At a blind corner inside a supermarket, the manager wants to install a single spherical mirror near the ceiling so that staff pushing trolleys along one aisle can see shoppers approaching from a perpendicular aisle 3.0m away.
(i) State which type of spherical mirror should be selected for this purpose and justify your choice by comparing its field of view and image size with those of the other two kinds of spherical mirrors.
(ii) The chosen mirror has a radius of curvature of 1.8m. Calculate the position and magnification of the image of a shopper who is 3.0m from the mirror along the principal axis.
(iii) Using the result of part (ii), explain whether the mirror will allow trolley-pushers to notice the shopper in sufficient time to avoid a collision. Base your answer on both the image position and its size.