There are a number of different conventions used for keeping track of the orientations of images in optics.
The "Cartesian" convention is used by Schroeder (1987). It is similar to that of Born and Wolf (1999) and Longhurst
(1967). In this convention, distances to the left of the vertex are negative, and distances to the right are positive.
Distances from the optical axis are positive if measured upwards. Primes are used to denote the image, whereas unprimed
quantities denote the object. This convention allows the treatment of reflected rays by letting
References
Born, M. and Wolf, E. Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, 7th ed. Cambridge, England: Cambridge University Press, 1999.
Hecht, E. Optics, 3rd ed. Reading, MA: Addison-Wesley, 1998.
Longhurst, R. S. Geometrical and Physical Optics. New York: Wiley, 1967.
Schroeder, D. J. "Sign Conventions." §2.1 in Astronomical Optics, 2nd ed. San Diego: Academic Press, pp. 7-8, 1999.