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Derivation of the thin lens equation?

  1. Jan 4, 2012 #1
    'm currently reading chapter 27 of the Feynman lectures, where he derives the thin lens equation for a single refracting surface. He arrives at the equation

    h^2/2s + nh^2/s' = (n-1)h^2/2r

    Where s is the object distance, s' is the image distance, n is the index of refraction of the second medium (the first is one), r is the radius of curvature, and h is the altitude of a triangle

    Where does the (n-1) come from? Wouldn't it simply be n?

    This is kind of vague, so please look at the second page of
    http://student.fizika.org/~jsisko/K...on Physics/Vol 1 Ch 27 - Geometric Optics.pdf

    I would be so grateful. Thanks.
  2. jcsd
  3. Jan 5, 2012 #2


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    Staff: Mentor

    All expressions in the equation are excess times as compared with the idea that light travels from O to Q in the air and then from Q to O' in the glass.

    [itex](n-1)\frac{h^2}{2R}[/itex] is about how much longer light travels between V and Q. [itex]n\frac{h^2}{2R}[/itex] is a total time of travel between V and Q, not excess time, for the excess time you have to subtract time it would take for the light to travel between V and Q in the air - which is just [itex]\frac{h^2}{2R}[/itex] (as we assumed the speed in air is just 1).
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