You are preparing to go shopping for a plane mirror that will behung on the wall

Question

You are preparing to go shopping for a plane mirror that will behung on the wall of your dressing room. Your overall height isH = 2.2 m, and the vertical distance from the floor to themid-line of your eyes is H1 = 2.09 m. You wantthe mirror to be tall enough to allow you to view your entire bodyfrom the tip of your head to the soles of your feet, while standinga horizontal distance D = 1 m from the mirror. Beingfrugal, you want to purchase the smallest possible mirror.

(a) What height d above the floor should thebottom of the mirror be mounted?

d = m   

(b) What is the minimum required mirror height (verticaldimension)?

hmin = m   

(c) If instead, you want to be able to view your entire body inthe mirror while standing at twice the distance away, D' =5.5 m, what is the minimum required mirror height in thiscase?

h'min = m    

(d) Return now to the mirror height and viewing distance of part(b). Suppose you wish to take a picture of yourself in the mirrorusing a camera that you hold exactly at mid-height (lens at adistance H/2 above the floor). What height sabove the floor should you place the top of themirror so that the top of you head is just included in the image?(Assume the camera field-of-view is wide enough to image the entiremirror.)

s = m    

(e) In the configuration of part (d), what amountDH of you lower body (feet andlegs) will be cut off in the photographic image?

DH = m

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