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Math Help - Mirrors

  1. #1
    Newbie iEricKim's Avatar
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    Mirrors

    A concave spherical mirror can be used to
    project an image onto a sheet of paper, allow-
    ing the magnified image of an illuminated real
    object to be accurately traced.
    a) If you have a concave mirror with a focal
    length of 12 cm, where would you place a
    sheet of paper so that the image projected
    onto it is twice as far from the mirror as the
    object is? Answer in units of cm.

    Okay. So I got it down to:
    1/f = 1/(2p) + 1/p
    which is:
    1/12 = p/2 + 1/p

    I'm pretty sure you just need to solve for "p" and then "q" would be twice of "p".

    "p" = distance of object from mirror
    "q" = distance of image from mirror

    How do I solve for "p"? I can't believe I forgot how to do this. T_T
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  2. #2
    Super Member
    earboth's Avatar
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    Quote Originally Posted by iEricKim View Post
    ...
    a) If you have a concave mirror with a focal
    length of 12 cm, where would you place a
    sheet of paper so that the image projected
    onto it is twice as far from the mirror as the
    object is? Answer in units of cm.

    Okay. So I got it down to:
    1/f = 1/(2p) + 1/p

    ...
    \dfrac1{2p}+\dfrac1p=\dfrac1f~\implies~\dfrac1{2p}  +\dfrac2{2p}=\dfrac1{12} ~\implies~\dfrac3{2p}=\dfrac1{12}~\implies~\dfrac{  2p}3=12~\implies~\boxed{p=18}

    Can you take it from here?
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