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Matrix optics; simple lens system

  1. Feb 2, 2012 #1
    1. The problem statement, all variables and given/known data

    Calculate the matrix for the optical system which takes rays from the object plane
    to the image plane for a simple lens and show how this leads to 1/v = 1/u + 1/f

    Also show that the matrix can be written in the form

    [tex]\left[ \begin{array}{cc} 1/M & b \\ 0 & M \end{array} \right][/tex]

    3. The attempt at a solution

    Ok... so the matrix for the system is going to be m3*m2*m1

    where m3 is the translation matrix for a distance "v"

    [tex]\left[ \begin{array}{cc} 1 & 0 \\ -v & 1 \end{array} \right][/tex]

    m2 is the thin lens matrix

    [tex]\left[ \begin{array}{cc} 1 & -1/f \\ 0 & 1 \end{array} \right][/tex]

    m1 is the translation matrix for a distance "u"

    [tex]\left[ \begin{array}{cc} 1 & 0 \\ u & 1 \end{array} \right][/tex]

    Multiplying these out, its obvious that it cannot be written in the required form. So far, does this look okay? I can't see anything immediately wrong with what I've done so far.
  2. jcsd
  3. Feb 2, 2012 #2
    bump ;)
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