  We analyze theoretically and experimentally the existence of a {\it magic
frequency} for which the absorption of a linearly polarized light beam by vapor
alkali atoms is independent of the population distribution among the Zeeman
sub-levels and the angle between the beam and a magnetic field. The phenomenon
originates from a peculiar cancelation of the contributions of higher moments
of the atomic density matrix, and is described using the Wigner-Eckart theorem
and inherent properties of Clebsch-Gordan coefficients. One important
application is the robust measurement of the hyperfine population.
