The new Cartesian sign convention is used while considering different terms for reflection through spherical mirrors.

In this convention, the pole (P) of the mirror is taken as the origin. The principal axis of the mirror is taken as the x-axis (X′X) of the coordinate system.

The sign convention is as follows:

The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.

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

All distances measured to the right of the origin (along +x-axis) are taken as positive, while those measured to the left of the origin (along −x-axis) are taken as negative.

Distances measured perpendicular to and above the principal axis (along +y-axis) are taken as positive.

Distances measured perpendicular to and below the principal axis (along −y-axis) are taken as negative.

Sign convention for spherical lenses

The new Cartesian sign convention is same as that for spherical mirrors.

The difference is that the distances are measured from the optical centre.

According to the sign convention, the focal length of a convex lens is positive and that of a concave lens is negative.