A designer wishes to install a single vertical plane mirror in a clothing store changing room. Shoppers’ eyes are typically at a height h above the floor, while their total height is H (h<H). The mirror’s lower edge is to be mounted at a distance d above the floor.
Answer the following questions in symbolic form (express all results in terms of H, h, and d).
(a) Derive an expression for the lowest point on the mirror that a shopper must be able to see in order to view their shoes. Assume the shoes are essentially at floor level.
(b) Derive an expression for the highest point on the mirror that must be visible for the shopper to see the top of their head.
(c) Hence obtain an expression for the minimum mirror height Lmin that guarantees the entire body is visible regardless of eye height h (provided h lies between 0 and H).
(d) For a 1.75m-tall shopper whose eyes are 1.65m above the floor, determine the numerical value of Lmin if the mirror’s lower edge is 0.40m above the floor. State whether increasing or decreasing d would shorten the required mirror length, and justify your answer.