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Thin-lens equation

  1. Oct 13, 2004 #1
    Hey. I understand the thin-lens equation and that it is 1/distance from lens to object + 1/distance from lens to image = 1/focal length. But, I was wondering how/why it works. If someone knows, I would appriciate the help. Thanks.
     
  2. jcsd
  3. Oct 14, 2004 #2

    krab

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    The idea of a lens is to have a linear relationship between the distance a ray passes through off axis, and the amount the ray is kinked on passing through. Let us call the former quantity [itex]r[/itex] and the latter [itex]\Delta\theta[/itex]. The proportionality constant is [itex]f[/itex], the focal length. So we have
    [tex]r=f\Delta\theta[/tex]
    If a ray comes from a point on axis a distance [itex]o[/itex] upstream of the lens, and if [itex]\theta_o[/itex] is the angle, then for small angles, [itex]\theta_o=r/o[/itex].
    If this ray comes to a point on axis a distance [itex]i[/itex] downstream of the lens, and if [itex]\theta_i[/itex] is the angle, then for small angles, [itex]\theta_i=r/i[/itex].
    Now, realize that
    [tex]\Delta\theta=\theta_o+\theta_i[/tex]
    and you have your formula.
     
  4. Oct 14, 2004 #3
    Thanks for the help.
     
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