Diffraction grating orders on semicircular screen

Steps:

• Compute d/λ = (2.0 × 10^{-6}) / (5.4 × 10^{-7}) ≈ 3.703, so maximum integer order m_max = 3 (since sinθ ≤ 1 requires |m| ≤ 3.703).
• Bright fringes occur at m = 0, ±1, ±2, ±3, satisfying d sinθ = mλ.
• Semicircular screen covers θ from -90° to +90°, so all orders are visible.
• Total bright dots: 7 (central plus three on each side).

Why D is correct:

• Grating equation limits visible orders to |m| ≤ floor(d/λ), yielding 2×3 + 1 = 7 symmetric spots.

Why the others are wrong:

• A: Counts only m=0, ignoring diffracted orders.
• B: Suggests m=0, ±1 (4 spots), but m=2,3 also fit.
• C: Implies m=0 to ±2 (5 spots), undercounting m=±3.

Final answer: D