Diffraction grating equation equates maxima positions

Steps:

• Grating equation: d sinθ = mλ, where d is slit spacing, θ is angle, m is order, λ is wavelength.
• For red light (λ = 720 nm), second-order maximum: d sinθ = 2 × 720 nm.
• For wavelength X, third-order maximum at same θ: d sinθ = 3X.
• Equate: 2 × 720 = 3X → X = 1440 / 3 = 480 nm.

Why A is correct:

• 480 nm satisfies the grating equation d sinθ = mλ for equal θ between second-order red and third-order X.

Why the others are wrong:

• B: 540 nm gives 3 × 540 = 1620 nm, exceeding 1440 nm from red light equation.
• C: 960 nm gives 3 × 960 = 2880 nm, twice the required value.
• D: 1100 nm gives 3 × 1100 = 3300 nm, far larger than 1440 nm.

Final answer: A