Determining the Speed of Light in 1862

The question asks to identify the scientist who obtained the first accurate value for the speed of light using a specific experimental setup—a rotating mirror apparatus—in the year 1862.

Jean Bernard Léon Foucault's Contribution

Jean Bernard Léon Foucault is the physicist who achieved this significant milestone. In 1862, he conducted an experiment using an improved version of a rotating mirror apparatus to measure the speed of light.

Foucault's setup involved reflecting light off a rapidly rotating mirror, then off a stationary mirror some distance away, and back to the rotating mirror. Because the rotating mirror turned slightly during the light's travel time, the reflected beam was deflected by a small angle. By measuring this angle, the speed of rotation of the mirror, and the distance the light traveled, Foucault could calculate the speed of light. His experiment yielded a value very close to the currently accepted value, establishing it as the first truly accurate measurement obtained using this optical method.

Analyzing Other Physicists

• Charles Wheatstone: He performed experiments related to the speed of light before Foucault, notably using a rotating mirror and later a rotating cogwheel apparatus around 1834. However, Foucault's 1862 experiment is specifically recognized for providing the first *accurate* value with his refined rotating mirror technique.
• Marie Alfred Alen Cornu: He conducted experiments in 1874, also using a rotating mirror method inspired by Foucault's work, achieving a more precise result ($299,940 \text{ km/s}$). But Foucault's 1862 measurement came first.
• Albert A. Michelson: Michelson significantly advanced the accuracy of light speed measurements using rotating mirrors, starting later than Foucault (his famous experiments were primarily in the 1880s and later). While Michelson's results were more accurate, Foucault obtained the *first accurate* value in 1862 as per the question's criteria.

Conclusion

Based on the historical context and the specific requirements of the question (1862, rotating mirror apparatus, first accurate value), Jean Bernard Léon Foucault is the correct answer.