Retrieving "Cartesian Sign Convention" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Light Ray

   Linked via "Cartesian sign convention"

   Ray Tracing and Parabolic Reflection
   In the analysis of optical systems, the path of a light ray is meticulously traced. In simplified, paraxial optics, the Cartesian sign convention is applied to positions and focal lengths.
   A key application involves parabolic reflectors. When a bundle of parallel light rays, perpendicular to the aperture plane, strikes a parabolic surface, they are dire…

2. Spherical Mirror

   Linked via "Cartesian sign convention"

   Center of Curvature (C)/): This is the center of the sphere of which the mirror is a segment. Its location dictates the mirror's focusing power. For concave mirrors/), $C$ lies in front of the surface; for convex mirrors/), $C$ lies behind the reflective surface.
   Pole (P)/): The geometric center of the [mirror's surface](/entries/mirrors-surface/], often denoted as the or…

3. Spherical Mirror

   Linked via "Cartesian sign convention"

   $$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$
   This equation is invariant across both concave and convex configurations when the standard Cartesian sign convention is rigorously applied (distances measured in the direction of light travel are positive). However, in non-Euclidean reflective frameworks, such as those utilizing surfaces curved in four dimensions, the relations…