From: boxman@voyager.net   
      
   On 5/9/2013 5:37 PM, Narasimham Gudipaty wrote:   
   > On Thursday, May 9, 2013 6:41:03 PM UTC+5:30, Narasimham Gudipaty   
   > wrote:   
   >> On May 7, 6:40 pm, boxman  wrote:   
   > ....   
   >   
   >> Thanks. So, in fact is it a point to point imaging effected through   
   >> a Cartesian aplanatic in the refracting portion? (Am unable to get   
   >> to see the book).   
   >   
   > Or,if used here in non-imaging application then wave-front does not   
   > arrive at target in the same phase as at source,right? I am trying to   
   > find at least one example anywhere.. as per Descartes' original   
   > expectation.   
   >   
   > Regards Narasimham   
   >   
   I'm not sure I understand your question completely, but I will explain   
   what I can to see if it helps.   
      
   If you have a point source F in a medium of refractive index n1, you can   
   concentrate the light emitted from that source onto a point G in a   
   medium of refractive index n2 using a refractive surface that is a   
   cartesian oval.  For this case, the optical path length from F to G is a   
   constant and is given by n1*t + n2*s = K where t is the length of the   
   ray in medium 1, s is the length of the ray in medium 2 and K is a   
   constant.  Using that relationship, you can derive parametric equations   
   for a given set of points that are a function of the angle phi which is   
   the angle of the ray to the optical axis passing through the points.   
      
   The Limacon of Pascal falls out of these equations when you have the   
   special case where K^2-f^2*n2^2=0 where f = distance along optical axis   
   from cartesian oval  to point G (i.e. the focal length) and n2 is less   
   than n1.   
      
   Don't know if that helps, but feel free to explain further what you are   
   looking for.   
      
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