A makeup mirror produces a magnification of 1.50 when a face is 12.0 cm away. What is the focal length of the mirror?

1. The magnification is positive and greater than one, so the image is upright and enlarged, the magnifier case for a converging mirror. 2. From m = minus di divided by do, the image distance is di = minus m times do. 3. Substituting with units, di = minus (1.50) times (12.0 cm) = -18.0 cm, negative because the image is behind the mirror. 4. Now use 1/f = 1/do + 1/di. 5. Substituting, 1/f = 1 divided by 12.0 cm plus 1 divided by (-18.0 cm) = 0.0833 per cm minus 0.0556 per cm = 0.0278 per cm. 6. Inverting, f = 36.0 cm, positive as a concave converging mirror requires. 7. Note that the face at 12.0 cm sits well inside the 36.0 cm focal length, which is the condition for the magnified virtual image. 8. Answering -36.0 cm imports the convex mirror sign and would contradict the enlarged upright image. _Source: OpenStax College Physics (CC BY 4.0), Ch 25 "Geometric Optics", section 25.7 Image Formation by Mirrors_