What are the sign conventions for mirrors and lenses? I always get confused!

The New Cartesian Sign Convention is crucial for solving numerical problems. Imagine the pole (for mirrors) or optical centre (for lenses) as the origin ($0,0$) of a coordinate system.

1. The object is always placed to the left of the mirror/lens, meaning light travels from left to right.
2. All distances are measured from the pole/optical centre.
3. Distances measured in the direction of incident light (to the right) are taken as positive.
4. Distances measured opposite to the direction of incident light (to the left) are taken as negative.
5. Heights measured upwards, perpendicular to the principal axis, are positive.
6. Heights measured downwards, perpendicular to the principal axis, are negative. This consistent system helps determine the signs for focal length ($f$), object distance ($u$), image distance ($v$), and heights ($h, h'$).