Final answer:
The focal length of the makeup mirror that produces a magnification of 1.50 when a person's face is 12.0 cm away is -8.0 cm.
Step-by-step explanation:
The focal length of a mirror can be determined using the magnification equation:
magnification = - (image distance / object distance)
In this case, the magnification is given as 1.50 and the object distance is 12.0 cm.
Rearranging the equation gives:
focal length = - (image distance / magnification)
Substituting the given values, we have:
focal length = - (12.0 cm / 1.50) = - 8.0 cm
Therefore, the focal length of the makeup mirror is -8.0 cm, indicating that it is a concave mirror since the focal length is negative.