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

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The discussion focuses on calculating the height of a tree using a plane mirror measurement technique. A plane mirror measuring 4.3 cm tall is positioned 32 cm from the observer's eye, with the tree located 28 m away from the mirror. An initial calculation suggested the tree's height is 205 meters, but this was deemed incorrect. Participants recommend using a ray diagram to visualize the light rays from the tree to the mirror, emphasizing the importance of extending these rays beyond the mirror for accurate height determination. The conversation highlights the need for careful application of geometric principles in such measurements.
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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.
 
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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?
 

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