Discussion
What is the temporal coherence length of a mercury vapour lamp emitting in the green portion of the spectrum at wavelength of 546.1 nm with an emission bandwidth of \(\Delta\nu = 6 \times 10^{8}\) Hz :
Answer: A
The temporal coherence length is 0.5 m.
The coherence time is about the inverse of the bandwidth, \(\tau_{c} \approx 1/\Delta\nu\), and the coherence length is the distance light travels in that time:
\[ \begin{aligned} l_{c} &= c\tau_{c} = \frac{c}{\Delta\nu} \\ &= \frac{3 \times 10^{8}}{6 \times 10^{8}} = 0.5\ \text{m} \end{aligned} \]
The wavelength 546.1 nm is not needed once the bandwidth is given in hertz. 2 m inverts the ratio, and 0.25 m and 1 m come from extra factors of two.
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