Kochetal.’s [J. Acoust Soc. Am.73, 1567–1570 (1983)] formulation of the impedance boundary condition normal mode identification algorithm is used to develop the relationship between the normal mode and geometric ray quantities for low frequency, where previous analyses, employing WKB or other high‐frequency approximations, may not be valid. The result shows that mode normalization is not uniquely relatedapriorito a mathematically meaningful horizontal wavenumber derivative of mode number. Instead, some auxiliary conditions must be invoked to uniquely define cycle distance as a single mode quantity (as opposed to the range periodicity of interference between two modes) given by a mode number derivative and corresponding in appropriate limits to the geometric ray cycle distance. A suggestion for constructing from this result an optimal eigenvalue predictor for numerical eigenmode calculations is discussed.