Abstract

The general equations of the path of a ray of light passing through the terrestrial atmosphere are outlined. The path of the ray tangent to the earth’s surface is calculated for the U. S. Standard Atmosphere. From this is prepared a table of horizon dip, horizon distance, and refraction for altitudes from sea level to 100,000 feet.

© 1938 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. R. McLeod, Phil. Mag. 38, 546 (1919).
    [Crossref]
  2. Meteorological Publication, M.O. 223.
  3. W. G. Brombacher, (1935).

1919 (1)

A. R. McLeod, Phil. Mag. 38, 546 (1919).
[Crossref]

Brombacher, W. G.

W. G. Brombacher, (1935).

McLeod, A. R.

A. R. McLeod, Phil. Mag. 38, 546 (1919).
[Crossref]

Phil. Mag. (1)

A. R. McLeod, Phil. Mag. 38, 546 (1919).
[Crossref]

Other (2)

Meteorological Publication, M.O. 223.

W. G. Brombacher, (1935).

Cited By

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

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Wave front of refracted ray.

Fig. 2
Fig. 2

Ray in terrestrial atmosphere.

Fig. 3
Fig. 3

Curves of dip, refraction and horizon distance.

Equations (21)

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

r 1 / r 2 = μ 2 / μ 1 ,
d ϕ = arc sin ( r 2 - r 1 ) / s .
= - r 1 ( d μ / d z ) ( z 2 - z 1 ) / s [ μ 1 + ( d μ / d z ) ( z 2 - z 1 ) ] , = - r 1 sin ϕ ( d μ / d z ) / [ μ 1 + ( d μ / d z ) ( z 2 - z 1 ) ] .
d ϕ / d z = - tan ϕ [ d μ / d z ] / μ ,
d ϕ = - d μ μ tan ϕ - tan ϕ R + z d z ,
log sin ϕ = - log μ - d z R + z = - log μ ( R + z ) + const.,
sin ϕ = A / ( R + z ) μ ,
sin ϕ = R μ 0 / ( R + z ) μ .
μ = 1 + a ρ ,
ρ = P / T P / T z = 0 ,
d δ / d z = - tan ϕ [ d μ / d z ] / μ ,
D = ( ψ + δ ) R .
a ( d δ d z ) = a ( - a ( d ρ / d z ) 1 + a ρ tan ϕ ) = - 1 ( 1 + a ρ ) 2 tan ϕ d ρ d z - a 1 + a ρ d ρ d z sec 3 ϕ R R + z 1 - ρ ( 1 + a ρ ) 2 = - d ρ d z tan ϕ ( 1 + a ρ ) 2 [ 1 + 1 - ρ cos 2 ρ · a 1 + a ] ,
sin ϕ = R R + z 1 + a 1 + a ρ .
a ( d δ d z ) = 1 a d δ d z · 1 1 + a ρ [ 1 + { 1 - ρ cos 2 ϕ a 1 + a } ] .
- 1 2 1 1 / ( R ( d ρ / d z ) z = 0 ) + a 0.109.
a d δ d z = 1 a d δ d z ;
δ ( a ) = a 0.000277 · δ ( 0.000277 )
a ϕ = a arc sin R R + z 1 + a 1 + a ρ a ϕ = 1 cos φ R R + z 1 - ρ ( 1 + a ρ ) 2 = ( 1 - ρ ) ( 1 + a ) ( 1 + a ρ ) tan ϕ ( 1 - ρ ) tan ϕ ,
ρ = 10 ( 0.2180 - 0.2074 z / 10 , 000 ft. )
sin ϕ = R R + z · 1.000277 1 + 0.000277 ρ ,