Physics · Ch 6 — Optics
Paraxial Rays and Marginal Rays
Paraxial Rays and Marginal Rays
Rays travelling very close to the principal axis, making only small angles with it, are called paraxial rays; they strike a spherical mirror very close to its pole. Rays travelling farther from the axis, striking the mirror closer to its rim, are called marginal rays. These two classes of rays are found to focus at slightly different points after reflection -- the underlying cause of a defect called spherical aberration. Because the paraxial rays make only small angles, the small-angle approximations (in radians) become valid, which is exactly what makes the mirror equation and every other simple formula in this chapter possible; this chapter deliberately restr …
What this figure shows. A hollow sphere is shown with a curved cap cut from it to form the mirror; the same physical cap can be used with either face silvered. Reflection at the concave (inner, cupped) surface makes it a concave mirror, shown converging incoming parallel rays; reflection at the convex (outer, bulging) surface makes it a convex mirror, shown spreading incoming parallel rays apart. Both mirrors share the same pole, centre of curvature and rad …
What this figure shows. A bundle of rays parallel to the principal axis strikes a concave mirror. The rays closest to the axis (paraxial rays) converge sharply through a single, well-defined focus F. The rays farther from the axis, closer to the mirror's rim (marginal rays), are shown converging to a noticeably different point, closer to the mirror itself, illustrating why this chapter's simple f = R/2 relation and mirror equation are valid only for the paraxial rays, and why using the full aperture of a large mirror introduces blurring (spherical ab …