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

As of my last update in September 2021, there was no standardized "new Cartesian sign convention" for spherical lenses. However, I can explain the conventional Cartesian sign convention that is widely used to describe the properties of spherical lenses in optics.

The Cartesian sign convention is used to define the directions of various quantities related to lenses and mirrors, such as object distance, image distance, focal length, and magnification. It provides a consistent framework for calculations in optics.

In this convention, the following sign conventions are generally used:

Object Distance (u): The object distance is measured from the object to the lens, along the optical axis. If the object is located on the same side as the incident light (incoming light), the object distance is considered positive. If the object is on the opposite side of the incident light, the object distance is considered negative.

Image Distance (v): The image distance is measured from the lens to the image formed by the lens, along the optical axis. If the image is formed on the opposite side of the outgoing light, the image distance is considered positive. If the image is formed on the same side as the outgoing light, the image distance is considered negative.

Focal Length (f): The focal length is the distance from the center of the lens to its focal point (the point where parallel rays converge after passing through the lens). For converging lenses (convex lenses), the focal length is considered positive, and for diverging lenses (concave lenses), the focal length is considered negative.

Magnification (m): The magnification of a lens is defined as the ratio of the height of the image (h_i) to the height of the object (h_o). If the image is upright and virtual, the magnification is considered positive. If the image is inverted, the magnification is considered negative.

Remember that the Cartesian sign convention is just a convention, and it's essential to use consistent sign conventions in calculations to ensure accurate results in optics problems.

If there has been any development or update to the Cartesian sign convention for spherical lenses after my last update in September 2021, I won't be aware of it. Please refer to more recent and authoritative sources to check for any new developments or changes in the sign convention.