Refraction at Single Spherical Surface

Refraction so far has been treated only at flat (plane) boundaries; it also takes place at spherical surfaces separating two transparent media. The same laws of refraction hold at every point of a spherical surface, with the normal at any point of incidence always passing through the surface's own centre of curvature (since the normal to a sphere is always radial). Two simplifying assumptions are made throughout this section: (a) the incident light is monochromatic (a single colour, so refractive index has one fixed value); and (b) only paraxial rays -- travelling very close to the principal axis -- are considered. The Cartesian sign convention used here is the same one already used for spherical mirrors. Studying refraction at a single spherical surface is the essenti …