Q.Define the power of a lens and state its SI unit. Explain why a converging (convex) lens is assigned a positive power and a diverging (concave) lens a negative power.

The power of a lens, $P=1/f$ with $f$ expressed in metres, measures how strongly the lens bends (converges or diverges) an incident beam: a short focal length bends light sharply and gives a large power, while a long focal length bends light gently and gives a small power. Its SI unit is the dioptre (D), the power of a lens whose focal length is exactly $1\ \text{m}$. Since the New Cartesian sign convention makes a convex (converging) lens's focal length positive (its real focus lies on the outgoing-light side) and a concave (diverging) lens's focal length negative (its focus is virtual, on the object side), taking the reciprocal preserves this same sign: a convex lens's power comes out positive and a concave lens's power comes out negative. This is genuinely useful in pra …

State the definition and unit, then trace the sign directly from the sign conve …

• Forgetting to convert $f$ to metres before taking the reciprocal (a very common numerical slip, e.g. leaving $f$ in cm).
• Reversing which sign of power belongs to which lens type. …