Mirror Placement for 1.60m Body: Answers Revealed

[Voltman]

Assume that your eyes are located at the top of your 1.60 m tall body.
a) What size plance mirror would you need to see your whole body if you were standing 1 m from it?
b) How far from the floor should the bottom edge of the mirror be placed?
c) How would your answers to (a) and (b) change if you assumed your eyes were 10 cm from the top of your head?
d) How would your answers to (a) and (b) change if you were 2 m from the mirror?


I'm not sure how to start these problems. However, I suspect that you'd have to know that the angle of incidence equals the angle of reflection since that seems the most relevant thing to what we've done so far. Anyway any explanations, tips or other help will be appreciated!

 

[tiny-tim]

Hi Voltman!

Tip: Draw both the object and the image, and treat the mirror like a window.

 

[nlightner]

a) To see your whole body, you would need a plane mirror that is at least 1.60 m tall (the same height as your body). This would allow you to see your entire body reflected in the mirror from a distance of 1 m.

b) The bottom edge of the mirror should be placed 1.60 m - 1 m = 0.60 m from the floor. This would ensure that your entire body is reflected in the mirror.

c) If your eyes were 10 cm from the top of your head, the size of the plane mirror needed to see your whole body would still be 1.60 m, but the bottom edge of the mirror should now be placed 1.60 m - 1 m - 0.10 m = 0.50 m from the floor. This is because the distance from your eyes to the bottom edge of the mirror has decreased by 10 cm.

d) If you were 2 m from the mirror, you would need a larger plane mirror to see your whole body. The size of the mirror would now need to be 1.60 m x 2 = 3.20 m tall. The bottom edge of the mirror should still be placed 0.60 m from the floor, as this is the height at which your eyes are located.