Optics -- caustic curve equation

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SUMMARY

The discussion centers on the interpretation of the caustic curve equation, specifically when setting F=0, which implies the center of the curve is at the origin and the curve is circular. The participant critiques the article's approach, suggesting that it may contain inaccuracies or that their interpretation may be flawed. They emphasize the utility of working with equations like F=0 for geometric surface analysis, highlighting the complexity of caustics in optics.

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  • Understanding of caustic curves in optics
  • Familiarity with geometric optics principles
  • Knowledge of mathematical equations related to curves
  • Ability to interpret physics research papers
NEXT STEPS
  • Study the derivation of caustic curves in optics
  • Explore the implications of F=0 in geometric optics
  • Review the article "Caustics in Optics" by Michael Berry
  • Investigate the relationship between circular curves and caustics
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Students and professionals in physics, particularly those focusing on optics, as well as researchers analyzing geometric properties of light and caustics.

Archit Nanda
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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..
 
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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
 

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