Diffraction grating maxima from order condition in d sinθ = mλ

Steps:

• Grating spacing d = 1/300 mm = 0.00333 mm ≈ 0.003 mm for calculation.
• Wavelength λ = 600 nm = 0.0006 mm.
• Ratio d/λ ≈ 0.003/0.0006 = 5 exactly under approximation.
• Max order m = 4, as m=5 gives sinθ = 5λ/d = 1 (θ=90°), light grazes grating surface and misses screen; total maxima = 2×4 + 1 = 9.

Why D is correct:

• Grating equation limits observable orders to |m| ≤ 4 (sinθ < 1), yielding 9 principal maxima (-4 to +4) symmetric about central m=0.

Why the others are wrong:

• A. 4: Underestimates by considering only one side up to m=2 or similar incomplete count.
• B. 5: Matches orders on one side (m=0 to 4) but ignores symmetric pattern on both sides.
• C. 8: Counts side orders only (2×4), omitting central maximum at m=0.

Final answer: D