We report the first use of an extremely thin vapor cell (thickness ∼ 400 nm) to study the magnetic-field dependence of laser-induced-fluorescence excitation spectra of alkali atoms. This thin cell allows for sub-Doppler resolution without the complexity of atomic beam or laser cooling techniques. This technique is used to study the laser-induced-fluorescence excitation spectra of Rb in a 50 G magnetic field. At this field strength the electronic angular momentum J and nuclear angular momentum I are only partially decoupled. As a result of the mixing of wavefunctions of different hyperfine states, we observe a nonlinear Zeeman effect for each sublevel, a substantial modification of the transition probabilities between different magnetic sublevels, and the appearance of transitions that are strictly forbidden in the absence of the magnetic field.For the case of right-and left-handed circularly polarized laser excitation, the fluorescence spectra differs qualitatively. Well pronounced magnetic field induced circular dichroism is observed. These observations are explained with a standard approach that describes the partial decoupling of I and J states.