= Solution
The required <resolving power of a diffraction grating> is
$$
\mathcal R_{\rm req}=\frac{589.3\,\mathrm{nm}}{0.6\,\mathrm{nm}}=982.2.
$$
For $N=260$ illuminated slits, $\mathcal R=260|m|$. In orders $1,2,3,4$, the ideal resolvable <wavelength> differences are respectively $2.267$, $1.133$, $0.756$ and $0.567\,\mathrm{nm}$. Thus
$$
\boxed{\text{The doublet is unresolved in orders 1--3; order 4 is the first potentially resolving order.}}
$$
Fourth order gives $\mathcal R=1040>982.2$, only a modest margin. It must also exist: for normal incidence the <grating equation> requires $D\geq4\lambda\simeq2.36\,\mu\mathrm m$, with $D>4\lambda$ needed to avoid an exactly grazing order. The relevant order must transmit appreciable <light intensity> rather than lie at a single-slit <diffraction> zero, and the source and detector widths must preserve this resolution.
The original question gives only the slit count, not the line spacing, slit width, usable <diffraction order> or instrumental broadening. It therefore supports the conditional conclusion “yes in fourth or higher usable order”, but not an unconditional historical claim that this particular instrument resolved the <sodium> <absorption line> doublet in its observed configuration.
Back to article page
