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Mathematical Demonstration - Lenses in contact

  1. Dec 14, 2006 #1
    Hi, I have been working on this for a little while and think I am approaching it incorrectly. If someone can help, I'd really appreciate it. This is for a basic introductory calculus based Physics class that I am in.

    1. Mathematically demonstrate the following equation with no numerical examples

    2. [tex] \frac{1}{f_{c}} = \frac{1}{f_{1}} + \frac{1}{f_{2}} [/tex] - This is the equation for the focal distance of two touching thin lenses.

    3. I have tried using the lens equation for the first and second lens, and solving for a distance of zero between them, but i can't figure out how to solve for where the image from the first lens would be, and therefore how the second lens would act on it

    Thanks Very Much.
    Last edited: Dec 14, 2006
  2. jcsd
  3. Dec 14, 2006 #2


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    Remove the slash before the 1 in the tex code. Try considering two lenses that are a distance d apart and having a look what happens. Wneh you have an equation for that see waht happens when d tends to zero.
  4. Dec 14, 2006 #3
    Hi Kurdt,

    Thanks for the info.

    Are you talking about this:

    [tex] \frac{f_2 (d - f_1) } { d - (f_1 +f_2) } [/tex]

    If so, I had seen that, but I am unsure of how to get to that from the given equation.

  5. Dec 14, 2006 #4


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    I am referring to that equation. Now as I say if you let d tend to zero you will obtain the equation you are after. I trust you know how to get to the equation with d.
  6. Dec 14, 2006 #5
    Just got it. For some reason I distributed d to both terms in the numerator instead of [tex] f_{2} [/tex].

    Thanks for your help.
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