An early method of measuring the speed of light (a variation of the Fizeau metho

Question

An early method of measuring the speed of light (a variation of the Fizeau method) made use of a rotating slotted wheel. A beam of light passes through a slot at the outside edge of the wheel, travels to a distant mirror, and returns to the wheel just in time to pass through the next slot in the wheel. One such slotted wheel has a radius of 5 cm and 500 slots along its edge. if the experimenter first observes a maximum in the intensity of light when the wheel is rotating at 36100 rpm, what is the velocity of light?

Explanation / Answer

   Agular displacement between two consequtive slots      =   2 / 500         rad    since one rotation   =   2    angular speed      =   36100   rpm   =   36100 * 2 / 60   rad/s                                                             =   601.67 * 2 rad/s    time taken by the light to pass between two consequtive slots       t   =    /       =   (2 / 500) / (601.67 * 2)       =   1/500 * 601.67       =   3.324 * 10-6 s    In the same time, the light reaches the mirror and comes back at tha wheel, if the distance from wheel and mirror be   d m, then total distance covered   =   2d    speed of light   c   =   2d / t                                  =   2 * d / 3.324 * 10-6                                  =   6.017 * 105 * d   m/s    knowing the distance d,   speed of light can be determined.

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