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Homework Help: Thin lens, optics

  1. Apr 1, 2010 #1

    fluidistic

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    1. The problem statement, all variables and given/known data
    Show that the minimum distance between 2 conjugate points (real object and image) for a positive thin lens is 4f.


    2. Relevant equations
    [tex]\frac{1}{f}=\frac{1}{S_o}+\frac{1}{S_i}[/tex].


    3. The attempt at a solution
    I assumed the lens to be biconvex (though I know that I can't. There are so many types of positive lens...).
    So I get that [tex]\frac{1}{f}=(n_1-n_0)\left ( \frac{2}{R} \right )[/tex].


    So I must show that [tex]S_0+S_1 \geq 4f[/tex].
    Using these 2 formulae, I reach that the inequation holds if and only if [tex]S_0+S_i \leq 2R[/tex] where R is the curvature radius of the thin lens. I'm stuck here. Are there any other equation I should use? Or am I in the right direction?
     
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  3. Apr 1, 2010 #2

    tiny-tim

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    Hi fluidistic! :smile:

    You're making this far too complicated!

    Just write Si - So as a function of So, and differentiate. :wink:
     
  4. Apr 1, 2010 #3

    fluidistic

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    Wow, this worked. Awsome! So I only needed the formula [tex]\frac{1}{f}=\frac{1}{S_o}+\frac{1}{S_i}[/tex] and your nice idea!:biggrin:

    Edit: Wait! Why did you choose the expression So-Si rather than minimizing So+Si?
     
  5. Apr 1, 2010 #4

    tiny-tim

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    oops! :rolleyes:
     
  6. Apr 1, 2010 #5

    fluidistic

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    But this worked! ahahahaha, I made an error but I reached the result. Wow, amazing. I'll retry. Ahahahah.
     
  7. Apr 1, 2010 #6

    fluidistic

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    Have you solved the problem? I'm getting stuck, I just don't reach anything. [tex]S_0+S_i=\frac{S_0S_i}{f}[/tex]. I have to minimize this function.
     
  8. Apr 1, 2010 #7

    tiny-tim

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    No, So + Si = So + 1/(1/f - 1/So) = So + fSo/(So - f) …

    carry on from there. :smile:

    (and I'm off to bed :zzz:)
     
  9. Apr 2, 2010 #8

    fluidistic

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    Worked! Thanks a lot.
     
  10. Mar 10, 2011 #9
    It is still unclear to me where to go from here. What should I be differentiating with respects to?

    Regards,
    Adam
     
  11. Mar 11, 2011 #10

    tiny-tim

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    Hi Adam! :smile:
    hmm … there's only one variable in the formula …
    … so i suppose you'd better differentiate wrt that! :wink:
     
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