"Snell's Law" for a Spherical Shell
Atmosphere with a Refractive Index of Radial Dependency
(1 + h/R) n sin z = n0 sin z0
= constant, where
h = elevation of point above sea level,
R = radius (sea level) of earth,
n(h) = atmospheric refractive index = 1 + (n0-1)e-h/H,
n0 = n(h = 0)
H = 7.996 km = "density scale height"
z = zenith angle.
We can also write then, that
| Comment | z0, h, R, H or n0 | z = z(z0, h, R, H, n0) |
| Sea level | h = 0 | z0 |
| Observer at ¥ | h = ¥ | 0 |
| Plane // model | R = ¥ | sin-1 [(n0/n) sin z0] Snell's Law |
| Source at zenith | z0 = 0 | 0 |
| No refraction | H = ¥, or n0 = 1 | sin-1{[R/(R + h)]sin z0} (earth curvature only) |