Diffraction grating · resolving power simulation

Add more slits to Young's two — why do the soft fringes sharpen into spectral lines, and what sets whether a grating can split two almost-identical colours?

▶ Run the simulationSee the measured result

Units: metres (fed doublet splitting 0.60 nm; NIST Na D₂ 588.99509, D₁ 589.59244, Δλ = 0.59735 nm — the module rounds each line to 0.1 nm)

How the lab tests it

Model the N-slit grating factor [sin(Nγ)/(N sinγ)]² (γ=πd·sinθ/λ) for the sodium doublet (D₂ 589.0 nm, D₁ 589.6 nm) through a 600-line/mm grating with N=600 lines illuminated; scan a noisy intensity profile across the 1st- and 2nd-order peaks, smooth and count the local maxima, and from the two 2nd-order peak angles recover each wavelength via λ=d·sinθ/m.

What it checks

the grating equation d·sinθ=mλ fixes the orders (here 0,±1,±2 — the 3rd needs sinθ>1 and is evanescent), and N slits squeeze each into a line of width ∝1/N. That sharpness sets the RESOLVING POWER R=λ/Δλ=m·N: the same 600-line grating fails to split the sodium doublet (Δλ=0.6 nm, R_needed≈982) in 1st order (R=600, one merged line) but RESOLVES it in 2nd order (R=1200, two lines) — resolution grows with BOTH line count and order. The lab recovers λ≈589.0 & 589.6 nm and Δλ≈0.6 nm from the noisy 2nd-order angles. The N-slit sequel to Young's two-slit comb: from weighing a wavelength to telling two apart.