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Plane Mirrors

  1. Mar 17, 2010 #1
    1. The problem statement, all variables and given/known data
    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?


    2. Relevant equations

    pythag. theorem?

    3. 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!
     
  2. jcsd
  3. Mar 18, 2010 #2

    rl.bhat

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    Homework Helper

    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.
     
  4. Mar 18, 2010 #3
    i got like 1.2m but it said it was wrong.
     
  5. Mar 18, 2010 #4

    rl.bhat

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    Homework Helper

    The formula becomes
    (H - 0.8)/1.5 = (1.9 - H)/3.5)
    Solve for H.
     
  6. Mar 18, 2010 #5
    thanks! i was close lol
     
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