Superposition of Bidirectional Scattering

• Stepping from $R_2$ to $R_1$ negates $\rho\mathrel{\stackrel{\mathrm{\Delta}}{=}}\displaystyle\frac{R_2-R_1}{R_2+R_1}$
• Transmission is 1 + reflection in either direction
• ``Kelly-Lochbaum'' scattering junction

Special Cases:

• $R_2=\infty\,\,\Rightarrow\,\,\rho = 1\quad$ (e.g., rigid wall reflection)
• $R_2=0\,\,\Rightarrow\,\,\rho = -1\quad$ (e.g., open-ended tube)
• $R_2=R_1\,\,\Rightarrow\,\,\rho = 0\quad$ (no reflection)