326 REFRACTION AND REFRACTIVE INDEX MODELS 



University of Florida. The particular case chosen for study was the 

 meteorological profile of May 7, 1957 (2000 L.T.) due to its heterogeneous 

 nature, showing a well-defined elevated layer at about 1 ,500 m. Fourteen 

 refractometer soundings from aircraft measurements taken at various 

 locations along the 487-km path (fig. 8.11) and six refractive index 

 profiles (deduced from radiosonde ascents from Cape Kennedy, Grand 

 Bahama Island, and Eleuthera Island) were read in order to plot a cross 

 section of the atmosphere which would represent as closely as possible 

 the actual refractive conditions at that time. Unfortunately, the data 

 near the surface (up to 300 m) were quite sparse compared to those 

 recorded in the Canterbury Project, and calibration and lag errors had 

 not been noted as carefully in this preliminary report; therefore, some 

 interpolation and considerable smoothing of refractive index values were 

 necessary when drawing isopleths. 



8.2.4. Ray Bending 



The classic expression for the angular change, t, or the bending of a 

 ray passing from a point where the refractive index is Wi to a second point 

 where the refractive index is rii is given in chapter 3 as 



r,^, = - Z'^cot^, (8.11) 



n 



where 6 is the local elevation angle. Equation (8.11) was evaluated by 

 use of 



ni,2 



where 



- gi + 02 



The value of 6 at each point was determined from Snell's law: 



niTi cos di = 712^2 cos 02 = constant, (8.13) 



where r is the radial distance from the center of the earth and is given 

 by a + h, where a represents the radius of the earth and h the altitude 

 of the point under consideration. For simplicity one may rewrite 



(8.13) as 



(1 + A^i X 10-«) (a + hi) cos Oi 



= (1 + A^2 X 10-6) (q + /j^) cos 02. (8.14) 



