Diffraction grating equation for second-order maxima

Steps:

• Grating equation: d sin φ = mλ, where m=2 for second order, φ is angle from central maximum.
• Beams P and Q are symmetric on opposite sides of central maximum.
• Angle θ between P and Q is 2φ.
• Substitute: sin(θ/2) = sin φ = 2λ/d.

Why C is correct:

• C gives sin(θ/2) = 2λ/d, matching the grating equation d sin φ = 2λ with θ = 2φ.

Why the others are wrong:

• A: Uses m=1 (λ/d), incorrect for second order.
• B: sin θ = 2 sin φ cos φ ≠ 2λ/d generally.
• D: Implies sin θ = 2λ/d, violating the double-angle relation.

Final answer: C