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Matrix methods for optics

  1. Mar 10, 2009 #1
    For my optics class we are trying to use matrices to "simplify" problems. The notes we are using can be found at: http://www.fen.bilkent.edu.tr/~ilday/courses/2006/415/geometric_optics.pdf

    We learned that:
    [x_out theta_out] = ...[first surface][medium][x_in theta_in]

    In the notes, the thin lens matrix is calculated from the multiplication of the two matrices for the curved interfaces? How does that fit the formula above? I am trying to learn how to do this so I can modify it for a thick lens.

    Also, how is the matrix for each interface calculated? (see work below or link)


    ----

    The medium is given by
    x_out = x_in + z*theta_in
    theta_out = theta_in

    Thus,

    [1 z
    0 1]..............(1)

    At the interface,
    x_out = x_in
    theta_1 = theta_in + theta_s
    theta_2 = theta_out + theta_s

    z = R - sqrt(R^2 - x_in^2) = 1/2 (x_in^2 / R)
    theta_s ~ x_in / R

    How on earth is the matrix for a curved interface calculated:
    M =
    [1 0
    (n1/n2 - 1)/R n1/n2]????? ....... (2)
     
  2. jcsd
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