What is meant by power of a lens? Define its $SI$ unit. You have two lenses $A$ and $B$ of focal lengths $+10\, cm$ and $-10\, cm$ respectively. State the nature and power of each lens. Which of the two lenses will form a virtual and magnified image of an object placed $8\, cm$ from the lens? Draw a ray diagram to justify your answer.

(A) Power of a lens is defined as the reciprocal of its focal length in metres. It represents the ability of a lens to converge or diverge light rays.
$SI$ unit: The $SI$ unit of power is dioptre $(D)$. One dioptre is the power of a lens whose focal length is $1\, m$.
For lens $A$: Focal length $f_A = +10\, cm = +0.1\, m$. Since the focal length is positive,it is a convex (converging) lens. Power $P_A = 1 / f_A = 1 / (+0.1\, m) = +10\, D$.
For lens $B$: Focal length $f_B = -10\, cm = -0.1\, m$. Since the focal length is negative,it is a concave (diverging) lens. Power $P_B = 1 / f_B = 1 / (-0.1\, m) = -10\, D$.
$A$ convex lens forms a virtual and magnified image when the object is placed between the optical centre and the principal focus $(f = 10\, cm)$. Since the object is placed at $8\, cm$,which is less than the focal length,lens $A$ will form a virtual and magnified image.