# Matrix methods for optical systems

1. May 14, 2010

### joriarty

1. The problem statement, all variables and given/known data
A single glass lens has a refractive index of 1.5 and radii of curvature R1 = 5cm and R2 = -5cm. Write down the analytical and numerical system matrices for the lens (note that the analytical system matrix should be written down in terms of the relevant refractive indices). Comparing the analytical and numerical system matrices, what is the focal length of the lens?

3. The attempt at a solution

I am not exactly sure what the difference is between an analytical and numerical system matrix, nor can I find any information on this in either my textbooks or course notes!

I know that a single refractive surface can be expressed using the matrix $$\left[ \begin{array}{cc} 1 & 0 \\ \frac{\left( \frac{1}{n}-1 \right)}{R} & \frac{1}{n} \end{array} \right]$$ and that the transfer matrix is $$\left[ \begin{array}{cc} 1-\frac{x}{f} & s_{0}-\frac{s_{0}x}{f}+x \\ -\frac{1}{f} & 1-\frac{s_{0}}{f} \end{array} \right]$$, but I don't really understand where to start with this question because I don't know what is meant by numerical and analytical system matrices. And the "write down" part of the question implies that these are explicitly written somewhere in my notes!