Optics · aperture · Fourier plane

Diffraction Studio

Change the slit width, pitch and count on an optical bench. Record the focal-plane pattern, inspect the single-slit envelope, and discover where entire diffraction orders vanish.

Detector position $\text{—}$

Relative intensity $\text{—}$

First envelope minimum $\text{—}$

Order spacing $\text{—}$

Recorded slit count $\text{—}$

Total aperture span $\text{—}$

APERTURE / FOURIER PLANE

Cut the opening. Shape the light.

Single-slit envelopeAn ideal reference, not another detector measurement.Field-contribution guidesConnect each opening through the lens to the selected focal position; schematic contributions, not ray tracing.Wavelength

\lambda

550\,\mathrm{nm}

Slit width

a

60\,\mu\mathrm m

Slit pitch

d

180\,\mu\mathrm m

Number of slits

N

2

Lens focal length

f

300\,\mathrm{mm}

Uniform monochromatic illumination, identical rectangular slits and an ideal Fourier lens. Detector lies one focal length behind the lens. Scalar paraxial theory; no aberrations, noise or finite pixel integration. Each scan is normalized to its own on-axis intensity, so peak height cannot compare transmitted power. Transverse sizes are enlarged.

The illuminated aperture, ideal lens and focal-plane detector form one model. Nanometres, micrometres and millimetres are converted explicitly; visual scales are enlarged.

Move the probe

0.000\,\mathrm{mm}

Mint: current record. Coral: saved record. Gold: single-slit envelope. The cursor selects an acquired sample; all numbers and CSV values stay linear. Screen brightness uses a square-root display mapping, clipped at one, to reveal faint fringes.

\frac{I(x)}{I(0)}=\operatorname{sinc}^2\!\left(\frac{\pi a x}{\lambda f}\right)\left|\frac1N\sum_{n=0}^{N-1}e^{-2\pi i(n-(N-1)/2)dx/(\lambda f)}\right|^2

The pattern is a deterministic ideal line scan, not photon counts or a reconstruction. The chart covers only the central horizontal slice of long rectangular slits. The optical layout is schematic and transverse scales differ from the propagation scale.

Return to two sources →MIT: interference and diffraction

CONTINUE EXPLORING

Aperture, propagation, measurement

Change one physical assumption at a time: slit count, coherence, aperture shape or propagation distance.

Start with the essentials

Focus question: Why does a narrower slit make the transmitted wave spread more widely?
One-sentence intuition: Tighter spatial confinement broadens direction; more periodic apertures sharpen the allowed directions.

Core mathematical model

Multi-slit intensity

\frac{I(x)}{I(0)}=\operatorname{sinc}^2\beta\left(\frac{\sin N\alpha}{N\sin\alpha}\right)^2,\quad\beta=\frac{\pi ax}{\lambda f},\quad\alpha=\frac{\pi dx}{\lambda f}

The first factor is the single-slit envelope; the second is fine structure from $N$ slits.

Minima and principal maxima

x_{\min}=\frac{m\lambda f}{a}\;(m\ne0),\qquad x_{\mathrm{order}}=\frac{m\lambda f}{d}

Slit width $a$ controls the envelope while spacing $d$ controls principal directions.

Common difficulties

Diffraction is not edge reflection

Typical misconceptionOnly rays touching the slit edges bend.

Better mental modelThe entire aperture contributes; the pattern comes from phase relations across a finite spatial range.

Envelope and fringes use different scales

Typical misconceptionChanging slit spacing should equally change the single-slit envelope.

Better mental modelSlit width sets the broad envelope; pitch and count set fringe positions and sharpness inside it.

Run the experiment

01
Narrow one slit
Choose Single slit, keep the scan, reduce the width and record again.
What to observe: The central maximum widens and the first minimum moves outward.
02
Add a second slit
Switch to Double slit, vary the pitch and record again.
What to observe: The envelope stays similar while internal spacing changes.
03
Add more slits
Choose Eight slits, then try Missing orders.
What to observe: More slits sharpen the principal maxima; the Missing orders preset suppresses every second nonzero order at an envelope zero.

Diffraction Studio

The aperture writes the pattern.

Aperture, propagation, measurement

Diffraction: how apertures redistribute direction