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A child looks at his reflection in a spherical tree ornament 12.0 cm in diameter, and sees an image of his face that us reduced by one-fourth. How far is his face from the ornament?

  • physics -

    The radius of curvature of the ornament is 6.0 cm and the focal length is half that, 3.0 cm. Because if is convex, the focal length is considered negative.

    For the image position,
    1/do + 1/di = 1/f = -1/3.0

    Since there is a demagnification of 1/4, di = -do/4
    I used a minus sign because the image will be virtual, behind the reflecting surface.
    1/do + 1/di = 1/do -4/do = -1/3
    -3/do = -1/3
    do = 9 cm.

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