Diffraction grating maxima from grating equation

Steps:

• Calculate grating spacing: d = 1 / 300 lines/mm = 1 / (300 × 10³) m = 3.33 × 10⁻⁶ m.
• Use grating equation d sinθ = mλ with λ = 400 × 10⁻⁹ m; maximum m where |sinθ| ≤ 1 gives m_max = floor(d/λ) = floor(8.33) = 8.
• Maxima occur for m = 0, ±1, ..., ±8, totaling 17 orders.
• Semicircular screen captures all θ from -90° to +90°, including all orders.

Why D is correct:

• Grating equation limits orders to m ≤ d/λ ≈ 8.33, yielding 17 maxima (2×8 + 1 for m=0) as per diffraction order formula.

Why the others are wrong:

• A: Counts only positive orders plus zero (9), ignoring symmetric negative orders.
• B: Counts only positive orders including zero, missing negatives.
• C: Doubles positive orders (8×2) but excludes central m=0 maximum.

Final answer: D