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Homework Help: Optical Path Length

  1. Apr 13, 2008 #1


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    1. The problem statement, all variables and given/known data

    Derive the optical length of the incident light being reflected back to the surface of the lens with radius r1.

    2. Relevant equations

    i have assumed that the surfaces can be given as r^2 = y^2+z^2
    there are 2 surfaces of the lens with radii r1 and r2

    3. The attempt at a solution

    is it simply subtracting the expression for r1 from the expression for r2?
    i have attemped using Fermats principle but cannot get very far
  2. jcsd
  3. Apr 14, 2008 #2
    I think I remember doing this problem a while back - if I'm right, the derivation is not simple. If nobody replies, give me some time to recall my memory...
  4. Apr 18, 2008 #3
    I don't know if you've managed to do the problem but you were on the right track.

    You asked whether or not you subtract the expression for r1 from r2 - that depends if you represented the reflected light ray's velocity as negative or if you've subtracted the entire reflected path. Either way should be fine, though I would probably stick with representing the reflected velocity as negative.
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