Worked example: A plane cuts the x, y, z axes at 2a, 3a and ∞ (parallel to z). Find its Miller indices, and the interplanar spacing for a = 0.4 nm. Step 1: Intercepts in units of a: (2, 3, ∞). Step 2: Reciprocals: (1/2, 1/3, 0). Step 3: Clear fractions — multiply by 6: (3, 2, 0). So the indices are (320). Step 4: Spacing d = a/√(3²+2²+0²) = 0.4/√13 = 0.4/3.606 ≈ 0.111 nm. Step 5: Check with Bragg's law for Cu Kα X-rays (λ = 0.154 nm): sinθ = λ/2d = 0.154/0.222 = 0.694 → θ ≈ 44°. Conclusion: reciprocals turn geometry into integers, and Bragg's law turns integers into measurable angles.