Diffraction Grating Lab

H2 Physics · Superposition — d sin θ = nλ, drawn at the angles it actually predicts

Double slit vs grating — same d, same λ

2 slits8 slits (grating)λ = 600 nmsingle-slit envelope (b = d/2)

Illuminated grating lines N8

Peak width ∝ 1/N. Drag to 2 and the amber curve becomes the double slit exactly.

FWHM n=1, 2 slits: 11.08°
FWHM n=1, 8 slits: 2.465°
sharper by: ×4.5

Narrow maxima pin θ precisely, and λ = d sin θ / n is only as good as θ.

ⓘ more

Both curves come from the same function, I/I₀ = [sin(Nφ/2) / (N sin(φ/2))]² with φ = 2πd sin θ/λ; N = 2 collapses it to the double-slit cos². Maxima sit at identical angles because d is identical — only the width changes, as λ/(Nd). The N slider stops at 40 so peaks stay wider than a pixel; a real 600 lines/mm grating lit over 2 mm uses 1200 lines, giving maxima about 600× narrower than a double slit. The envelope checkbox multiplies in (sin β/β)², β = πb sin θ/λ, which is why outer orders of a real grating look dimmer.

Try first: drag lines/mm up — watch high orders vanish.

Controls

Grating rulings N600 /mm

d = 1/N = 1.667 µm = 1667 nm

Wavelength λ600 nm

Longer λ → larger θ for every order.

Highlight order n

d sin θ = nλ — right now

d: 1666.7 nm
λ: 600 nm
n: 1
sin θ = nλ/d: 0.3600
θ = sin⁻¹(nλ/d): 21.10°
d sin θ: 600.0 nm
n λ: 600.0 nm

Bottom two rows are the equation — identical at every setting.

Orders — n_max = 2

n_max = ⌊d/λ⌋ = ⌊2.778⌋ = 2

n = 3 would need sin θ = 1.080 > 1 — no such direction exists.

total maxima = 2n_max + 1 = 5

n	sin θ	θ
0	0.000	0.00°
±1	0.360	21.10°
±2	0.720	46.05°
±3	1.080	does not exist
±4	1.440	does not exist

ⓘ more

Every row is sin θ = nλ/d. Orders die the moment that number passes 1, because no angle has a sine above 1 — nothing physical is being cut off, the direction simply does not exist. Each n appears twice, once either side of the normal, so the count is 2n_max + 1. Grating rulings in the scene are schematic; their density tracks the slider but the spacing is not to scale.

What this confirms

›LO (l) — d sin θ = nλ — every ray in the scene is drawn at θ = sin⁻¹(nλ/d), and the two bottom rows of the live card, d sin θ and nλ, stay identical at every setting of every slider.
›LO (l) — counting the principal maxima — n_max = ⌊d/λ⌋ updates live, and the greyed rows show exactly why: sin θ = nλ/d would exceed 1. Total maxima = 2n_max + 1.
›LO (l) — more rulings, fewer orders — raising lines/mm shrinks d, so nλ/d hits 1 sooner: a finer grating spreads the orders wider and kills the outer ones.
›LO (m) — using a grating to find λ — Measure λ mode hides the wavelength, leaves you a known d and a readable θ, and grades λ = d sin θ / n against the true value. n = 0 is refused, because the undeviated order carries no wavelength information.
›Notes: grating vs double slit — both come from I/I₀ = [sin(Nφ/2)/(N sin(φ/2))]²; maxima sit at the same angles because d is the same, but the FWHM falls as λ/(Nd). Sharper maxima mean a sharper θ, and λ inherits that precision.
›Notes: white light through a grating — θ increases with λ, so each order fans into a spectrum with red deviating most, while the zero order stays white (sin θ = 0 for every λ). From n = 2 the orders overlap, since 2 × 700 nm > 3 × 400 nm regardless of d.

Modelled as normal incidence on a transmission grating, with the grating treated as N identical narrow slits of spacing d. Syllabus 9749 Topic 12, learning outcomes (l) and (m).