 Solution

ID: past-exam-of-the-optics-and-electrodynamics-course-of-the-university-of-cambridge/2021/section-b/b5/e/solution

On the

x

axis the two geometric delays are identical:

t_{1} = t_{2} = \frac{k x}{2 ω} .

Their field wave amplitudes therefore add as equal copies at zero relative delay. Stationarity removes dependence on the common delay, giving

I (x) = I_{0} + Re Γ (0) = 2 I_{0},

independent of

x

in the ideal overlapping plane-wave region. The corresponding mean normal energy flux through a transverse plane is

2 I_{0}

. There is no increasing path difference along the bisector, so finite temporal optical coherence does not produce a longitudinal visibility envelope on this axis.

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