

Visually discerning the curvature of the Earth

David K. Lynch
Appl. Opt. 47(34) H39-H43 (2008)

Visibility of Distant Mountains as a Measure of Background Aerosol Pollution

William M. Porch, David S. Ensor, and Robert J. Charlson
Appl. Opt. 14(2) 400-403 (1975)

View More...

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)
Fig. 1.
Fig. 1. Geometry of finding the distance to an elevated object.

Download Full Size | PDF

Fig. 2.
Fig. 2. Schematic curvature of light rays in a concentric atmosphere with given lapse rates. An observer sees rays coming from the various directions indicated by the arrows.

Download Full Size | PDF

Fig. 3.
Fig. 3. Schematic ray paths due to rectilinear geometry, normal refraction, and abnormal refraction due to inversion layers.

Download Full Size | PDF

Fig. 4.
Fig. 4. (a) Geometry for curved light ray in spherical geometry and (b) most simple approximation of its left part in flat Earth geometry.

Download Full Size | PDF

Fig. 5.
Fig. 5. (a) Decrease of effective scattering coefficient as a function of minimum height of the light ray (for ${H} = {8}\;{\rm km}$, ${{h}_{\max}} = {4}\;{\rm km}$) and (b) corresponding visual range for a given wavelength averaged scattering coefficient ${\beta _0}$ at sea level.

Download Full Size | PDF

Fig. 6.
Fig. 6. Geometry for a symmetrical light ray with given minimum height.

Download Full Size | PDF

Fig. 7.
Fig. 7. Map including two observation sites in the Pyrenees and two observed objects in the Alps. Details, see text (image with some added distances and lines based on Google Maps).

Download Full Size | PDF

Fig. 8.
Fig. 8. Record long-distance observation of an Alps mountain peak in a distance of 443 km from the Pyrenees. (a) Scenery, (b) enlarged part with identified peaks, (c) original photo, courtesy photographer Marc Bret.

Download Full Size | PDF

Fig. 9.
Fig. 9. Record airplane observation; (a) wider panorama; (b) Mount Blanc enlarged, from a distance of about 538 km (details, see text). Courtesy photographer Ramon Ibarz.

Download Full Size | PDF

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

x ≈ 2 R E h o b s .
x ≈ 2 R E h o b s + 2 R E h o b j .
k = 35 − α 150 .
L ( x ) = L 0 e − β ( λ ) x ,
− ln ⁡ ( C ) = β ⋅ d .
d = 3.9 β .
β ( h ) = β 0 e − h H ,
β e f f ≈ β 0 H h max − h min [ e − h min H − e − h max H ] .
C = e − β d 2 ( 1 − a + a e − β d 1 ) .
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use