A passenger-side rear-view mirror on a vehicle is a section of a spherical surface with a radius of curvature of 1.20m. The vehicle manufacturer wants objects that are 0.40m tall to appear no larger than 0.15m tall when they are just close enough to be noticed by the driver. For design purposes, treat the objects as point sources on the principal axis.
(1) Determine the focal length of the mirror, including its algebraic sign.
(2) The manufacturer wants the virtual image of an object to appear 0.40m behind the mirror. Calculate the object distance that satisfies this requirement.
(3) For the object distance found in part (b), calculate the magnification and confirm that the design goal for apparent height is met.
(4) If the object moves twice as far from the mirror as the distance found in part (b), state qualitatively how the image distance and magnification will change, and justify your answer without performing additional calculations.