Physics · Ch 9 — Optics
Cartesian sign convention
Cartesian sign convention
A sign convention is essential throughout geometrical optics, because the numerical relation between object distance , image distance and focal length for a mirror or a lens would otherwise look completely different for every different case (concave versus convex, real versus virtual object, and so on). A properly applied sign convention lets a SINGLE formula cover every one of these cases at once. The most convenient choice, because it parallels ordinary coordinate geometry, is the Cartesian sign convention, built from five rules.
- All distances are measured from the optical centre or pole. For common optical elements such as spherical mirrors and thin lenses, this optical centre coincides with the element's own geometric centre.
- Figures are always drawn with the incident rays travelling from LEFT to RIGHT. A diverging beam of incident rays corresponds to a real point object; a converging beam of incident rays corresponds to a virtual object; a parallel beam corresponds to an object at infinity. Consequently, a real object is always shown to the LEFT of the pole, and a virtual object or image is shown to the RIGHT of the pole.
- The principal axis is conveniently chosen as the x-axis, with its origin placed at the pole.
- Distances measured to the LEFT of the pole are NEGATIVE; distances to the RIGHT of the pole are POSITIVE.
- Distances measured ABOVE the principal axis are POSITIVE; distances BELOW it are NEGATIVE. …
What this figure shows. A diagram establishing the sign-convention axes for optics: a horizontal principal axis (labelled like an x-axis) passing through the pole/optical centre P of a mirror or lens, with incident light travelling from LEFT to RIGHT. The region to the LEFT of the pole is marked as the NEGATIVE distance zone along the axis, and the region to the RIGHT of the pole as the POSITIVE zone. A perpendicular (vertical) direction through the pole is also marked, with the region ABOVE the principal axis positive and BELOW the axis negative. The figure is purely a labelled coordinate-axis schematic (no actual mirror/lens curve drawn on it, or a minimal schematic pole marker only), establishing the reference frame that ev …
What this figure shows. A two-part figure illustrating the convention that real objects are drawn to the LEFT of the pole and virtual ones to the right. Part (a) shows a bundle of light rays DIVERGING outward from a single point O positioned to the left of the pole/mirror-or-lens, with the rays spreading apart as they travel rightward toward the optical element -- this diverging-beam geometry is captioned as corresponding to a REAL point object. Part (b) shows a bundle of rays CONVERGING toward a single point O' positioned to the right of the pole (i.e. rays that have not yet met, still travelling rightward, but aimed so they would meet at a point beyond/after the optical element if not intercepted) -- this converging-beam geometry is captioned as corresponding to a VIRTUAL object. Neither part shows any numeric values; both are schematic ray-bundles used only to fix the diverging-versus-converging, real-versus-virtua …