How to calculate relative phase of reflected and transmitted plane waves

[mathplease]

not relating to any specific homework question:

how can i go about calculating the relative phase of reflected / transmitted fields for normally incident plane waves?

for example, i know how to calculate the relative amplitude of the reflected field from the reflection coefficient:

$$\Gamma$$ = E_r/E_i = ($$\eta$$₂-$$\eta$$₁)/($$\eta$$₂+$$\eta$$₁)

however, what if i want to calculate the relative phase?

 

[Born2bwire]

The reflection coefficient should include the change in amplitude and phase. You can get phase shifts if you are talking about lossy materials but given your expression for the reflection coefficient I think you are probably only dealing with lossless materials at the moment. If you are only talking about lossless dielectrics and PEC, then the only phase shift you will get is a 180 degree phase shift with PEC under the appropriate conditions to cancel out the field on the surface.

 

[mathplease]

The reflection coefficient should include the change in amplitude and phase. You can get phase shifts if you are talking about lossy materials but given your expression for the reflection coefficient I think you are probably only dealing with lossless materials at the moment. If you are only talking about lossless dielectrics and PEC, then the only phase shift you will get is a 180 degree phase shift with PEC under the appropriate conditions to cancel out the field on the surface.

ah i see. if the conductivity of the material is low can i assume it to be lossless material?