Diffraction grating maximum order from grating equation

Steps:

• Diffraction grating equation: d sin θ = n λ, with λ = c / f.
• Maximum intensity maximum occurs at highest n where θ ≤ 90°, so sin θ ≤ 1.
• Set sin θ = 1 for n_max: n_max = d / λ.
• Substitute λ: n_max = d / (c / f) = (d f) / c.

Why D is correct:

• It directly follows from the grating equation d sin θ = n λ at sin θ = 1 and λ = c / f.

Why the others are wrong:

• A: Equals λ / d, the reciprocal of n_max, giving minimum spacing ratio instead.
• B: Dimensionally inconsistent (yields s⁻², not dimensionless) and inverts the formula.
• C: Identical to D mathematically, but listed separately—likely a formatting error; use D as stated.

Final answer: D