You are preparing to go shopping for a plane mirror that wil

You are preparing to go shopping for a plane mirror that will be hung on the wall of your dressing room. Your over all height is H = 2.4 m. and the vertical distance from the floor to the mid-line of your eyes is H_1 = 2.24m. You want the mirror to be tall enough to allow you to view your entire body from the tip of your head to the soles of your feet, while standing a horizontal distance D = 1.5 m from the mirror. Being frugal, you want to purchase the smallest possible mirror.

Solution

a) Height above floor = 1/2 * eye height = 2.24 / 2

= 1.12 m

b) mirror height = 2.24 + 1/2 (2.4 - 2.24) = 2.32 m

h_min = 2.32 - 1.12 = 1.2 m

c) h_min = 1.2 m

Remains the same

d) Height of top of mirror = 1.2 + 0.5 = 1.7 m

e) 0 m

f) Double times = 2 * 2.1 = 4.2 m/s