Height of Mirror Needed to See Table in Mirror

AI Thread Summary
To determine the minimum height of a mirror needed to see the top of a table from a distance, one must consider the geometry of reflection. The height of the mirror must be calculated using similar triangles formed by the line of sight from the eye to the top of the table and the reflection point on the mirror. The proposed formula, (H - 0.8)/1.5 = (1.9 - H)/3.5, helps find the height of the mirror (H) in relation to the height of the table (0.8 m) and the distance from the observer to the mirror (3.5 m). The initial guess of 1.2 m for the mirror height was incorrect, indicating a need for careful calculation. Ultimately, solving the equation will yield the precise minimum height required for the mirror.
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Homework Statement


You are 1.9 m tall and stand 3.5 m from a plane mirror that extends vertically upward from the floor. On the floor 1.5 m in front of the mirror is a small table, 0.80 m high.

a) What is the minimum height the mirror must have for you to be able to see the top of the table in the mirror?


Homework Equations



pythag. theorem?

The Attempt at a Solution


i know the mirror has to be half as tall as the person in order to see their body but I'm not sure how to use this knowledge to translate it to the table. thanks for your help!
 
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Can you draw the ray diagram?
Let h be the height of the table and H be the minimum height of the mirror from the ground.
A ray from the top of the table T falls on the mirror at M and reflects towards your eye E. Draw two parallel lines from T and M to the ground. Parallel line from T meets the mirror at N and parallel line from M meets you at P.
Now you can varify easily that the triangles EPM and TNM are similar. So the sides of the triangles are proportional. With these hints try to find the minimum height of the mirror.
 
i got like 1.2m but it said it was wrong.
 
The formula becomes
(H - 0.8)/1.5 = (1.9 - H)/3.5)
Solve for H.
 
thanks! i was close lol
 

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