Q.What is focal power of a spherical mirror or of a lens? What may be the reason for using P = 1/f as its expression?

[!TLDR] Focal power P=1/f measures a mirror's or lens's converging/diverging ability; using 1/f directly (rather than f) lets powers of combined elements simply ADD. [!ANSWER] P = 1/f, in dioptres; chosen because focal powers of elements in contact/series add algebraically, unlike focal lengths.

The focal power of a spherical mirror or of a lens is defined as P = 1/f, the reciprocal of its focal length, measured in dioptres (D) in SI units when f is in metres. It captures the mirror's or lens's converging (positive P) or diverging (negative P) ABILITY -- a shorter focal length (stronger bending of light) corresponds to a LARGER focal power. The main reason for defining and using P = 1/f, rather than simply working with f directly, is that when several thin lenses (or a lens-mirror system) are placed together in contact or combined in series, their individual POWERS add up algebraically to give the combination's overall power (P = P1 + P2 + P3 + ...), which is a far simpler relation than trying to combine focal lengths directly (which would instead require adding RECIPROCALS of f, i.e. exactly what P already is). Defining power as 1/f from the start makes every combination calculation a simple addition. [!ANSWER] P = 1/f, measured in dioptres; the reason for this particular form is that powers of combined elements simply ADD, unlike focal lengths.

Define P=1/f as the reciprocal of focal length, then explain the specific motivation: focal powers of combined lenses add directly, which is far more convenient than combining focal lengths.

Defining focal power correctly but failing to give the actual reason for choosing the reciprocal form (that it makes powers of combined elements additive).