# I use a cosmetic mirror to magnify my eyelashes. My 1.2-cm long eyelashes are magnified to 1.6 cm when placed 5.8 cm from the mirror, how can I determine the image distance for such an upright image?

Jan 24, 2015

-7.73 cm, negative meaning behind the mirror as a virtual image.

Where:
$r$ is the radius of curveture of your mirror;
$C$ is the centre of curvature;
$f$ is the focus (=$\frac{r}{2}$);
${h}_{o}$ is the object height $= 1.2 c m$;
${d}_{o}$ is the object distance $= 5.8 c m$;
${h}_{i}$ is the image height $= 1.6 c m$;
${d}_{i}$ is the image distance =?;

I use the magnification $M$ of the mirror to relate my parameters as:
$M = {h}_{i} / \left({h}_{o}\right) = - {d}_{i} / \left({d}_{o}\right)$
Or:
$\frac{1.6}{1.2} = - {d}_{i} / 5.8$ and

${d}_{i} = - 7.73 c m$