Solving Matrix Mod for Ray Optics

[girlinphysics]

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 y_2 (height of the emerging ray) and \alpha_2 (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 y_2 and \alpha_2? And how do I solve this system of matrices?

 

[Mark44]

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 y_2 (height of the emerging ray) and \alpha_2 (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 y_2 and \alpha_2? And how do I solve this system of matrices?

You don't "solve" the system - just do the indicated multiplication. If you're unclear about how to do that, do a web search for "matrix multiplication".

 

[Ray Vickson]

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 y_2 (height of the emerging ray) and \alpha_2 (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 y_2 and \alpha_2? And how do I solve this system of matrices?

For the tex: If you want
\pmatrix{-f_2/f_1&f_1+f_2\\0&-f_1/f_2} \pmatrix{y_0\\0}
just put it all on one line. Right-click on the line above (and choose to display as tex) in order to see the commands used. Of course, you could use displayed fractions instead; try it and see.