The principle of the constancy of the velocity of light, which stated that the light velocity is invariant to the motion of the emitter, was well established and directly proven by many experiments. Interestingly, the further assumption that the light velocity is also independent of the motion of the observer was, arguably, never conclusively proven by any experiment for a century. This paper tried to address some perceived technical difficulties in such experiments and proposed two experiments to test this assumption. One is to directly measure the light speed as to moving sensors, with the setup designed in such a way that the concerns of time synchronization and dilation can be avoided. Another experiment is to test the isotropy of the light speed to a high-speed particle by measuring the momentum to acceleration ratio. The experiment results, if positive, will provide direct proof of the assumption. Otherwise, it may imply a need for further investigation. Since the light speed invariance to moving observers is a key assumption of some fundamental physical theory, either way, the experiments will have significant importance.