Final answer:
The Michelson-Morley experiment demonstrated the constancy of the speed of light, showing that it is independent of the motion of Earth around the Sun and leading to the rejection of the ether theory.
Step-by-step explanation:
The question revolves around the outcome of the Michelson-Morley experiment. The correct answer is C) Demonstrated the constancy of the speed of light. This groundbreaking experiment was designed to detect the presence of the ether, a medium then thought necessary for light to propagate through space. However, the experiment consistently failed to show any change in the interference pattern of light beams, regardless of the Earth's movement around the Sun. This led to the understanding that the speed of light in a vacuum is independent of the motion of any observers, thereby contradicting the ether theory and supporting the idea that the speed of light is constant.