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In the Fizeau experiment on measurement ...

In the Fizeau experiment on measurement of the velocity of light the distance between the gear wheel and the mirror is `l = 7.0 km`, the number of teeth is `z = 720`. Two successive disappearances of light are observed at the folllowing rotation velocities of the wheel: `n_(1) = 283rps` and `n_(2) = 313` rps. Find the velocity of light.

Text Solution

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In the Fizean experiment, light disppears when the wheel rotates to bring a tooth in the position fromerly occupied by a gap in the time taken by light to go from the wheel to the mittor and back. Thusdistance travelled `= 2l` Suppose the `n^(th)` tooth after the gap has come in place of the latter. Then time taken
`= (2(m-1)+1)/(2zn_(1))sec.` in the first case
`= (2m+1)/(2zn_(1))` sec in the second case `= (1)/(z(n_(2)-n_(1)))`
Then `c=2l z(n_(1)-n_(1)) = 3.024 xx 10^(8)m//sec`
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