Consider a small segment of the fiber, whose length in its rest frame is d ℓ ℓ ′ . The time intervals, d t ± ± ′ , it takes the left and right moving light rays to traverse the segment in the rest frame coincide and are given by d t ± ± ′ = n c d ℓ ℓ ′ Let d ℓ ℓ = | d x | be the length of this small segment in the lab frame. By the relativistic length contraction formula, d ℓ ℓ ′ = γ γ d ℓ ℓ ≈ ≈ d ℓ ℓ correct to first order in the velocity v of the segment. The time intervals d t ± ± for traversing the segment in the lab frame are given by Lorentz transformation as: d t ± ± = γ γ ( d t ′ ± ± v ⋅ ⋅ d x ′ c 2 ) ≈ ≈ n c d ℓ ℓ ± ± v c 2 ⋅ ⋅ d x correct to first order in the velocity v . In general, the two beams will visit a given segment at slightly different times, but, in the absence of stretching, the length d ℓ ℓ is the same for both beams.