Passenger-side rear-view mirrors on automobiles are typically convex and are often labeled with the warning, “Objects in mirror are closer than they appear.” Consider a spherical convex mirror of radius 1.5 m mounted on the passenger door. A cyclist 12 m behind the car and in the same lane is observed by the driver.
(1) Explain qualitatively why the convex mirror causes the cyclist to appear farther away than the actual 12 m distance. Your explanation should reference both the type of image formed and the relationship between object distance and image distance for a convex mirror.
(2) Describe how the image’s angular size (the angle it subtends at the driver’s eye) compares with the angular size that would be observed in a plane mirror of the same width placed at the same location. Provide reasoning based on the mirror type and object placement.
(3) The driver replaces the mirror with a concave mirror of the same radius, keeping the mirror orientation the same. Predict and explain the qualitative changes, if any, in the perceived distance and orientation of the cyclist’s image.