Magnification in Near Point Focusing

In near point focusing, a simple microscope's object is placed so that the final virtual image forms at the near point, meaning the image distance is (with sign convention) $v=-D$, where $D$ is the standard 25 cm least distance of distinct vision. Rewriting the lens magnification $m=v/u$ using the lens equation $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ -- specifically $m=\frac{f-v}{f}$ -- and substituting $v=-D$ gives $m=\frac{f-(-D)}{f}=\frac{f+D}{f}$, i.e. $\boxed{m=1+\dfrac{D}{f}}$. This is the larger of the two possible simple-microscope magnifications (compare normal focusing, $m=D/f$), but it requires the eye to st …