An electric room heater uses a concave mirror with a radius of curvature of 50.0 cm to project a real image of its hot coils 3.00 m in front of the mirror. Using f equals R over 2, how far are the coils from the mirror?

1. The focal length is half the radius of curvature: f = R/2 = 50.0 cm / 2 = 25.0 cm, positive because the mirror is concave. 2. The image distance is given as d_i = 3.00 m = 300 cm, positive because the image is real. 3. Rearranging the mirror equation gives d_o = (d_i f) / (d_i - f). 4. Substituting values: d_o = (300 x 25.0) / (300 - 25.0) = 7500 / 275. 5. Carrying out the division gives d_o = 27.3 cm. 6. 12.5 cm is half the focal length rather than the object distance, and 50.0 cm just repeats the radius of curvature. 7. 300 cm repeats the image distance rather than solving for where the coils actually sit. _Source: OpenStax Physics (CC BY 4.0), Ch 16 "Mirrors and Lenses", section 16.1 Reflection_