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39. Review Conceptual Example 1 before attempting this problem.
A person whose eyes are 1.70 m above the floor stands in front of a plane
mirror. The top of her head is 0.12 m above her eyes. (a) What is the height of the shortest mirror in
which she can see her entire image? (b) How far above the floor should the bottom edge of the mirror be
placed? |
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The figure above shows the
various rays needed. We have one from
the feet to the eyes and one from the eyes to the top of the head. |
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The Law of reflection says the
angles I have called qL
which are the angles of incidence and reflection which must be the
same. Therefore
the bottom of the mirror to the height of the eyes must be ½ the height from
the eyes to the feet as can be seen in the diagram since those two angles are
the same. Similarly from the height of
the eyes to the top of the mirror there is another set of incidence and
reflecting angles which must be the same, so the
mirror must have the distance of ½ the height from the top of the head to the
eyes. So we can add these two
distances together the to get the total length
required of the mirror. |
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Note: This is really just
one-half the total height of the person! |
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The distance off the floor is
one half the eyes to feet distance so here |
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