 Normal-incidence grating width bound

At normal incidence, an ideal grating of $N$ lines and period $d$ resolves a small wavelength separation $\delta \lambda$ in order $m$ by the Rayleigh condition $|m|N\gtrsim \lambda /\delta \lambda$. Combining this with $|m|\lambda =d|\sin \theta |$ yields $W=Nd\gtrsim {\lambda }^2/(\delta \lambda |\sin \theta |)\ge {\lambda }^2/\delta \lambda$. The final expression is a limiting lower bound as diffraction approaches grazing. Finite usable diffraction angle, unequal line strengths, aberrations and intrinsic linewidth can all demand a larger instrument or a more detailed criterion.