Suppose the speed of light is determined experimentally to be 299,796 ± 4 km/s.If the total path length for your interferometer is exactly 11.0 m,how big an error in the time required for the light to travel through the apparatus corresponds to the uncertainty (±4 km/s)in the speed of light? A)4.9 $\times$ 10^-13 s B)2.7 $\times$ 10^-3 s C)3.7 $\times$ 10^-8 s D)4.9 $\times$ 10^-10 s E)9.2 $\times$ 10^-12 s

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Quizplus · Accepted Answer

The error in time, $\Delta t$, can be calculated using the formula $\Delta t = \frac{\Delta v \times t}{v}$, where $\Delta v$ is the uncertainty in the speed of light, $v$ is the speed of light, and $t$ is the time taken for light to travel the given path. Given $\Delta v = 4$ km/s (or $4000$ m/s), $v = 299,796$ km/s (or $299,796,000$ m/s), and the path length is $11.0$ m, the time $t = \frac{11.0}{299,796,000}$. Plugging these values into the formula gives an error in time which, when calculated correctly, matches the order of magnitude and the format of choice A, $4.9 \times 10^{-13}$ seconds.

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