Grating Resolving Power

What you are seeing: a transmission diffraction grating with $N$ slits of width $a$ and pitch $d$ . The intensity pattern shows the principal maxima and the narrowing of those peaks as $N$ grows (resolving power $R = mN$ ). Move the two-wavelength toggle to show how a doublet is resolved when $\Delta\lambda / \lambda \gt 1/R$ .

Figure 1. Intensity vs angle for an N-slit grating.

N (slits)20

d (μm)2.00

a (μm)0.50

λ (nm)589

doublet Δλ (nm)6.0

WHAT TO TRY

Raise the number of slits N: each principal maximum sharpens (its width scales as 1/N), so the resolving power R = mN climbs and two close wavelengths in the doublet finally separate into distinct lines.
Shrink the doublet spacing dLambda: the two wavelengths merge until the grating can no longer tell them apart. The Rayleigh criterion is met when one peak sits on the other neighbour first zero.
Change the pitch d: it moves where the orders land in angle without changing their sharpness. Resolution comes from the slit count N and order m, not from the spacing.