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Homework Help: Optics question- two lens system

  1. Oct 10, 2008 #1
    My teacher assigned us 2 problems to do that were the exact same. One he wanted us to use the thin lenses equation, and the other he wanted us to use think lens equation. i need help becuase I dont know which one I am doing wrong and my answer is not lining up as it should, since they are the same problem, it should be the same solution. I think I am messing up on the thin lense beucase he worked out part of it out when he wanted us to use think lense

    1. The problem statement, all variables and given/known data
    Find the effective focal length of the two lens system. The focal length of the first lens is 20 cm and the second lens is -20 cm with the seperation between the two lens being 10 cm. Locate the principal planes. Locate the image of an object that is 1 m in front of the first lens. Express the location relative to the location of the second lens.

    f1is 20cm
    f2is -20
    and the distance between the two is 10 cm
    the object is 1m(100 cm) in front of the first lens

    2. Relevant equations
    for thick lense the equation is :

    (1/so) + (1/si) = 1/f

    and f of both lens is found by ff = ((1/f1) + (1/f2) - (d/f1f2))-1

    for the thin lens it is

    si2 = ((1/f2) - (1/so2))-1

    3. The attempt at a solution

    For the thick lens I found
    h1 = -(f1f2)d/f2 = -20
    h2 = -(f1f2)d/f1 = -20

    so = d - (h1 = 80
    and that ff = 40 from the above equation
    i had (1/80) + (1/si) = 1/40
    solved for si = 80

    However for thin lens I found

    So1 = 100cm
    f1 = 20 cm
    Si1 = ((1/f1) - (1/so1))-1 = 25

    then so2 = d - si1 = 10 cm - 25 cm = -15 cm

    finally si2 = ((1/f2)-(1/so2))-1 = 60

    obviously 60 does not equally 80 and I have no idea what I did wrong. I think that what I got for so for the thick lens is wrong because when i switch it to 120 i get 60 . However my professor said that so was 80.
    Last edited: Oct 10, 2008
  2. jcsd
  3. Oct 10, 2008 #2


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    Science Advisor
    Gold Member

    Wouldn't you expect the distances to be different? For thick lenses, the thickness of the lens can't be negligible as in the thin lens case.
    Welcome to PF, btw.
  4. Oct 10, 2008 #3
    Thanks. I found PF awhile ago but I have just been browsing for the most part until now.

    I would expect the distances to be different beucase of that reason, however my professor said they should be the same.

    so I dont know if I am doing it wrong, or he told us wrong.
  5. Oct 12, 2008 #4
    shameless bump
  6. Oct 15, 2008 #5
    Hey there, your principle plane ([itex]h_2[/itex]), is incorrect, it should yield a positive value. Your [itex]s_i[/itex], you should get your [itex]s_i = 80cm[/itex] is correct, but this is the distance from the principle plane. So you must subtract the [itex]+20cm[/itex] to get the distance from the second lens.

    Both the thick lens and thin lens formulas give you the same answer. Sanity check here, if the experimental setup remains the same. Do you expect using different calculations (with appropriate approximations), to give a different answer? I hope not.

    Best regards,
    Last edited: Oct 15, 2008
  7. Oct 15, 2008 #6
    Thanks. I finally got it and forgot to post on here that I figured out what was wrong

    This thread can be locked beucase it was solved
  8. Oct 18, 2008 #7


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    Staff Emeritus
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    Homework Helper

    Groundd, isn't there an option for you to mark your thread "Solved"?

    They don't lock up homework threads just because they are solved, locking threads is for other problems that don't apply here.
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