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Math Help - Mirrors

  1. #1
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    Mirrors

    Hey guys,

    I got a question here:

    Facing a slightly steamed-over mirror, hold one eye shut and trace the outline of your face in the mirror. Explain why the outline is exactly 1/2 the width and 1/2 the height of your face.

    I have no idea how to approach this question and anyyy help would be greatly appreciated.
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  2. #2
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    Hello GreenDay14
    Quote Originally Posted by GreenDay14 View Post
    Hey guys,

    I got a question here:

    Facing a slightly steamed-over mirror, hold one eye shut and trace the outline of your face in the mirror. Explain why the outline is exactly 1/2 the width and 1/2 the height of your face.

    I have no idea how to approach this question and anyyy help would be greatly appreciated.
    Study the attached diagram.

    The line AB represents the width of your face, with E as your right eye. A'B' is the reflection of your face in the mirror, which lies along the line MPQ.

    Then it is well known that the distances of the object and its reflection from the mirror are equal. So
    AM = MA'

    \Rightarrow AM = \tfrac12AA'
    A ray of light from A hits the mirror at P and is reflected into your eye, E, producing an image of A at A'. So EPA' is a straight line, with P the apparent point on the mirror of the position of A'.

    Similarly for Q: this is the apparent point on the mirror of the position of B'.

    By similar triangles, since AM = \tfrac12AA', we can easily prove that PQ = \tfrac12A'B' = \tfrac12AB.

    Grandad
    Attached Thumbnails Attached Thumbnails Mirrors-untitled.jpg  
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