Diffraction grating equation determines maxima positions

Steps:

• Apply grating equation d sinθ_m = mλ for normal incidence.
• For first-order (m=1), sin15° = λ/d, so λ/d ≈ 0.2588.
• For second-order (m=2), sinθ_2 = 2(λ/d) ≈ 0.5176, so θ_2 = arcsin(0.5176) ≈ 31°.
• Angle between maxima is θ_2 - θ_1 ≈ 31° - 15° = 16°.

Why C is correct:

• Matches θ_2 - θ_1 from grating equation d sinθ_m = mλ, yielding exactly 16° for the separation.

Why the others are wrong:

• A. 7°: Incorrectly halves the first-order angle, ignoring equation scaling.
• B. 15°: Equals θ_1, not the difference between orders.
• D. 32°: Doubles the correct difference, possibly confusing θ_2 with separation.

Final answer: C