From: mathma18@gmail.com   
      
   On Saturday, May 11, 2013 1:43:15 AM UTC+5:30, Boxman wrote:   
   > 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.   
      
   Dear Boxman and all others,   
      
   Requesting for your specific comments to clear up it fully. The following   
   seems to me right.I worked on it.Shall much appreciate your responses.    
      
    Which of the following four statements are true?    
      
   (Spherical aberration free aplanat lens of single material of refractive index   
   > 1 , say 1.5.  Assume dense medium lens at left and rarer medium (air) at   
   right on the x-axis. Light travels from left to right in situations mentioned   
   below, i.e., 1 & 3    
   emerging out of dense medium, 2 & 4 entering into dense medium)   
      
   1.	Planar wave-front from inside the lens focuses to a point in air F with   
   shrinking /converging spherical waves. For this to happen, lens shape is a   
   hyperbola.   
       
   2.	Planar wave-front from outside the lens focuses to a point F inside lens   
   with shrinking /converging spherical waves. For this to happen, lens shape is   
   an ellipse.   
       
   In 1 and 2 above expanding wave-fronts in reverse order give rise to straight   
   planar beams.   
      
   3.	Spherical expanding wave-front issuing from focus F1 inside the lens   
   focuses to a point F2 in air with shrinking /converging spherical waves. For   
   this to happen, lens shape is a Cartesian Oval of dimpled ball type.   
       
   4.	Spherical expanding wave-front front issuing from focus F1 from outside the   
   lens focuses to a point F2 in the lens with shrinking /converging spherical   
   waves. For this to happen, lens shape is a Cartesian Oval egg type.    
      
   In 3 and 4 above F1 and F2 can be swapped.   
      
   Regards   
   Narasimham G.L.   
      
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