The phase relation between reflected and transmitted waves, and some consequences

The relative phase of waves reflected from and transmitted through a symmetric stratification is (under certain constraints) known to be an odd multiple of π/2. The phase difference is shown to change by π when the reflectivity passes through zero. Continuity arguments indicate that a surprisingly large proportion of symmetric stratifications share the property of zero reflectance at certain angles. The results apply to acoustic and particle waves, as well as to electromagnetic waves of both polarizations.