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?

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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?

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Answer 1 · 2015-01-24T08:00:18

-7.73 cm, negative meaning behind the mirror as a virtual image.
Graphically your situation is:
enter image source here
Where:
$r$ $r$ is the radius of curveture of your mirror;
$C$ $C$ is the centre of curvature;
$f$ $f$ is the focus (= $\frac{r}{2}$ $r/2$ );
$h_{o}$ $h_o$ is the object height $= 1.2 c m$ $=1.2 cm$ ;
$d_{o}$ $d_o$ is the object distance $= 5.8 c m$ $=5.8 cm$ ;
$h_{i}$ $h_i$ is the image height $= 1.6 c m$ $=1.6 cm$ ;
$d_{i}$ $d_i$ is the image distance $= ?$ $=?$ ;

I use the magnification $M$ $M$ of the mirror to relate my parameters as:
$M = \frac{h_{i}}{h_{o}} = - \frac{d_{i}}{d_{o}}$ $M=h_i/(h_o)=-d_i/(d_o)$
Or:
$\frac{1.6}{1.2} = - \frac{d_{i}}{5.8}$ $1.6/1.2=-d_i/5.8$ and

$d_{i} = - 7.73 c m$ $d_i=-7.73 cm$

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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?

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