Chapter 16, Problem 63E

Continuing from Exercise 62, the behavior of a ray propagating through free space a distance d can be modeled with the ABCD matrix $\left[\begin{array}{ll}1\hfill & d\hfill \\ 0\hfill & 1\hfill \end{array}\right]$. (a) Show that the same result is obtained (r_out, θ_out) whether a single ABCD matrix is used with d, or two cascaded matrices are used, each with d/2. (b) What are the units of A, B, C, and D, respectively? (c) A thin lens can be reasonably represented by the ABCD matrix $\left[\begin{array}{cc}1& 0\\ -\frac{1}{f}& 1\end{array}\right]$. If the input ray is given by r_in = 1 cm, θ_in = 12°, and f = 10 cm, compute r_out and θ_out.