Calculating Tree Height: Using a Plane Mirror to Measure 205m

[Punkyc7]

the image of a tree just covers the length of a plane mirror 4.3 cm tall when the mirror is held 32 cm from the eye. The tree is 28 m from the mirror.

What is the height of the tree?


so I set up a ratio

.043/.32=(28-.32)/h

and solved for h and got 205 meters, but I am not sure if that is correct.

 

[gneill]

No, 205 meters is not correct.

Draw a ray diagram. A ray from the top of the tree should just touch the top of the mirror. Another ray from the bottom of the tree should just touch the bottom of the mirror. The rays reflecting from the mirror surface, we are told, come together at the distance of the viewer's eye, some 32cm in front of the mirror.

What would happen if you were to extend the lines of those rays past the mirror?