How far from a lens having a focal length of $+ 50 \mathrm {~mm}$ must the object be placed if it is to form a virtual image that is $3.0$ times the size of the object?
A) $33 \mathrm {~mm}$
B) $54 \mathrm {~mm}$
C) $42 \mathrm {~mm}$
D) $48 \mathrm {~mm}$

Question

Quizplus · Accepted Answer

For a lens (convex in this case, given the positive focal length), the lens formula is $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$, where $f$ is the focal length, $v$ is the image distance, and $u$ is the object distance. For a virtual image, $v$ is negative and the magnification $m = -\frac{v}{u}$ is positive. Given $m = 3$, we solve for $u$ with $f = +50$ mm.

How Far from a Lens Having a Focal Length Of +50 mm+ 50 \mathrm {~mm}+50 mm

How Far from a Lens Having a Focal Length Of $+ 50 \mathrm {~mm}$