Solving Matrix Mod for Ray Optics

In summary, the conversation discusses the use of matrix methods in ray optics and the system matrix for this method. The individual is seeking help to find y_2 and \alpha_2 and has set up the system using matrices. However, they are unsure about how to solve this system of matrices and are advised to search for "matrix multiplication" for further guidance.
  • #1
girlinphysics
25
0
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?
 
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  • #2
girlinphysics said:
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?
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".
 
  • #3
girlinphysics said:
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?

For the tex: If you want
[tex] \pmatrix{-f_2/f_1&f_1+f_2\\0&-f_1/f_2} \pmatrix{y_0\\0}[/tex]
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.
 

1. What is matrix mod for ray optics?

Matrix mod for ray optics is a mathematical technique used to solve problems involving the propagation of light through optical systems. It involves representing the optical system as a matrix and using matrix operations to calculate the properties of the light rays passing through the system.

2. How is matrix mod different from other methods of solving ray optics problems?

Matrix mod is different from other methods, such as ray tracing, in that it allows for a more efficient and accurate calculation of the properties of light rays. It also allows for the analysis of more complex optical systems that may not be easily solved using other methods.

3. What are the advantages of using matrix mod for ray optics?

The advantages of using matrix mod for ray optics include its efficiency, accuracy, and ability to solve complex optical systems. It also allows for the analysis of multiple optical elements and the combination of different types of optical elements in a single system.

4. Are there any limitations to using matrix mod for ray optics?

While matrix mod for ray optics is a powerful tool, it does have some limitations. It is most effective for paraxial rays, meaning those that are close to the optical axis. It also assumes that the optical elements are thin and do not introduce any aberrations or distortions.

5. How can I learn more about using matrix mod for ray optics?

There are many resources available for learning about matrix mod for ray optics, including textbooks, online tutorials, and scientific papers. It may also be helpful to consult with an expert in the field or take a course specifically focused on this topic.

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