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.

(c) Having measured the image distance di and the image height hi of the tree, as well as the image distance of the sun, how would you use these numbers to determine the distance to and the actual height of the tree?


An application of the mirror equation and the magnification equation will give the distance to and the height of the tree.


An application of the mirror equation alone will give both the distance to and the height of the tree.


An application of the magnification equation alone will give both the distance to and the height of the tree.

Explanation / Answer

i am assuming it is a concave mirror: 1/f = 1/u + 1/v Distance to sun is 1.496 x 10(11) (that is 10 to the power of 11) Find focal length between sun and sun image: 1/f = 1/1.496 x10(11) + 1/1.075 get common denominator of 160,820,000,000 so you will have 1.075 + 1.496 x10(11) over 160,820,000,000 so you will end up with 1/f = 149,600,001,100/160,820,000,000 but we want f, not 1/f so turn the fraction around and get f = 1.075 now you start again and substitute into a new formula: 1/f = 1/u + 1/v this is for the tree now. the same mirror is being used to measure the distance to tree, so it has the same focal length. we know what its focal length is from previous calculation, 1.075. so sub into i/f formula: 1/f - 1/v = 1/u 1/1.075 - 1/ 1.189 = 1/u proceed as first example, ie common denominator etc, you should have 1/u = 0.1109/ 1.2748425 turn it around to get u= 11.5 m

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