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Converging lens solve for all variables given f, Hi, and Ho

  1. May 7, 2017 #1
    1. The problem statement, all variables and given/known data

    RgwwJmfVduBPWG4cfwnHZTMzsxsMgsBWP1VjmUP3g1E70Ct1Dl96lejtSL8ErrTMberzTnY5Q9__GcW9Tk=w1836-h117-no.jpg

    What is directly given in the problem:
    Converging lens with f=1.43m
    Hi = 2m

    2. Relevant equations

    Hi/Ho = di/do
    M = Hi/Ho = di/do
    1/f = 1/do + 1/di

    3. The attempt at a solution

    Ho = 2m * 20 = 40m
    Not sure how I can get do from this. All of the equations seem to need di.
     
  2. jcsd
  3. May 7, 2017 #2
    You can get the object height from the magnification. Since the image is [itex]20[/itex] times smaller than the object, [itex]M=1/20[/itex]. We also know that [itex]H_i=2 \, m[/itex].

    To get the distance to the coaster, multiply [tex]\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}[/tex] through by [itex]d_o[/itex] and substitute [itex]1/M=20[/itex] for [itex]d_o/d_i[/itex]. You know the focal length, so it shouldn't be difficult to solve for [itex]d_o[/itex] from there.
     
  4. May 8, 2017 #3

    andrevdh

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    Homework Helper

    the image is 20x smaller than the object so

    hi = 1/20 ho

    giving us

    hi/ho = 1/20

    but hi/ho = di/do

    so we also have that

    di/do = 1/20

    so that we have that the object distance in terms of the image distance is

    do = .... ?
     
  5. May 8, 2017 #4
    Multiply the equation [tex]\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}[/tex] through by [itex]d_o[/itex]. This gives you the equation [tex]\frac{d_o}{f}=\frac{d_o}{d_o}+\frac{d_o}{d_i}[/tex] [itex]d_o/d_o=1[/itex] and [itex]d_o/d_i=1/M[/itex] Solve for the remaining [itex]d_o[/itex].
     
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