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Ray tracing with transfer matrix method

  1. Sep 24, 2015 #1
    Hi,
    I'm new in physics and optics so I need a little help. I've a simple optical system from 2 thin lenses.
    The first thin lens has a focal distance of 50 [mm] , and the second one has 25 [mm]. The 2 lenses are separated by 40 [mm] and the object is placed 75 [mm] before the first lens.

    I've to find the position of the final image and simulate howto propagate the rays across the optical system.

    So, I made a little program to determine the ray transfer matrix of the system.
    This is the transfer matrix of the system:
    \begin{bmatrix} 0.20-0.028x & 55-2.7x \\ -0.0028 & -2.7 \end{bmatrix}

    where the x variable is the final image distance from the last lens.

    If I do the following:
    \begin{equation} 55-2.7x = 0\end{equation}
    Then x = 20.37 [mm] , this is the image distance, exactly what I was looking for.
    So the system matrix is:
    \begin{bmatrix} -0.37036 & 0.001 \\ -0.0028 & -2.7 \end{bmatrix}

    My problem is:

    I have lots of input rays to simulate the ray propagation, but I can't understand the output rays.

    For example :
    \begin{equation}
    \begin{bmatrix} y \\ θ \end{bmatrix}
    =
    \begin{bmatrix} 0.0002 \\ -0.54 \end{bmatrix}

    \end{equation}
    where y is the input height and θ is the input angle in radian.
    \begin{equation}
    \begin{bmatrix} 0.0002 \\ -0.54 \end{bmatrix}
    =
    \begin{bmatrix} -0.37036 & 0.001 \\ -0.0028 & -2.7 \end{bmatrix}

    \begin{bmatrix} 0 \\ 0.2 \end{bmatrix}
    \end{equation}

    Could you help me explain the output ray of the system?

    I apologize for the wall of text :)
     
  2. jcsd
  3. Sep 25, 2015 #2

    Simon Bridge

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    A ray input at height 0 and grad 0.2 will output at height 0.0002 and gradient -0.54 ... draw a box for your system of lenses, draw the input and output lines at the appropriate ends of the box.
     
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