Diffraction & Resolving Power Lab

H2 Physics · Superposition — one gap, one slit, one resolution limit: all of them λ/b

Ripple tank — wide gap vs narrow gap

Huygens sum over the gap, computed live

Try first: drag gap b down until b ≈ λ.

Tank controls

Gap width b70 mm

Wavelength λ14 mm

Wave speed is fixed, so changing λ changes f — as in a real tank.

Readout

b / λ: 5.00
sin θ₁ = λ / b: 0.200
θ₁ (edge of central beam): 11.5°

b ≫ λ — little spreading

Wavefronts pass almost straight through; only the edges curl.

ⓘ more

Brightness is auto-scaled so the shape, not the transmitted power, is what you compare. A narrow gap really does pass less energy — it just spreads what it passes through every direction.

Single slit — where the first minimum lands

I = I₀ sinc²(π b sinθ / λ), sampled per pixel

Slit controls

Slit width b5.0 µm

Narrower slit → wider pattern. Shared with Station 3.

Wavelength λ550 nm

First minimum: formula vs curve

λ / b: 0.1100
sin θ₁ measured off curve: 0.1100
θ₁: 6.32°
central max width 2θ₁: 12.63°
1st secondary max: 4.72 % of I₀

Top two rows agree to 4 dp — sinθ = λ/b is not an approximation here, it is where sinc² first hits zero.

ⓘ more

Minima sit at sinθ = nλ/b, so on the sinθ axis they are exactly evenly spaced: every maximum after the first is λ/b wide, while the central one spans −λ/b to +λ/b — twice as wide. Flip the axis toggle to see the even spacing.

Rayleigh criterion — two stars, one aperture

Individual patterns plus their sum, θ measured in units of θ_min

Aperture + separation

Angular separation θ1.00 × θ_min

Cross 1.00 slowly — that crossing is the Rayleigh criterion.

Aperture b5.0 µm

Same b as Station 2 — its first minimum is this resolution limit.

Resolving power

JUST RESOLVED

θ ≈ θ_min — central max of one sits on the first minimum of the other.

θ_min = λ / b: 110000.0 µrad
θ_min in degrees: 6.303°
θ_min in arcseconds: 22689.1″
θ actual: 22735.1″
measured dip below peaks: 19.2 %

Same rule, real numbers: a 2 mm eye pupil at 550 nm gives θ_min = 1.15′ (335 µrad).

ⓘ more

Syllabus case. Image of a point is a streak, spread only across the slit.

What this confirms

›LO (e) — meaning of diffraction: Station 1 shows waves bending into the geometric shadow after a gap. Freeze the wavefronts and the curled edges stay put.
›LO (f) — ripple tank, wide gap and narrow gap: b/λ ≥ 4 gives an almost straight beam with slight edge-curl; b/λ → 1 gives semicircular wavefronts. Same tank, same λ, only b changed.
›Notes: “diffraction is pronounced when λ ≈ b” — the verdict chip flips at that ratio, and the θ₁ rays on the tank swing out to match.
›LO (j) — sinθ = λ/b: the minimum measured off the computed sinc² curve equals λ/b to 4 decimal places at every b and λ. The formula is not fitted to the graph; the graph lands on it.
›Central maximum is 2λ/b wide: marked on both sides at ±λ/b, with the next maxima only λ/b wide. Switch the axis to sinθ and the minima become evenly spaced.
›LO (k) — Rayleigh criterion θ ≈ λ/b: at θ = 1.00 θ_min the dashed “1st min of S₁” line sits exactly on the peak of S₂ — that is the criterion, drawn. The dip measures ≈ 19 % for a slit, ≈ 26 % for a circular aperture.
›Circular apertures carry the 1.22: toggling to a circular aperture uses the real Airy function (first zero of J₁ at 3.8317), giving θ_min = 1.22 λ/b — the version used for eyes and telescopes.
›Resolving power improves with wider b or shorter λ: Station 3 shares its b with Station 2, so widening the slit shrinks both the diffraction pattern and θ_min together.