Object Height In a Plane Mirror

[rmcgovern]

Homework Statement

The image of a tree just covers the length of a plane mirror 3.80 cm tall when the mirror is held 40.0 cm from the eye. The tree is 20.0 m from the mirror. What is the height of the tree?

Homework Equations

m=y'/y, s=s'=20m (from problem statement)

The Attempt at a Solution

At first I simply thought the height of the image in the plane mirror is equal to the height of the object, this however is incorrect. Where I am puzzled is how to factor in the distance of the observer from the mirror, and how the object height can be different from the image height when lateral magnification in a plane mirror=1. Any suggestions on how to begin this problem are greatly appreciated, geometric optics are proving to be quite difficult for me to grasp.

 

[CWatters]

how the object height can be different from the image height when lateral magnification in a plane mirror=1.

There is no substitute for actually going and looking in a mirror! Look at the top edge of the mirror. I bet you can see an image of the ceiling above and behind you. You try this outdoors you might even be able to see the sky reflected in the mirror. How high is the sky yet its image fits in the mirror :-)

Joking aside... Draw the set up with the tree as described in the problem. Draw a ray of light from the top of the tree to your eye via the mirror. Behind the mirror draw an image of the tree and a dotted line to your eye.

To answer the question apply the principle of "similar triangles".

If you get stuck post your drawing.

 

[rmcgovern]

Thanks for your help! A correctly drawn diagram led me right to the solution.