You are preparing to go shopping for a plane mirror that will be hung on the wal

Question

You are preparing to go shopping for a plane mirror that will be hung on the wall of your dressing room. Your overall height is H = 1.8 m, and the vertical distance from the floor to the mid-line of your eyes is H1 = 1.61m. 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 = 2.2 m from the mirror. Being frugal, you want to purchase the smallest possible mirror.

1.What height d above the floor should the bottom of the mirror be mounted?

2.What is the minimum required mirror height (vertical dimension)?

3.If instead, you want to be able to view your entire body in the mirror while standing at twice the distance away, D' = 4.3 m, what is the minimum required mirror height in this case? 4.Return now to the mirror height and viewing distance of part (2). Suppose you wish to take a picture of yourself in the mirror using a camera that you hold exactly at mid-height (lens at a distance H/2 above the floor). What height s above the floor should you place the top of the mirror 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 entire mirror.)

5.In the configuration of part (4), what amount H of your lower body (feet and legs) will be cut off in the photographic image?

6.If you move toward the mirror at 2 m/s, how fast will your image be moving toward you?

Explanation / Answer

a). Height above floor = 1/2 eye height, = 805cm.
b) Mirror height. 1.61 + 1/2 (1.8 - 1.61) = 1.705m to top.
1.705 - .805 = 0.9m. mirror length.
c) Remains the same. Only angle of incidence and reflection alters.
d) Height of camera lens = 0.9m. Height of top of head = 1.8m.
Height of top of mirror = (0.9 + .5) = 1.4m from floor.
e) Bottom of mirror is .5m above floor. Camera is 1m above floor. So legs and feet are visible to it.
f) Double, = 4m/sec.

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