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I'm looking for two things:

  1. Something like the third equation in the chosen answer in the link, but for spherical mirrors, and
  2. Something that covers conventions for the radii of curvature and focal lengths of both thin lenses and spherical mirrors (concave and convex).

Comparison of conventions for thin lenses with a no-convention equation provided: https://physics.stackexchange.com/a/169649/111287

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The resource that made the most sense to me was Khan Academy's lesson on the issue, which establishes that the Cartesian convention can be applied to both thin lenses and spherical mirrors and goes as follows:

  1. The direction in which the incident light is traveling is called positive
  2. In the case of a thin lens, focal lengths and radii of curvature are signed by using the first surface the light strikes, with f = R/2, and R is the position of the would-be circle's center taking the optical system's pole to be the origin
  3. For object and image heights, call up positive
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