DERIVATIONS 



85 



-EARTH'S 

 SURFACE 



Figure 3.20. Geometry for the derivation of Snell's Law in spherical coordinates. 



the bounding surface between layers M and M', by Snell's law we have 



(n+rfn) sin [90° - id+dd)] = n sin i/^. (3.63) 



Now from the triangle CQP-, in which CQ = r and CP = r -\- dr, and 



2The assumption involved in this triangle is that the path of the ray in M' is a 

 straight line, which, of course, can only be true in an isotropic medium. Hence, it 

 can only be true for an infinitesimal layer in the troposphere. Thus only a differential 

 form of Snell's law, (3.65), in polar coordinates, can be obtained by the use of the 

 geometry of figure 3.20; not the finite form, (3.68), which has the same appearance. 



