Deuterium (D)-tritium (T) nuclear fusion reaction has the potential as an energy source in the future. In both magnetic confinement and inertial confinement fusion reactors, the solid D-T will generally be supplied as fusion fuel. The efficiency of nuclear fusion reaction depends on the quality of solid D-T fuel, which is related to the composition, homogeneity, helium-3 (3He) content, and so on. However, there is no technique for the in-situ examination method of solid D-T fuel. In this study, we considered a simple and precise method for the characterization of solid hydrogen isotopologues at cryogenic temperature using the refractive index measurement, and the distribution of hydrogen isotopologue composition and homogeneity were evaluated. To evaluate without the effect of tritium decay, the homogeneity of the hydrogen(H2)-deuterium(D2) mixture was measured at first. By the in-situ refractive index measurement at cryogenic temperature, the homogeneity of solid H2-D2 mixture was roughly quantified. The phase diagram of the H2-D2 mixture shows a solid solution type. D2-rich crystal first appeared from the liquid phase as a primary crystal. The composition of D2 in liquid phase was homogeneous, whereas it reduces by obeying the liquidus line in the phase diagram with the crystallization. On the other hand, the composition of the H2-D2 mixture in solid phase was inhomogeneous. Because the mobility of H2 and D2 in solid phase was too slow to be homogeneous solid. The compositions of H2-D2 mixture in liquid and solid phases could be evaluated by the in-situ refractive index measurement in time. Consequently, the refractive index measurement showed great potential for the inspection method of solid D-T fuel in fusion reactors.