Sign Convention

To turn the geometry of mirror (and, later, lens) image formation into a single formula that works for every combination of concave/convex mirror and real/virtual object and image, ray optics adopts one fixed convention for the sign of every distance measured -- the New Cartesian Sign Convention. All distances are measured from the pole $P$ of the mirror (or the optical centre of a lens). The object is always taken to be placed to the left of the mirror/lens, so that incident light travels, by convention, from left to right. Distances measured in the same direction as the incident light (i.e. to the right of $P$) are taken as positive, and distances measured against the direction of incident light (i.e. to the left of $P$) are taken as negative. Heights measured upward, above the principal axis, are taken as positive, and heights measured downward are taken as negative. Applying this rule consistently has several immediate, memorable consequences: the object distance $u$ is always negative, because a real object always sits to the left of the mirror/lens; the focal length of a concave mirror is negative (its focus is on the same, left, side as the object) while the focal length of a convex mirror is positive (its focus is behind the mirror); and a real image, which forms in front of a mirror on the same side as the object, has a negative image distance $v$, while a virtual image, which forms …