What is the approximate wavelength of a light whose first-order bright band forms a diffraction angle of 45.0 degrees when it passes through a diffraction grating that has 500 point 0 lines per mm ?

For a diffraction grating, bright bands satisfy mλ = d sin θ. The grating spacing is d = 1 mm ÷ 500 = 0.002 mm = 2.0 × 10⁻⁶ m, and the first order means m = 1. Thus λ = (2.0 × 10⁻⁶ m) sin 45.0° ≈ 1.414 × 10⁻⁶ m = 1414 nm, so the answer is 1414 nanometers.

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