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For single-slit diffraction, the condition for dark fringes is given by a sinθ = mλ, where 'a' is the slit width, 'θ' is the angle of the fringe from the central maximum, 'm' is the order of the fringe (m=1 for the first dark fringe), and 'λ' is the wavelength. For small angles, sinθ ≈ y/L, where 'y' is the position of the fringe from the center and 'L' is the distance to the screen.So, y = mλL / a.Given: λ = 580 nm = 580 x 10^-9 m, a = 0.300 mm = 0.300 x 10^-3 m, L = 1.0 m, m = 1.y = (1) * (580 x 10^-9 m) * (1.0 m) / (0.300 x 10^-3 m) = 1.933 x 10^-3 m = 1.933 mm. The closest option is 1.93 mm.