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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)Reply

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)Reply

The reflection coefficient for transmission lines in terms of characteristic impedance is given by,

${\displaystyle \Gamma ={\frac {Z_{2}-Z_{1}}{Z_{2}+Z_{1}}}}$

where the subscripts refer to the first and second medium respectively. From,

${\displaystyle Z={\sqrt {L \over C}}}$ and

${\displaystyle v={\omega \over \beta }={1 \over {\sqrt {LC}}}}$

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,

${\displaystyle \Gamma ={\frac {L_{2}v_{2}-L_{1}v_{1}}{L_{2}v_{2}+L_{1}v_{1}}}}$

which implies that the phase inversion occurs at,

${\displaystyle v_{2}={L_{1} \over L_{2}}v_{1}}$

and not at,

${\displaystyle v_{2}=v_{1}}$

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)Reply