Derive the expression

$\displaystyle \frac{A+B}{A-B}=\frac{k_1}{k_2}\frac{C+D}{C-D}=\frac{k^2_1}{k^2_2}$

Using

$\displaystyle A+B=C+D$ and $\displaystyle k_{1}A- k_{1}B = k_{2}C- k_{2}D$

$\displaystyle C e^{i k_{2}L}+D e^{- ik_{2}L} = F e^{i k_{1}L}$ and $\displaystyle k_{2}C e^{ ik_{2}L}- k_{2}D e^{-i k_{2}L} = k_{1}F e^{i k_{1}L}$

$\displaystyle k_2 L=\pi/2$

I can get

$\displaystyle \frac{A+B}{A-B}=\frac{k_1}{k_2}\frac{C+D}{C-D}$

But can't see how to get

$\displaystyle \frac{k^2_1}{k^2_2}$, probably easy but can't see it.

James