Final answer:
To find the focal length of the makeup mirror, the mirror equation 1/f = 1/do + 1/di and the magnification equation m = -di/do were used with the given magnification of 1.50 and distance of the object (person's face) at 12.0 cm. The resulting focal length is 8.00 cm.
Step-by-step explanation:
The question is asking to determine the focal length of a makeup mirror that produces a magnification of 1.50 when a person's face is 12.0 cm away from the mirror. To find the focal length, we can use the mirror equation and the magnification equation.
The mirror equation is 1/f = 1/do + 1/di, where 'f' is the focal length, 'do' is the distance of the object from the mirror, and 'di' is the distance of the image from the mirror. The magnification 'm' is given by m = -di/do. Since we know 'm' = 1.50 and 'do' = 12.0 cm, we can rearrange the magnification equation to find 'di' = -m * do, which gives us 'di' = -1.50 * 12.0 cm = -18.0 cm. Plugging 'do' and 'di' into the mirror equation gives us 1/f = 1/12 + 1/(-18), which simplifies to f = 8.00 cm.