Q.What are the Cartesian sign conventions for a spherical mirror?

A spherical mirror is a part cut from a hollow, silvered sphere; reflection at the concave (inner) surface gives a concave mirror, and reflection at the convex (outer) surface gives a convex mirror. Key terms: the centre of curvature $C$ is the centre of the sphere the mirror is part of; the radius of curvature $R$ is that sphere's radius; the pole $P$ is the geometric centre of the mirror surface; the principal (optical) axis is the line through $P$ and $C$; the focus $F$ is the point on the axis where paraxial rays parallel to the axis converge (concave) or appear to diverge from (convex) after reflection; the focal length $f=PF$; and the focal plane is the plane through $F$ perpendicular to the axis. To keep formulas consistent in every situation, TN Physics uses the Cartesian sign convention: incident light is taken left to right; all distances are measured from the pole (the origin); distances measured …