Optics -- caustic curve equation

[Archit Nanda]

I went through this article:
http://users.df.uba.ar/sgil/physics_paper_doc/papers_phys/ondas_optics/caustica1.pdf
But I think that when we do F=0, we are assuming the centre of the curve to be the origin and assuming the curve to be a circle, because only then will we be able to say that OP=ON (i.e. F=0)..either the article has some issues or I am interpreting it wrongly..please help..

 

[Andy Resnick]

What the author did is simply re-write r = R cos() sec() as r-R cos() sec() = 0. For technical reasons, it's often easier to work with equations like F = 0 instead of r = something, especially if you are talking about the geometry of surfaces.

Caustics are really fun to study (IMO)- check this out:

https://michaelberryphysics.files.wordpress.com/2013/07/berry089.pdf