Question

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.

Answer 1

First you may do some ray tracing and discover that your image will be VIRTUAL behind the mirror.
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).