Question
What is the cartesian sign convention used for spherical mirrors?

Answer

According to the cartesian sign convention, the pole of the mirror is taken as the origin. The principal axis is taken as the X-axis of the frame of reference. The sign conventions are as follows.
(i) The object is always kept on the left of the mirror. All distances parallel to the Principal axis are measured from the pole of the mirror.
(ii) All distance measured towards the right of the pole are taken to be positive, while those measured towards left are taken to be negative.
(iii) Distance measured vertically upwards from the Principal axis are taken to be positive.
(iv) Distances measured vertically downwards from the Principal axis are taken to be negative.
(v) The focal length of concave mirror is negative while that of a convex mirror is positive.

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