Question

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?

Answer 1

-7.73 cm, negative meaning behind the mirror as a virtual image.
Graphically your situation is:

Where:
`r` is the radius of curveture of your mirror;
`C` is the centre of curvature;
`f` is the focus (=`r/2`);
`h_o` is the object height `=1.2 cm`;
`d_o` is the object distance `=5.8 cm`;
`h_i` is the image height `=1.6 cm`;
`d_i` is the image distance `=?`;

I use the magnification `M` of the mirror to relate my parameters as:
`M=h_i/(h_o)=-d_i/(d_o)`
Or:
`1.6/1.2=-d_i/5.8` and

`d_i=-7.73 cm`