The influence of sample thickness of different concentration magnetic fluid on the magnetic-field-induced birefringence is studied. Experimental results show that the birefringence of magnetic fluid sample decreases with the thickness of magnetic fluid with certain concentration. The variation of birefringence with the externally magnetic field strength is different for samples with different thicknesses. For the thin sample, its birefringence increases gradually with the magnetic field and then saturates at relatively high magnetic field. For the thick sample, the birefringence varies non-monotonously or oscillates with the externally magnetic field. The magnetic fluid concentration has obvious influence on the thickness-dependence of the birefringence. The higher the concentration, the smaller the thickness of the sample for the occurrence of non-monotonous or oscillating variation of birefringence with magnetic field. The underlying physical mechanisms are clarified. The transition magnetic field is defined and employed to analyze the corresponding phenomena quantitatively.