What is the approximate wavelength of a light whose first-order bright band forms a diffraction angle of 45.0° when it passes through a diffraction grating that has 500.0 lines per mm?

For a diffraction grating, bright bands satisfy d sin θ = mλ. The spacing is d = 1/500.0 mm = 0.00200 mm = 2000 nm; for the first order, m = 1, so λ = 2000 nm × sin(45.0°) ≈ 2000 × 0.707 = 1414 nm. The correct choice is D, 1414 nm.

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