When using a shaving mirror with a focal length of 72 cm to view the image the face, if the face is 18 cm from the mirror, determine the image distance and the magnification of the face.

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When using a shaving mirror with a focal length of 72 cm to view the image the face, if the face is 18 cm from the mirror, determine the image distance and the magnification of the face.

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Answer 1 · 2015-03-13T00:10:06

First you may do some ray tracing and discover that your image will be VIRTUAL behind the mirror.
![Hecht Optics 2nd http://ed.](https://useruploads.socratic.org/FhtsBB2TtWsRkIQW2AIQ_mirror1.jpg)
Then use the two relationships on mirrors:

1) $1/(d_o)+1/(d_i)=1/f$ where $d$ are distances of object and image from the mirror and $f$ is the mirror`s focal length;

2) the magnification $m=-(d_i)/(d_o)$ .

In your case you get:

1) $1/18+1/d_i=1/72$
$d_i=-24 cm$ negative and virtual.

2) $m=-(-24)/18=1.33$ or 1.33 times the object and positive (upright).

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When using a shaving mirror with a focal length of 72 cm to view the image the face, if the face is 18 cm from the mirror, determine the image distance and the magnification of the face.

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