Reflection and transmission coefficients at a scalar-wave interface ($R,T$)

For incident and transmitted normal wavenumbers $q_0$ and $q_1$, continuity of a scalar field and its normal derivative gives

The reflection coefficient is the complex ratio between reflected and incident wave amplitudes. Its modulus determines amplitude attenuation and its argument determines the phase shift on reflection.

The transmission coefficient is the complex ratio between transmitted and incident wave amplitudes. Flux transmission may also contain an impedance or normal-wavenumber factor and therefore need not equal $|T{|}^2$.