# Amplitude reflection coefficient for high to low refractive index

 Sci Advisor PF Gold P: 1,777 Yes, the reflection coefficient going from a high to low index of refraction is negative. The change in sign means that the reflected wave has a phase shift of 180 degrees. As for the total transmission coefficient, it becomes more complicated because the total reflected and transmitted through a slab is going to be a result of multiple reflections within the slab. For example, you have a contribution from a beam that transmits through directly, t_1*t_2, then you have a contribution from the first order reflection off of the second interface, t_1*r_2*r_2*t_2, and so on and so on. This is a bit simplified because I haven't accounted for interference between these various orders due to the phase differences. It is possible to calculate the result. For example, the refletion coefficient for normal incidence is $$\Gamma_{in} = \frac{\Gamma_{12}+\Gamma_{23}e^{i2k_2d}}{1+\Gamma_{12}\Gamma_{23}e^{i2k _2d}}$$ Where $$\Gamma_{ij} = \frac{\eta_j-\eta_i}{\eta_j+\eta_i}$$ and k_2 is the wavenumber in the slab, d is the thickness of the slab, and \eta is the impedance of the medium which is $\sqrt{\frac{\mu}{\epsilon}}$ while the index of refraction is $\sqrt{\mu_r\epsilon_r}$. If the permeability of the slab case is homogeneous then we can see that \Gamma_{ij} gives us the same result if we use the equation I gave using wave impedance or the equation using index of refraction.