Confusion about EM Transmission coefficient - critical angle

[ThiagoEMag]

Hi,

The reflection coefficient (R) of an EM wave is, as far as I know, 1 if there is total reflection and -1 if there is total reflection AND the phase changes by 180º.

However, we also know that the transmission coefficient is given by T = R + 1 (or by its own formula, which should give the same result)

That seems to mean that if the R is one (total reflection), T would be two. How can that be possible? I have a situation in which I did the calculations and that's the result I got, but it doesn't make sense to me. Shouldn't T be always 0 when there is total reflection, or did I misunderstand its meaning?

 

[Tom_K]

As far as I know T + R = 1 and T = 1 – R where R is the unsigned magnitude of the reflection coefficient.

Positive and negative values of R are useful in determining whether the reflection is caused by an open or short or some other impedance value, but only the unsigned value of R should be added or subtracted from T.

 

[blue_leaf77]

I believe you get T=R+1 from the continuity of the fields at the boundary. If so this implies that both T and R in that equation are actually the fields coefficient, that is the fraction of the field amplitude plus the phase change that is being transmitted and reflected, respectively. Since T and R are the fields coefficients, they can be complex, that's why you said there are cases where R=-1, this corresponds to the phase of 180 degree. In other words, one cannot say too much about the conservation of energy if one stays with this equation.
In your notation, the equation for energy conservation should be $|T|^2+|R|^2=1$, which is the equation Tom_K wrote above in a different notation.