A plane mirror made of a very thin piece of glass lies flat on the ground. As sh
ID: 1260108 • Letter: A
Question
A plane mirror made of a very thin piece of glass lies flat on the ground. As shown in the following figure, one end of the mirror is 2.4 m from you and the other end is 37 m from a nearby tree. You are 1.6 m tall, and the mirror has a length L. The mirror is arranged so that you can just see the image of the top of the tree at one edge of the mirror, and you can just see a point halfway up the tree at the other edge of the mirror.
(a) How tall is the tree?
m
(b) What is L?
m
Explanation / Answer
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A plane mirror made of a very thin piece of glass lies flat on the ground. As shown in the following figure, one end of the mirror is 1.9 m from you and the other end is 37 m from a nearby tree. You are 1.9 m tall, and the mirror has a length L. The mirror is arranged so that you can just see the image of the top of the tree at one edge of the mirror.
http://i965.photobucket.com/albums/ae135...
(a) How tall is the tree? in m
(b) If you can just see a point halfway up the tree at the other edge of the mirror, what is L? in m
Answer: h = 1.9m
d1 = 1.9m
d2 = 37m
Therefore, ?1 = 45 degrees.
Since the angle of reflection is 90 degrees, the other triangle will also be isosceles.
So, the height of the tree is d2 + L.
Not really sure how you would find it without L...?
tan(?2) = 1.9/(1.9+L)
tan(?2) = .5*h2/37
1.9/(1.9+L) = .5 * (37 + L)/37
2 * 37 * 1.9 = (1.9 + L) * (37 + L)
140.6 = 70.3 + 38.9L + L^2
L^2 + 38.9L - 70.3 = 0
L = 1.7302 m
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