Question

discuss the cartesian sign conventions for spherical mirrors.

Answer 1

objects is placed in left side...
we measure distance from the pole...
any distance that is known the left of the pole is taken to be negative(-ve) and right of the pole is taken (+ve) ....
and up (+ve) down (-ve)....

Answer 2

$\huge\mathfrak\red{Heya\:Mate}$

$\huge\sf{Here\:is\:your\:Answer:-}$

Sign Convention for Reflaction by Spherical Mirrors use the pole of the mirror as Origin. The principal axis of the mirror is taken as the x-axis of the coordinate system.

$\underline{The\: convention \:are \:as\: follows:-}$

✔️ The object is always placed to the left of the mirror.

✔️ All distance parallel to the principal axis are measured from the pole of the mirror.

✔️ All the distance measured to the right of the orgin are taken as positive while those measured to the left of the origin is taken as negative.

✔️ Distances measured perpendicular to and above the principal axis are taken as positive.

✔️ Distance measured perpendicular to and below the principal axis are taken as negative.

Hope it helps you!!