To improve rear-view visibility, an automobile manufacturer evaluates two mirror designs for a passenger-side mirror: (i) a plane mirror and (ii) a convex spherical mirror. In normal traffic conditions, a following car that is 1.8 m wide is typically located 10.0 m behind the mirror along the central axis. The current convex design has a focal point located 0.40 m behind the mirror surface.
(a) For the existing convex mirror, calculate the apparent width of the following car as seen by the driver. Assume the car’s width is perpendicular to the principal axis.
(b) For the same traffic scenario, compute the apparent width of the car if a plane mirror were installed instead.
(c) The engineering team proposes reducing the apparent width to 0.30 m, keeping the car at the same 10.0 m distance. Determine the focal length a new convex mirror must have to meet this specification.
(d) Discuss qualitatively two potential trade-offs the driver might experience when switching from the focal length found in part (c) to the plane mirror considered in part (b). Frame your discussion in terms of field of view, depth perception, and safety considerations.