Curved mirror the focal point of the optical device. Boxes 1 and 3 feature summing the angles of a triangle and comparing to π radians (or 180°). Box 2 shows the Maclaurin series of formula_16 up to order 1. The derivations of the ray matrices of a convex spherical mirror and a thin lens are very similar. Curved mirror A curved mirror is a mirror with a curved reflecting surface. The surface may be either "convex" (bulging outwards) or "concave" (bulging inwards). Most curved mirrors have surfaces that are shaped like part of a sphere, but other shapes are sometimes used in
Luneburg lens one side, and formula_14 only on the other: The parameter formula_19 is a constant for any given ray, but differs between rays passing at different distances from the centre of the lens. For rays passing through the centre, it is zero. In some special cases, such as for Maxwell's fish-eye, this first order equation can be further integrated to give a formula for formula_14 as a function or formula_13. In general it provides the relative rates of change of formula_14 and formula_13, which may be integrated numerically to follow the path of the ray through the lens. Luneburg lens A