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girlinphysics
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Mod note: Moved from a technical section, so is missing the homework template.
I am using matrix methods to do ray optics but my knowledge on matrices is behind.
I found the system matrix to be
\begin{bmatrix} \frac{-f_2}{f_1} & f_1 + f_2 \\ 0 & \frac{-f_1}{f_2} \end{bmatrix}
I want to find [itex]y_2[/itex] (height of the emerging ray) and [itex]\alpha_2[/itex] (angle of emerging ray...which should equal zero) so I set up the system as follows:
\begin{bmatrix} y_2 \\ \alpha_2 \end{bmatrix} = \begin{bmatrix} \frac{-f_2}{f_1} & f_1 + f_2 \\ 0 & \frac{-f_1}{f_2} \end{bmatrix} \begin{bmatrix} y_0 \\ \alpha_0 \end{bmatrix}
(Apologies for the tex I couldn't figure out how to put it in one line)
Is this the correct way to set it up in order to find [itex]y_2[/itex] and [itex]\alpha_2[/itex]? And how do I solve this system of matrices?
I am using matrix methods to do ray optics but my knowledge on matrices is behind.
I found the system matrix to be
\begin{bmatrix} \frac{-f_2}{f_1} & f_1 + f_2 \\ 0 & \frac{-f_1}{f_2} \end{bmatrix}
I want to find [itex]y_2[/itex] (height of the emerging ray) and [itex]\alpha_2[/itex] (angle of emerging ray...which should equal zero) so I set up the system as follows:
\begin{bmatrix} y_2 \\ \alpha_2 \end{bmatrix} = \begin{bmatrix} \frac{-f_2}{f_1} & f_1 + f_2 \\ 0 & \frac{-f_1}{f_2} \end{bmatrix} \begin{bmatrix} y_0 \\ \alpha_0 \end{bmatrix}
(Apologies for the tex I couldn't figure out how to put it in one line)
Is this the correct way to set it up in order to find [itex]y_2[/itex] and [itex]\alpha_2[/itex]? And how do I solve this system of matrices?
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