Strength of electromagnetic, acoustic and Schr\"{o}dinger reflections

The notion of reflection strength $S$ of a plane wave by an arbitrary non-absorbing layer is introduced, so that the intensity of reflection is $R$=tanh$^{2}S$. We have shown that the total strength of reflection by a sequence of elements is expressed through particular element strengths and mutual phases between them by a simple addition rule; in particular, its possible maximum is the sum of the absolute strengths of constituents. We show that the standard Fresnel reflection may be understood in terms of variable $S$ as a sum or difference of two separate contributions, due to an impedance step and a speed step. Strength of reflection for propagating acoustic and quantum mechanical waves is also discussed. The one-dimensional wave equation describing propagation and reflection of waves in a layered medium is transformed into an exact first-order system for the amplitudes of coupled counter-propagating waves. Any choice of such amplitudes, out of continuous multitude of them, allows one to get an accurate numerical solution of the reflection problem. We discuss relative advantages of particular choices of amplitude.