A clear glass light bulb sits 0.750 m from a convex lens whose focal length is 0.500 m. What are the image distance and the magnification?

1. Fix the sign convention first: the object distance do is positive, f is positive for this convex lens, and a negative image distance would mean a virtual image on the object's side. 2. The thin lens equation is 1/do + 1/di = 1/f, which rearranges to 1/di = 1/f - 1/do. 3. Substituting with units, 1/di = 1 divided by 0.500 m minus 1 divided by 0.750 m. 4. This is 2.000 per metre minus 1.333 per metre = 0.667 per metre. 5. Inverting, di = 1 divided by 0.667 per metre = 1.50 m, and the positive sign puts the image on the far side of the lens. 6. The magnification is m = minus di divided by do = minus 1.50 m divided by 0.750 m = -2.00. 7. The +2.00 option drops the minus sign built into the magnification equation and would wrongly call the image upright. 8. The -1.50 m option ignores that the object sits farther out than the focal length, which always gives a positive image distance. _Source: OpenStax College Physics (CC BY 4.0), Ch 25 "Geometric Optics", section 25.6 Image Formation by Lenses_