*47. Concept Questions A tall tree is growing across a river from you. You would

Question

*47. Concept Questions A tall tree is growing across a river from you. You would like to know the di?tance between yourself and the tree, as well as its height, but are unable to make the measurements directly. However, by using only 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. (a) What kind of mirror, concave or convex, must you use? Why (b) You will need to know the focal length of the mirror. The sun is shining. You aim the mirror at the sun and form an image of it. How is the image distance of the sun related to the focal length of the mirror? (c) Having measured the image distance d and the image height hy of the tree, as well as the image distance of the sun, de- scribe how you would use these numbers to determine the distance and height of the tree. Problem A mirror produces an image of the sun, and the image is located 0.9000 m from the mirror. The produce an image of the tree. The image of the tree is 0.9100 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? same mirror is then used to

Explanation / Answer

47. Because the sun is very far away, it will be considered as at infinity

so as per lens equation, 1/f = 1/do + 1/di

so 1/do = 0 (infinity)

so 1/f = 1/di

therefore, di = f

It means the focal length is equal to the image distance. so to find object distance for tree, we will need lens equation

1/f = 1/do + 1/di-tree

where f = di (distance of image of sun)

Therefore, 1/do = 1/di - 1/di-tree

To find height of tree

hi/ ho = -di / do

we can find ho from this

Now, to solve with numbers, we are given

di ( sun image's distance) = 0.9 m

di-tree = 0.91 m

Using lens equation,

1/do = 1/0.9 - 1/0.91 ( Remember distance of image of sun is equal to focal length)

do = 81.9 m

Now to find height of tree

hi/ ho = -di / do

0.12 / ho = - 0.91 / 81.9

ho = 10.8 m

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