MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures
Problem
A school bus is 2.6 m wide. A rear-view mirror is mounted 0.60 m in front of the driver’s eyes. The driver must be able to see the full width of the bus when the tail of the bus is at least 10 m behind the mirror.
(a) State whether a concave or a convex spherical mirror should be chosen for this purpose and give one reason for your choice.
(b) Treating the mirror as small compared with the distances involved, show that the required linear magnification does not exceed 0.05.
(c) Using the magnification obtained in part (b), calculate the maximum value of the focal length and hence the minimum radius of curvature the mirror must have.