What is the approximate wavelength of a light whose second-order dark band forms a diffraction angle of 15.0° when it passes through a diffraction grating that has 250.0 lines per mm?

The grating spacing is the reciprocal of its line density: d = 1/(250.0 lines/mm) = 0.00400 mm = 4.00 × 10⁻⁶ m. For a second-order dark band, the destructive-interference condition is d sin θ = (2 + 1/2)λ. Thus λ = (4.00 × 10⁻⁶ m) sin 15.0° / 2.5 ≈ 4.14 × 10⁻⁷ m = 414 nm, so the approximate wavelength is 414 nm.

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