Focal length of a sphere with refractive index gradient

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SUMMARY

The discussion centers on determining the focal length of a 1mm sphere with a parabolically varying refractive index. The relationship between the gradient of the refractive index and the focal length is crucial for understanding optical properties. Participants seek an analytic solution or approximation formula to calculate the focal length based on the refractive index function provided. Clarity on the specific function describing the refractive index is essential for further analysis.

PREREQUISITES
  • Understanding of optical physics, specifically lens and sphere optics.
  • Familiarity with refractive index concepts and gradient functions.
  • Knowledge of analytical methods for solving optical equations.
  • Basic calculus for interpreting functions and their derivatives.
NEXT STEPS
  • Research the formula for focal length in gradient-index optics.
  • Explore parabolic refractive index profiles and their applications.
  • Learn about numerical methods for solving optical equations.
  • Investigate existing literature on analytic solutions for refractive index variations.
USEFUL FOR

Students in optics, physicists, and engineers working with optical systems, particularly those focusing on gradient-index materials and their applications in lens design.

mypony4eva
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Homework Statement



We take a sphere (1mm) which has a parabolically changing refractive index, which is given in a function.

Homework Equations



Depending on the gradient of the refractive in the sphere, how does it correlates with the focal length.

The Attempt at a Solution



I know I saw somewhere an analytic solution (or at least an analytically derived approximation) formula somewhere, but I don't have a clue where to find it.
 
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You said " refractive index, which is given in a function". What function is that? Please provide all the information in the problem.
 

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