1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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 ;)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook