A tall tree is growing across a river from you. You would like to know the dista

Question

A tall tree is growing across a river from you. You would like to know the distance between yourself and the tree, as well as its height, but are unable to make the measurements directly. However, by using a mirror to form an image of the tree and then measuring the image distance and the image height, you can calculate the distance to the tree as well as its height. Suppose that this mirror produces an image of the sun, and the image is located 0.8528 m from the mirror. The same mirror is then used to produce an image of the tree. The image of the tree is 0.9980 m from the mirror. (a) How far away is the tree? (b) The image height of the tree has a magnitude of 0.12 m. How tall is the tree?

Explanation / Answer

(a)
Because the sun is far enough away to essentially be considered at "infinity", its image is formed at a distance equal to the focal length -- that is, f = 0.8528 m

1/f = 1/Di + 1/Do
1/0.8528 m = 1/0.9980 m + 1/Do
1.1726 = 1.002 + 1/Do
0.171 = 1/Do
Do = 5.86 m

(b)
m = -Di/Do = Hi/Ho
m = - 0.9980 m / 5.86 m = - 0.17 (the - means inverted)
Ho = -Hi / m = -0.12 m / -0.17
Ho = 0.705 m

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