Question

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?

236 nm
353 nm
943 nm
1414 nm

Answer 1

Use d sinθ = mλ with m = 1. d = 1/(500 mm⁻¹) = 0.002 mm = 2.0×10⁻⁶ m.
λ = d sin45° = 2.0×10⁻⁶·0.7071 ≈ 1.414×10⁻⁶ m = 1414 nm.