(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a cylindrical piece of material of a constant thicknessdand radiusr=a, but made out of a material with position-dependent index of refraction. How must the index of refraction vary with radial distancersuch that the cylindrical piece act as a lens with a focal length off. Assumed<<a, i.e., a thin lens.

3. The attempt at a solution

Ok, first I remind myself that light follows the path, where the optical path length is stationary. So I write

[tex]

\Gamma = \int {n\left( {r,\phi ,z} \right)} \,rdrd\phi dz.

[/tex]

I can integrate dz and dφ out, since we only want to look at the r-dependence. Now, I need to find dGamma/dr = 0, but that just gives me n(r)=0, which is clearly wrong. Can you give me a hint?

Best,

Niles.

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# Homework Help: Optics: Find the index of refraction

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