Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2015 / S19 / 1 / b

Let $D(d)=\left(\begin{array}{cc}1& d\\ 0& 1\end{array}\right)$ be the drift beam transfer matrix. Start immediately before the first lens and end immediately before its counterpart in the next FODO cell. Matrices act on column vectors from right to left. With $A=1/f_1$ and $B=1/f_2$, where both focal lengths are signed in the chosen plane,The two drifts account for both gaps. Direct multiplication gives $\det M=1$ andFor the equal-strength focusing-defocusing case, $f_1=f>0$ and $f_2=-f$:Choosing a different start within the cell gives a conjugate matrix, with the same trace and eigenvalues. If $f_2$ is specified as a positive magnitude of a defocusing lens, its signed value in these formulas is $-f_2$.