A mirror is used to produce an image with magnification of \( \frac{1}{4} \). If the distance between object and its image is \( 40 \, \text{cm} \), then the focal length of the mirror is ______.
\( 10.7 \, \text{cm} \)
\( 10 \, \text{cm} \)
\( 15 \, \text{cm} \)
\( 12.7 \, \text{cm} \)
