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 0.8610 m from the mirror. The same mirror is then used to produce an image of the tree. The image of the tree is 0.9902 m from the mirror. (a) How far away is the tree? (b) The image height of the tree has a magnitude of 0.20 m. How tall is the tree?

Answer 1

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

1/0.8610 - 1/ 0.9902 = 1/u

proceed as first example, ie common denominator etc,

you should have 1/u = 0.1515

turn it around to get u= 6.600 m