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 0.9496 m from the mirror. The same mirror is then used to produce an image of the tree. The image of the tree is 1.0421 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

We have formed an image of the tree and sun and measured it. So, we have used a concave mirror which forms real and inverted images which can be caught on screen.

We are using the cartesian coordinate system in which for a concave mirror, all u (object distance), v (image distance) and f (focal length) are negative.

Sun can be considered to be at infinity(very far). So, the rays of the sun which are parallel converge at focus.

So, we conclude that the focal length of the concave mirror isn f= -0.9496 m

image distance v of the tree is v = - 1.4024 m

using the mirror formula 1/f = 1/v + 1/u

1/ (-0.9496) = 1/ (-1.4024) + 1/u

1/u = - 0.340011658

u = - 2.941075618 m

So, the tree is at a distance of 2.941075618 m from you.

mirror magnification m = h'/h = - v/u

h' = image height = -0.12 since concave mirror forms real and invereted images

h' /h = - (v/u)

- 0.12 / h = - (- 1.4024 / - 2.941075618 ) = - 0.47683235

h = -0.12 / -0.47683235 = 0.251660777 m

So, the tree is 0.25166 m tall.

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