The complex image method

The classical image method extends to the case of an impedance boundary condition, and also to the case of reflection from the boundary between two homogeneous media. The latter solution was given by Balth van der Pol in 1935 and the impedance boundary case was included in a 1944 review article on sound waves in rooms by Philip M. Morse and Richard H. Bolt. Unfortunately, these solutions are seldom mentioned in text books on acoustics, and hence these solutions have been rediscovered more than once, and also quite recently. This will be exemplified here by a brief review of the literature. The main result is a simple derivation of the complex image method. The derivation is particularly simple in the case of an impedance boundary condition, but the derivation is valid for reflection of spherical waves from an arbitrary layered medium.