Q.Describe spherical aberration for spherical lenses. What are different ways to minimize or eliminate it?

[!TLDR] Spherical aberration in lenses is the paraxial-vs-marginal-ray focus mismatch, giving a circle of least confusion; reduced via curved-face orientation, a specific R1:R2 ratio, separated converging lenses, or a convex+concave combination. [!ANSWER] Marginal rays focus closer than paraxial rays -> circle of least confusion; minimized by: (i) curved face toward incident rays, …

Just as for spherical mirrors, the thin-lens formula assumes paraxial rays (small aperture, rays close to and nearly parallel to the axis). For a lens of finite aperture, rays farther from the axis (marginal rays) come to focus at a slightly different point than paraxial rays, so no perfectly sharp point-image forms -- only a smallest blur, the circle of least confusion, with associated longitudinal and transverse spherical aberration, defined exactly as for mirrors. Four practical ways exist to minimize or eliminate this: (i) the cheapest fix -- for a plano-convex or plano-concave lens, orient the CURVED face toward the incident (real object) rays; reversing this orientation makes the aberration noticeably worse, so this is a free, no-extra-parts fix available purely from how the lens is mounted.

(ii) For a given refractive index there is a specific ratio of the two radii of curvature that nearly eliminates spherical aberration entirely: R1:R2 = 1:6 for n=1.5, or 1:5 for n=2 -- i.e. deliberately choosing an asymmetric (rather than symmetric double-convex) lens shape purely to minimise this defect.

(iii) Using two thin CONVERGING lenses separated by a distance equal to the DIFFERENCE between their two focal lengths, with the lens of LARGER focal length facing the incident rays, considerably reduces the aberration. …

Describe the physical cause (marginal rays focusing differently than paraxial rays, exactly paralleling mirror spherical aberration) and list al …

Naming only one or two of the four remedies (commonly forgetting the specific R1:R2 ratio method or the two-separated-convergi …