84 



TROPOSPHERIC REFRACTION 



Figure 3.19. Bending geometry on a spherical earth with concentric layers. 



If one considers figure 3.20, Snell's law in polar coordinates (3.1) and 

 the refraction formula (3.2) may be obtained from the more familiar 

 form of Snell's law. 



Assume that the earth is spherical and that the atmosphere is arranged 

 in spherical layers. In figure 3.20 let C be the center of the earth, the 

 observer and COZ the direction of his zenith. Let n and n+dn be the 

 indices of refraction in two adjacent thin layers M and M' . Let LP be 

 the section of a ray in M' which finally reaches the observer at 0. At 

 P it is refracted along PQ. Similarly, it is refracted at the surfaces be- 

 tween successive layers and the final infinitesimal element of its path is 

 TO. 



Draw the radii CP and CQ. Let angle PQF = 6, angle LPS = 6 -\- dd, 

 and angle QPF = \p. Then, since the radius CP is perpendicular at P to 



