Which of the following is NOT correct according to the sign convention for spherical lenses?

Correct option is A

The correct answer is (a) Focal length of a convex lens is taken as negative.

Explanation:
• According to the strict rules of the New Cartesian Sign Convention for spherical lenses, the geometric optical centre (O) of the lens is universally taken as the fixed origin (0,0).
• Statement (a) is definitively incorrect because the standard focal length of any standard convex lens is practically and mathematically always taken as positive.
• Statement (b) is fully correct; the reference object is physically always placed strictly to the left of the lens so that all incident light rays fall predominantly from left to right.
• Statement (c) is fully correct; all horizontal distances measured directly in the direction of the incident light (which is naturally to the right of the optical centre) are rigorously considered positive.
• Statement (d) is fully correct; the standard focal length of a diverging concave lens is mathematically always taken as explicitly negative.

Information Booster:
• Vertical heights accurately measured perpendicularly above the principal horizontal axis (like upright virtual images) are conventionally designated as positive values.
• Conversely, vertical heights accurately measured perpendicularly below the principal horizontal axis (like real inverted images) are firmly designated as negative values.

Additional Knowledge:
Object is always placed on the left of the lens. (Option b)
• This represents a universally agreed standard convention that strategically ensures the object distance (u) formally remains a consistently negative variable for calculations.

Distances measured to the right of the optical centre are positive. (Option c)
• This logical convention perfectly mirrors the standard mathematical Cartesian coordinate system where the positive x-axis predictably extends far to the right.

Focal length of a concave lens is taken as negative. (Option d)
• Because the principal focus (F) of a standard concave lens is entirely virtual and functionally lies on the left side of the lens, its assigned focal length remains strictly negative.

So the correct answer is (a)