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(A) The magnification $m$ for a lens is given by the ratio of image distance $v$ to object distance $u$,expressed as $m = \frac{v}{u}$.From the lens f

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$v = \frac{1-m}{P}$

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(A) The magnification $m$ for a lens is given by the ratio of image distance $v$ to object distance $u$,expressed as $m = \frac{v}{u}$.From the lens formula,$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$,we can write $\frac{1}{u} = \frac{1}{v} - \frac{1}{f} = \frac{f-v}{vf}$.Substituting this into the magnification formula: $m = v 	imes \frac{f-v}{vf} = \frac{f-v}{f} = 1 - \frac{v}{f}$.Rearranging the equation: $\frac{v}{f} = 1 - m$,which implies $v = f(1 - m)$.Since power $P = \frac{1}{f}$ (in meters),we substitute $f = \frac{1}{P}$ into the equation.Therefore,$v = \frac{1-m}{P}$.

If the image formed by a thin convex lens of power $P$ has magnification $m$,then the image distance $v$ is:

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