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1 year ago in Optics , Physics By RobertMug

Fermat’s principle for a lens with spherical aberration

In my coursework, Fermat's principle elegantly explains image formation for perfect lenses. However, in the lab, we always deal with real lenses exhibiting spherical aberration, where rays from a single point don't converge perfectly. This seems to contradict the principle. I'm seeking a clarification on how the principle of least time is mathematically or conceptually satisfied even in these imperfect, real-world scenarios.

Fermat'sPrinciple SphericalAberration

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By Archana Bagga Answered 1 year ago

This is an excellent question that bridges ideal theory and practical optics. The key is that Fermat's principle states light takes a path of stationary optical length, which can be a local minimum, maximum, or saddle point not necessarily a global minimum. In a lens with spherical aberration, rays from an off-axis point take different paths to the image plane. Each individual ray's path is still stationary for its specific entry point on the lens. The aberration means there are multiple stationary paths, leading to a blurred focus rather than a single convergence point. The principle holds for each ray individually; the system's flaw is in not making all those stationary paths coincide.

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Fermat’s principle for a lens with spherical aberration

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