Q.Explain spherical aberration for spherical mirrors. How can it be minimized? Can it be eliminated by some curved mirrors?

[!TLDR] Spherical aberration is the focus-shift (toward the pole) for rays far from the axis, giving a blurred circle of least confusion instead of a sharp point; it is minimized with a small aperture and fully eliminated only by a parabolic mirror. [!ANSWER] Focus shifts toward the pole for margi …

Spherical aberration is the defect in which a spherical mirror does not bring ALL parallel incident rays to one single sharp focus: rays close to the axis (paraxial) focus at the paraxial focal point Fp, but rays farther from the axis (marginal rays) focus progressively closer to the pole, at a different point Fm. Because of this focus-shift, no single sharp point-image forms on any screen; instead, the smallest possible blur -- the circle of least confusion -- appears at some intermediate screen position, with its radius called the transverse spherical aberration and the axial separation between Fm and Fp called the longitudinal spherical aberration. It can be MINIMIZED (though not fully removed) for a spherical mirror by restricting the aperture to keep rays closer to paraxial. It CAN be completely ELIMINATED, but only by using a mirror of a different shape: a PARABOLIC mirror. By the geometric definition of a parabola (every point on it equidistant from a fixed directrix line and a fixed focus point), eve …

Describe the physical cause (marginal rays focusing closer to the pole than paraxial rays) and its consequence (circle of least confusion), then distinguish minimizi …

Claiming spherical aberration can be fully eliminated just by using a smaller spherical mirror -- restricting aperture only reduces …