A camera maker wants to replace an 800 mm focal length telephoto lens with a mirror. What radius of curvature must the mirror have?

1. The mirror must have the same focal length as the lens it replaces, so f = 800 mm. 2. For a spherical mirror the focal length is half the radius of curvature, f = R divided by 2. 3. Rearranging gives R = 2f. 4. Substituting with units, R = 2 times 800 mm = 1600 mm. 5. Answering 400 mm halves the focal length instead of doubling it, which is the usual direction error with f = R divided by 2. _Source: OpenStax College Physics (CC BY 4.0), Ch 25 "Geometric Optics", section 25.7 Image Formation by Mirrors_