A page is held 7.50 cm from a concave lens whose focal length is -10.0 cm. What image distance and magnification result?

1. Set the convention: do is positive at 7.50 cm, and f is negative at -10.0 cm because the lens is concave and diverging. 2. Rearranging the thin lens equation gives 1/di = 1/f - 1/do. 3. Substituting with units, 1/di = 1 divided by (-10.0 cm) minus 1 divided by 7.50 cm. 4. This is -0.1000 per cm minus 0.1333 per cm = -0.2333 per cm. 5. Inverting, di = -4.29 cm, so the image is on the same side as the page and is virtual. 6. The magnification is m = minus di divided by do = minus (-4.29 cm) divided by 7.50 cm = +0.571. 7. Positive and less than one means upright and a little over half the size, and the image sits closer to the lens than the page does. 8. The -30.0 cm answer belongs to the converging case with f = +10.0 cm and appears whenever the minus sign on f is dropped. _Source: OpenStax College Physics (CC BY 4.0), Ch 25 "Geometric Optics", section 25.6 Image Formation by Lenses_