Talk:Reflection phase change

Phase shifts other than 180 degrees
I believe the 180 degree phase shift is actually an approximation. If you use the full complex refractive index (absorption included)you get phase shifts such as 160 degrees. See http://www.opticsinfobase.org/josa/abstract.cfm?uri=josa-54-5-612 — Preceding unsigned comment added by 131.111.185.3 (talk) 14:18, 5 March 2015 (UTC)
 * Yes, the same result is evident from the transmission line case if complex values for impedance are considered. SpinningSpark 11:58, 30 January 2022 (UTC)

Application to transmission lines
The reflection coefficient for transmission lines in terms of characteristic impedance is given by,
 * $$\Gamma = \frac {Z_2 - Z_1}{Z_2 + Z_1}$$

where the subscripts refer to the first and second medium respectively. From,
 * $$Z = \sqrt{L \over C}$$ and
 * $$ v = {\omega \over \beta} = {1 \over \sqrt{LC}}$$

for a lossless line, where L and C are respectively the inductance and capacitance per unit length, the reflection coefficient in terms of velocities is,
 * $$\Gamma = \frac {L_2 v_2 - L_1 v_1}{L_2 v_2 + L_1 v_1}$$

which implies that the phase inversion occurs at,
 * $$ v_2 = {L_1 \over L_2} v_1 $$

and not at,
 * $$ v_2 = v_1 $$

This can equally be stated in terms of capacitance or permeability/permittivity. Can anyone shed any light on this? SpinningSpark 12:13, 30 January 2022 (UTC)