Question

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?

26 nm
32 nm
414 nm
518 nm

Answer 1

Use d sinθ = mλ.

d = 1/(250 mm⁻¹) = 1/(250×10³ m⁻¹) = 4.00×10⁻⁶ m.
m = 2, sin15° = 0.258819.

λ = d sinθ / m = (4.00×10⁻⁶)(0.258819)/2 = 5.18×10⁻⁷ m ≈ 518 nm.

Answer: 518 nm.