Physics

Physics

Problem

A beam of wavelength λ\lambda passes through a single slit of width aa and produces its first dark fringe at a small angle θ\theta from the central maximum on a distant screen. If the slit width is doubled to 2a2a while the wavelength remains the same, what happens to the angular position θ′\theta' of the first dark fringe? (Assume θ\theta and θ′\theta' are small enough that sin⁡θ≈θ\sin\theta\approx\theta.) a) θ′  ≈  2θ\theta'\;\approx\;2\theta b) θ′  ≈  θ2\theta'\;\approx\;\dfrac{\theta}{2} c) θ′  ≈  θ\theta'\;\approx\;\theta d) θ′  ≈  4θ\theta'\;\approx\;4\theta

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