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Homework Help: The Radius of Curvature

  1. Oct 19, 2011 #1
    1. The problem statement, all variables and given/known data

    Parallel light in air enters a transparent medium of refractive index 1.33 and is focused 35 mm behind the surface. Calculate the radius of curvature of the surface of the medium

    2. Relevant equations

    [itex]f = \frac{R}{2}[/itex]

    [itex]\frac{1}{f}=(n-1) \left( \frac{1}{R_1}-\frac{1}{R_2} \right)[/itex]

    3. The attempt at a solution

    The correct answer must be 8.68 mm, I can't see how they got this answer.

    We know that the focus is 35 mm, so if we use the equation

    [itex]R=2f=2 \times 35 = 70 \ mm[/itex]

    But this is not correct and it doesn't take into account the refractive index.

    So, I also tried using the lens-maker's equation:

    [itex]\frac{1}{35} = (1.33-1) \left( \frac{1}{R}- 0 \right) \implies R = 17.9[/itex]

    I wasn't sure what to use for the second radius so I used 0, and I didn't get the correct answer. So how can I get 8.68 mm?
     
  2. jcsd
  3. Oct 19, 2011 #2
    I don't think you understood the problem correctly. You have light in one medium entering another medium through a parabolic surface. Not sure the level of your class, but since it's posted in intro phys, I'll just give you the formula.

    [tex]F=n_ 2 R/(n_2-n_1)[/tex]
     
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