Give the relationship of magnification with focal length of a spherical mirror.

(N/A) The magnification $m$ of a spherical mirror is defined as the ratio of the height of the image to the height of the object,which is also given by $m = -v/u$.
Using the mirror formula $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$,we can derive the relationship between magnification,focal length $(f)$,and object distance $(u)$ or image distance $(v)$.
By substituting $v = \frac{fu}{u-f}$ into $m = -v/u$,we get $m = \frac{f}{f-u}$.
Similarly,by substituting $u = \frac{fv}{v-f}$ into $m = -v/u$,we get $m = \frac{f-v}{f}$.
Thus,the relationship is $m = \frac{f-v}{f} = \frac{f}{f-u}$.