Diffraction grating equation links order n to sin θ via wavelength λ

Steps:

• Grating spacing d = 1 / (300 lines/mm) = 1/300 mm, or in consistent units, d = 10^{-3}/300 m.
• Diffraction equation: d sin θ = n λ, rearranged to n = (d/λ) sin θ.
• Plot of n vs. sin θ has slope G = d/λ.
• Thus, λ = d / G = 1 / (G × 300 × 10^3) m, assuming standard unit conversion.

Why C is correct:

• Option C matches λ = 1 / (G × grating density in lines/m), directly from slope G = d/λ and d = 1/density.

Why the others are wrong:

• A: Ignores unit conversion from mm to m, yielding incorrect λ scale.
• B: Inverts the relationship, giving G = λ/d instead of d/λ.
• D: Misapplies equation as sin θ vs. n, swapping slope meaning.

Final answer: C