What you are looking at
Plane waves hit a barrier with N equally-spaced slits. The strip on the right is the screen; beside it, the
intensity profile. At N = 2 this is exactly the double-slit experiment — then each extra slit you add
sharpens the bright fringes without moving them.
Where the lines fall — and why they don't move
Neighbouring slits are a distance d apart, so their waves arrive in step whenever the path difference is a
whole number of wavelengths:
d·sinθ = m·λ (m = 0, ±1, ±2, …)
This condition involves only the
spacing, not the number of slits — which is why the maxima stand
still as N grows. The number of visible orders is capped by sinθ ≤ 1 at |m| ≤ d/λ.
Why more slits mean sharper lines
The full N-slit intensity is
I(θ) = I₀ · [ sin(Nφ/2) / sin(φ/2) ]², φ = 2πd·sinθ/λ
At a principal maximum all N waves agree, so the amplitude is N times bigger — intensity
N².
But step slightly off-angle and the N phasors curl into a closed loop and cancel: the line's width shrinks
as
1/N. Tall and thin is exactly what a spectrometer needs — two nearby wavelengths give two
distinguishable lines, with resolving power λ/Δλ = mN.
From lab curiosity to workhorse
Real gratings pack thousands of slits per millimetre, so each wavelength leaves at its own crisp angle:
point one at a star and the chemistry of its atmosphere reads off as a barcode of lines. CD and DVD surfaces,
with their micrometre track spacing, act as accidental reflection gratings — that's their rainbow shimmer.
Things to try
Slide N from 2 to 40 and watch the fringes sharpen into lines (the little ripples between them are the N−2
secondary maxima — see them fade in relative height). Change λ and watch every line except m = 0 slide —
red bends more than blue here, opposite to a prism. Widen d and the orders crowd inward as more of them fit.