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The Michelson experiment is a historical and significant scientific endeavor, initiated by Albert A. Michelson, to determine the speed of light. In this experiment, instead of using a toothed wheel like in Fizeau's method, Michelson used a rotating, multi-sided mirror. This mirror reflected light over a defined path, allowing for precise measurements. The light traveled from the rotating mirror to a fixed reflector and back, covering a total round-trip distance. By meticulously timing the mirror's rotation, Michelson was able to compute the time required for light to complete the round trip. This experiment was groundbreaking in refining our understanding of light's velocity, achieving results very close to what we accept today as the speed of light.

In Michelson's approach to measuring light's speed, the rotating mirror played a crucial role. The eight-sided mirror was designed to rotate at a very high speed. This rotation allowed the light beam to be deflected precisely, controlling the direction and timing of the light's path. Each face of the mirror directed the light along a specific path towards a fixed reflector and then back again. By observing at which rotation speed the light successfully navigated the round-trip path without missing the subsequent face, Michelson could relate the mirror's rotation to the time taken by light. This brilliant use of a rotating mechanism allowed for high accuracy in calculating time intervals, which were imperative for the experiment's success.

The Fizeau method is among the earliest techniques developed to measure the speed of light. Originating from an experiment by Hippolyte Fizeau in the mid-19th century, it involved shining light through a rotating toothed wheel. The key to Fizeau’s method was using the wheel to intermittently block the light, similar to how a multi-sided mirror interrupts the light path in Michelson's experiment. As the wheel rotated, the speed at which the light was blocked and allowed through gaps created a measurable time delay. By adjusting the wheel's speed until the returning light went through the succeeding gap, the speed of light could be estimated. Michelson's experiment shared this ingenious timing concept but replaced the toothed wheel with a mirror to enhance precision.

The concept of revolution time is fundamental when working with rotating objects in physics experiments. In the context of Michelson's experiment, revolution time refers to the duration it takes for the rotating mirror to complete one full cycle. At a speed of 528 revolutions per second, the time for one complete revolution is computed as the reciprocal of this speed. Therefore, it takes approximately \( \frac{1}{528} \) seconds for the mirror to make a full spin. Understanding this revolution time is essential, as it helps in dividing the revolution further into fractions (one-eighth in this case) to align with the specific phase where the light completes its journey along the defined path. Knowing the precise timing of these rotations ensures the accuracy of light speed measurements.

Calculating distance and time is pivotal in experiments like Michelson's, where precise measurements lead to significant scientific conclusions. The round-trip distance of the light in the Michelson experiment was 71.0 km, necessitating conversion into meters (71,000 m) for standardization in calculations. By determining the time it took for light to travel this distance, using the fraction of revolution time, scientists could accurately compute the speed of light. The formula for speed, \( v = \frac{d}{t} \), was used with the known distance and the measured time (\( \frac{1}{4224} \) seconds), leading to the calculation of light's speed as \( 71,000 \text{ m} \times 4224 \text{ s}^{-1} \). Such systematic distance and time calculations underpin many key physics discoveries and provide a bridge to understanding natural concepts like the speed of light.