Question

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2. Leon Foucault (French physicist) measured the speed of light with a rotating mirror in 1862. Albert Michelson (American physicist) refined Foucault's method to make a series of measurements over many years. His 1924 measurement was a major advance. The drawing shown below is a simplified description. SOURCE MIRRO TE LESCOPE OCTAGON AL RO ATING MIRROR Image of the source is seen in the telescope. When the mirror starts rotating, the image disappears. When the speed of rotation is progressively increased, the image reappears at a particular speed of revolution. This was correctly interpreted as the next face of the octagonal mirror taking the place of the previous face exactly. Use the following data to calculate the speed of light in such a measurement. Distance between the fixed mirror and the rotating mirror 35.0 km Speed of rotating mirror = 3.21 x 104 rpm

Answer 1

Here speed of rotating mirror is = 3.21x10⁴ rpm = 535 rps
Now time to complete on rotation i.e. time period of rotating mirror T = 1/535 = 1.869x10^-3 s

Time taken by next face to take place previous face is t =T/8 = 2.3364x10^-4s
in this time interval distance travelled by light is d = 2x35.0 = 70.0 km = 7.00x10⁴ m

Now speed of light c = d/t = 2.996x10⁸ m/s