Suppose you are getting ready to go somewhere where you want to look nice, so, before you leave, you check to see how you look in the mirror. You are also interested in seeing how well your shoes go with the rest of your outfit, but you can't see your feet in the mirror. The reflection in the mirror goes only to your knees. Do you move closer to the mirror to be able to see your feet or do you move farther away?
It turns out that if you are standing straight up and the mirror is also vertical, it won't make any difference. No matter whether you move closer or farther away, you will always be able to see to the same point on your legs. Consider the following diagram
T is the top of the mirror, B is the bottom of the mirror, E is the location of your eye, and L is as far down on your legs as you can see. F is your feet, and W is the point on your waist which is at the same level as the bottom of the mirror. The law of physics that governs reflections is called Snell's Law which says that the angle of incidence, /EBW is the same size as the angle of reflection, /LBW. From this we can extract the following given information.
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Given: |
AT is perpendicular to AF EF is perpendicular to AF BW is parallel to AF |
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Snell's Law |
/EBW = /LBW |
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To prove: |
EW = WL |
This says that the distance from your eye to how far down you can see on your leg will always be twice the distance from the level of you eye to the level of the bottom of the mirror, no matter where you stand.