1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Thin lens, optics

  1. Apr 1, 2010 #1

    fluidistic

    User Avatar
    Gold Member

    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?
     
  2. jcsd
  3. Apr 1, 2010 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper

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

    fluidistic

    User Avatar
    Gold Member

    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

    User Avatar
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper

    Hi Adam! :smile:
    hmm … there's only one variable in the formula …
    … so i suppose you'd better differentiate wrt that! :wink:
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook