A convex spherical mirror with a radius of curvature of 14.5 cm produces a virtu
ID: 2011551 • Letter: A
Question
A convex spherical mirror with a radius of curvature of 14.5 cm produces a virtual image one half the size of the real object. Where is the object? _____cm (from the object)Explanation / Answer
Equations: 1/f = 1/di + 1/do (General equation), f (focal length) = r (radius of curvature)/2 hi/ho = -di/do -->magnification equation (1) Since the virtual image is one half the size of the real object: hi/ho = 1/2 1/2 = -di/do. (2) Solve for di--> di = -do/2 (3) 1/f = 1/di + 1/do = 1/(-7.25) = 1/(-do/2) + 1/do = -2/do + 1/do = -1/do -->The reason why f is negative is because the spherical mirror is CONVEX. (3a) 1/(-7.25) = -1/do -->The object will be -7.25cm away.