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!

Combining lenses

  1. Nov 4, 2009 #1
    1. The problem statement, all variables and given/known data
    2 thin lenses separated by 10cm. First has a focal length of 20cm, the second has a focal length of 30cm.


    2. Relevant equations
    Lens transfer matrix for each lens:
    [tex]\begin{bmatrix}
    1-\frac{D_2d_{21}}{n_{t1}} &-D_1-D_2+\frac{D_1D_2d_{21}}{n_{t1}} \\
    \frac{d_{21}}{n_{t1}} & 1-\frac{D_2d_{21}}{n_{t1}}
    \end{bmatrix}[/tex]


    3. The attempt at a solution
    Since the thickness of the 2 lens is assumed to be zero we have:
    [tex]A_1=\begin{bmatrix}
    1 & \frac{-1}{f_1}\\
    0 & 1
    \end{bmatrix}[/tex]
    For the first lens and
    [tex]A_2=\begin{bmatrix}
    1 & \frac{-1}{f_2}\\
    0 & 1
    \end{bmatrix}[/tex]
    for the second. Therefore we have:
    [tex]A=A_2TA_1=A_2=\begin{bmatrix}
    1 & \frac{-1}{f_2}\\
    0 & 1
    \end{bmatrix}\begin{bmatrix}
    1 & 0\\
    d & 1
    \end{bmatrix}\begin{bmatrix}
    1 & \frac{-1}{f_1}\\
    0 & 1
    \end{bmatrix}=\begin{bmatrix}
    1-\frac{d}{f_2} & \frac{-1}{f_1}-\frac{1}{f_2}+\frac{d}{f_1f_2}\\
    d & 1-\frac{d}{f_1}
    \end{bmatrix}=\begin{bmatrix}
    \frac{2}{3} & \frac{-1}{15}cm^{-1}\\
    10cm & \frac{1}{2}
    \end{bmatrix}=\begin{bmatrix}
    A_{11} & A_{12}\\
    A_{21} & A_{22}
    \end{bmatrix}[/tex]

    Since the system is assumed to be in air, the focal length is the same on both sides of the system. SO we have:

    [tex]f=\frac{1}{-A_{12}}=15cm[/tex]
    [tex]\overline{H_1O_1}=(1-A_{11})f=5cm[/tex]
    [tex]\overline{H_2O_2}=(1-A_{22})f=7.5cm[/tex]

    Where H denotes the principle planes and O denotes the lenses.
    So here's the problem, recall that the lenses are separated by only 10cm, this forces principle plane #2 to be in front (left of) principle plane #1. How can this be true? What did i do wrong?
     
    Last edited: Nov 4, 2009
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Combining lenses
  1. Achromatism of lenses (Replies: 10)

  2. 2 converging lenses (Replies: 6)

  3. Two Thin Lenses (Replies: 1)

  4. Lenses and lasers (Replies: 3)

Loading...