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Trouble with mirror equations, need help.

  1. Oct 1, 2006 #1
    heres the problem:
    a dentist wants a small mirror that, when 2.20cm from a tooth, will produce a 4.5x upright image. what kind of mirror must be used and what must its radius of curvature be?

    so i did the following calculations with the mirror equations i learned:

    m=4.5

    equation to get the di [​IMG]

    4.5*(-2.20) = di di=-9.9

    1/do+1/di=1/f

    1/(-2.2) + 1/(-9.9) = 1/f

    1/(-2.2)=(-0.454545455)
    1/(-9.9)=(-0.101010101)

    (-0.454545455)+(-0.101010101)=(-0.555555556)

    1/(-0.555555556)=f

    1/(-0.555555556)=(-1.8)

    f=(-1.8)

    f2 = r

    -1.8 * 2 = -3.6

    so the radius is -3.6 and i guess it is concave as only concave mirrors 1.0+ magnify? that's wrong as my book says the correct answer is 5.66cm, concave. what am i doing wrong:confused:
     

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  3. Oct 1, 2006 #2

    Doc Al

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    Staff: Mentor

    The object distance should be +2.2, not -2.2.
     
  4. Oct 2, 2006 #3
    ok, thanks alot. so doesn't "- di/2.2" mean that both di and 2.2 are negative values?
     
  5. Oct 2, 2006 #4

    Doc Al

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    Staff: Mentor

    Not sure what you mean. Think of it this way. You know that do is positive: do = +2.2 cm. The magnification is positive, since the image is upright: m = +4.5. Since m = -di/do, that tells you that di is negative: di = -m*do = -9.9 cm.
     
  6. Oct 2, 2006 #5
    what about convex mirrors? can i use exactly the same equations for them? on my next task (m=0.33 do=20) i had to calculate the radius for this convex mirror and i got -19.7, so if - means that the image is inverted, and as far as i know convex ones don't generate inverted images, should i remove the - or something?

    and does a magnification of 2.0 mean that the di is just twice as short as do while m0.5 means that di is twice as long as do?
     
  7. Oct 2, 2006 #6

    Doc Al

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    Staff: Mentor

    The basic equations are the same.
    A negative magnification means that the image is inverted, but a negative radius just means that the mirror is convex.

    No, just the opposite. Review the definition of magnification, given by the equation: m = -di/do

    So a magnification of 2.0 means that di is twice as long as do.
     
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