State and explain the new Cartesian Sign convention for spherical lenses.

Hint: The calculation of parameters involved in the optical phenomena are highly sensitive to the directions of all the known parameters included in the calculation. We should abide by the sign conventions used popularly to get solutions in the same way.

Complete answer:
The new Cartesian sign convention involves the systematic approach to the distance parameters involved in the calculation of the unknowns in any spherical lenses. This sign convention urges the observer to consider all the distances from the optic center of the spherical. The sign convention defines all the measurements to the right and upward direction to be positive and the rest to be negative.
The main features of the new Cartesian sign convention are:
(i)The optical center of the spherical lens is considered as the origin on the given plane. All the measurements are to be taken from this point O.
(ii) The measurements to the left of the spherical lens, preferably, the side from which the ray incidents on the lens is considered as negative. The other side, to the right of the lens, is considered positive.
(iii) The measurements above the principal axis are considered to be positive, whereas the measurements below the principle axis is negative.

The new Cartesian sign convention is described in the above figure and the explanation.

Note:
The signs involved in the object distance, image distance, height of the object and so on are often mistreated which results in large errors which will be mostly irretrievable from the calculations. We should strictly follow the sign convention to avoid errors.