Diffraction grating equation determines the slope Steps:

• The diffraction grating equation is $d \sin \theta = n \lambda$, where $d$ is line spacing and $n$ is order.
• Line density $N$ lines per metre means $d = 1/N$.
• Substitute: $\sin \theta = n \lambda / d = n N \lambda$.
• Graph of $\sin \theta$ vs. $\lambda$ is linear with gradient $n N$.

Why D is correct:

• Gradient $\frac{d(\sin \theta)}{d\lambda} = n N$ from the equation $\sin \theta = n N \lambda$.

Why the others are wrong:

• A. $N/n$ inverts order and density, not matching the formula.
• B. $n$ omits density factor $N$.
• C. $N$ omits order factor $n$.

Final answer: D